Physics
Solutions Manual
HOLT
ISBN-13: 978-0-03-099807-2
ISBN-10: 0-03-099807-7
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Teacher’s Solutions Manual
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Contents iii
Section I Student Edition Solutions
Chapter 1 The Science of Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-1-1
Chapter 2 Motion in One Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-2-1
Chapter 3 Two-Dimensional Motion and Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-3-1
Chapter 4 Forces and the Laws of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-4-1
Chapter 5 Work and Energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-5-1
Chapter 6 Momentum and Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-6-1
Chapter 7 Circular Motion and Gravitation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-7-1
Chapter 8 Fluid Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-8-1
Chapter 9 Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-9-1
Chapter 10 Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-10-1
Chapter 11 Vibrations and Waves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-11-1
Chapter 12 Sound. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-12-1
Chapter 13 Light and Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-13-1
Chapter 14 Refraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-14-1
Chapter 15 Interference and Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-15-1
Chapter 16 Electric Forces and Fields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-16-1
Chapter 17 Electrical Energy and Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-17-1
Chapter 18 Circuits and Circuit Elements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-18-1
Chapter 19 Magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-19-1
Chapter 20 Electromagnetic Induction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-20-1
Contents
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Contentsiv
Chapter 21 Atomic Physics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-21-1
Chapter 22 Subatomic Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-22-1
Appendix I Additional Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-Apx I-1
Section II Problem Workbook Solutions
Chapter 1 The Science of Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-1-1
Chapter 2 Motion in One Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-2-1
Chapter 3 Two-Dimensional Motion and Vectors
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
II-3-1
Chapter 4 Forces and the Laws of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-4-1
Chapter 5 Work and Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-5-1
Chapter 6 Momentum and Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-6-1
Chapter 7 Circular Motion and Gravitation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-7-1
Chapter 8 Fluid Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-8-1
Chapter 9 Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-9-1
Chapter 10 Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-10-1
Chapter 11 Vibrations and Waves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-11-1
Chapter 12 Sound. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-12-1
Chapter 13 Light and Reflection
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
II-13-1
Chapter 14 Refraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-14-1
Chapter 15 Interference and Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-15-1
Chapter 16 Electric Forces and Fields
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
II-16-1
Chapter 17 Electrical Energy and Current
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
II-17-1
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Contents v
Chapter 18 Circuits and Circuit Elements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-18-1
Chapter 19 Magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-19-1
Chapter 20 Electromagnetic Induction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-20-1
Chapter 21 Atomic Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-21-1
Chapter 22 Subatomic Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-22-1
Section III Study Guide Worksheets Answers III-1
solutions
Student Edition
Solutions
I
Section
Holt Physics
I
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
The Science of Physics
Student Edition Solutions
2. mass = 6.20 mg a. 6.20 mg ×
1 ×
1
1
m
0
−
g
3
g
×
1 ×
1
1
k
0
g
3
g
=
time = 3 × 10
−9
s b. 3 × 10
−9
s ×
1 ×
1
1
m
0
−
s
3
s
=
distance = 88.0 km c. 88.0 km ×
1 ×
1
1
k
0
m
3
m
=
3. a. 26 × 0.02584 = 0.67184 =
b. 15.3 ÷ 1.1 = 13.90909091 =
c. 782.45 − 3.5328 = 778.9172 =
d. 63.258 + 734.2 = 797.458 =
797.5
778.92
14
0.67
8.80 × 10
4
m
3 × 10
−6
ms
6.20 × 10
−6
kg
The Science of Physics, Section 2 Review
The Science of Physics, Practice A
Givens Solutions
1. diameter = 50 µm 50 µm ×
1 ×
1
1
µ
0
m
−6
m
=
2. period = 1 µs1 µs ×
1 ×
1
1
µ
0
s
−6
s
=
3. diameter = 10 nm a. 10 nm ×
1 ×
1
1
n
0
m
−9
m
=
b. 1 × 10
−8
m ×
1 ×
1
1
m
0
−
m
3
m
=
c. 1 × 10
−8
m ×
1 ×
1
1
µ
0
m
−6
m
=
4. distance = 1.5 × 10
11
m 1.5 × 10
11
m ×
1 ×
1
1
T
0
m
12
m
=
1.5 × 10
11
m ×
1 ×
1
1
k
0
m
3
m
=
5. mass = 1.440 × 10
6
g 1.440 × 10
6
g ×
1 ×
1
1
k
0
g
3
g
=
1.440 × 10
3
kg
1.5 × 10
8
km
1.5 × 10
-1
Tm
1 × 10
−2
µm
1 × 10
−5
mm
1 × 10
−8
m
1 × 10
−6
s
5 × 10
−5
m
Section One—Student Edition Solutions I Ch. 1–1
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
The Science of Physics, Chapter Review
Givens Solutions
11. 2 dm a. 2 dm ×
1 ×
1
1
d
0
m
–1
m
×
1 ×
1
1
m
0
−
m
3
m
=
2 h 10 min b. 2 h ×
60
1
m
h
in
= 120 min
120 min + 10 min = 130 min
130 min ×
1
6
m
0
i
s
n
=
16 g c. 16 g ×
1 ×
1
1
µ
0
g
−6
g
=
0.75 km d. 0.75 km ×
1 ×
1
1
k
0
m
3
m
×
1 ×
1
1
c
0
m
−2
m
=
0.675 mg e. 0.675 mg ×
1 ×
1
1
m
0
−
g
3
g
=
462 µm f. 462 µm ×
1 ×
1
1
µ
0
m
−6
m
×
1 ×
1
1
c
0
m
−2
m
=
35 km/h g.
35
h
km
×
36
1
0
h
0s
×
1 ×
1
1
k
0
m
3
m
=
12. 10 rations a. 10 rations ×
1
1
d
0
e
1
k
r
a
a
r
t
a
io
ti
n
o
s
n
=
2000 mockingbirds b. 2000 mockingbirds ×=
10
−6
phones c. 10
−6
phones ×
10
1
−
µ
6
p
p
h
h
o
o
n
n
e
es
=
10
−9
goats d. 10
−9
goats ×
10
1
−
n
9
g
g
o
o
a
a
t
ts
=
10
18
miners e. 10
18
miners ×
10
1
1
E
8
m
m
i
i
n
n
e
e
r
rs
=
13. speed of light =
3.00 ×
s
10
8
m
×
36
1
0
h
0s
× 1 h ×
1 ×
1
1
k
0
m
3
m
=
3.00 × 10
8
m/s
∆t = 1 h
14. 1 ton = 1.000 × 10
3
kg 1.000 × 10
3
kg ×
1
8
p
5
er
k
s
g
on
=
mass/person = 85 kg Note that the numerical answer, 11.8 people, must be rounded down to 11 people.
11 people
1.08 × 10
9
km
1 examiner
1 nanogoat
1 microphone
2 kilomockingbirds
1 kmockingbirds
1 × 10
3
mockingbirds
1 dekaration
9.7 m/s
4.62 × 10
−2
cm
6.75 × 10
−4
g
7.5 × 10
4
cm
1.6 × 10
7
µg
7.8 × 10
3
s
2 × 10
2
mm
Holt Physics Solution ManualI Ch. 1–2
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 1–3
I
20. a. 756 g + 37.2 g + 0.83 g + 2.5 g = 796.53 g =
b.
3
3
.5
.2
6
m
3s
= 0.898119562 m/s =
c. 5.67 mm × p = 17.81283035 mm =
d. 27.54 s − 3.8 s = 23.74 s =
21. 93.46 cm, 135.3 cm 93.46 cm + 135.3 cm = 228.76 cm =
22.
l
= 38.44 m w = 19.5 m 38.44 m + 38.44 m + 19.5 m + 19.5 m = 115.88 m =
26. s = (a + b + c) ÷ 2 r =
r, a, b, c, and s all have units of L.
length =
=
=
(l
en
gt
h
)
2
= length
Thus, the equation is dimensionally consistent.
27. T = 2p
Substitute the proper dimensions into the equation.
time =
=
(t
im
e)
2
= time
Thus, the dimensions are consistent.
28. (m/s)
2
≠ m/s
2
× s
m
2
/s
2
≠ m/s
The dimensions are not consistent.
29. Estimate one breath every 5 s.
70 years ×
36
1
5
y
d
ea
a
r
ys
×
1
24
da
h
y
×
36
1
0
h
0s
×
1b
5
re
s
ath
=
30. Estimate one heart beat per second.
1 day ×
1
24
da
h
y
×
36
1
0
h
0s
×
1b
s
eat
=
31. Ages will vary.
17 years ×
36
1
5
y
d
ea
a
r
ys
×
1
24
da
h
y
×
36
1
0
h
0s
=
32. Estimate a tire’s radius to be 0.3 m.
50 000 mi ×
1.6
1
0
m
9k
i
m
×
1
1
0
k
3
m
m
×
2 p
1
(0
r
.
e
3
v
m)
=
4 × 10
7
rev
5.4 × 10
8
s
9 × 10
4
beats
4 × 10
8
breaths
length
[length/(time)
2
]
L
a
g
(length)
3
length
length × length × length
length
(s − a)(s − b)(s − c)
s
115.9 m
228.8 cm
23.7 s
17.8 mm
0.90 m/s
797 g
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
33. Estimate 30 balls lost per game.
81 games ×
3
1
0
g
b
am
all
e
s
=
34. Estimate
1
4
lb per burger and 800 lb per head of cattle.
5 × 10
10
burgers ×
1
0
b
.2
u
5
rg
lb
er
=
1 × 10
10
lb
2 × 10
3
balls
Givens Solutions
I
5 × 10
10
burgers ×
1
0
b
.2
u
5
rg
lb
er
×
1
80
h
0
ea
lb
d
=
35. population = 8 million people Estimate 5 people per family.
5
8
pe
m
o
i
p
ll
l
i
e
o
p
n
e
p
r
e
f
o
am
ple
ily
= 2 million families
Estimate that 1/5 of families have a piano.
Number of pianos = (2 million families)
1
5
= 400,000 pianos
Estimate 3 tunings per day per tuner, with 200 work days per year.
Number of pianos tuned each year (per tuner) = (3)(200) = 600
Number of tuners ==
36. diameter = 3.8 cm Find the number of balls that can fit along the length and width.
l
= 4 m w = 4 m h = 3m
4 m ×
0.
1
03
b
8
al
m
l
= 100 balls
Find the number that can be stacked to the ceiling.
3 m ×
0.
1
03
b
8
al
m
l
= 80 balls
Multiply all three figures to find the number of balls that can fit in the room.
100 balls × 100 balls × 80 balls =
A rough estimate: divide the volume of the room by the volume of a ball.
37. r = 3.5 cm a. C = 2pr = 2p (3.5 cm) =
A = pr
2
= p (3.5 cm)
2
=
r = 4.65 cm b. C = 2pr = 2p (4.65 cm) =
A = pr
2
= p (4.65 cm)
2
=
38. 5 × 10
9
bills ×
1
1
b
s
ill
×
36
1
0
h
0s
×
1
14
da
h
y
×
36
1
5
y
d
ea
a
r
ys
=
Take the $5000. It would take 272 years to count 5 billion $1 bills.
272 years
67.9 cm
2
29.2 cm
38 cm
2
22 cm
8 × 10
5
balls
7 × 10
2
tuners
400,000 pianos
600 pianos/year per tuner
2 × 10
7
head of cattle
Holt Physics Solution ManualI Ch. 1–4
Copyright © by Holt, Rinehart and Winston. All rights reserved.
I
Section One—Student Edition Solutions I Ch. 1–5
39. V = 1 quart ×
3.78
4
6
q
×
u
1
a
0
r
−
ts
3
m
3
= 9.465 × 10
−4
m
3
V = L
3
L =
3
V
=
3
9.465 ×
10
−4
m
3
=
9.818 × 10
−2
m
Givens Solutions
42. d = 1.0 × 10
−6
m number of micrometeorites per side:
l
= 1.0 m
1.0 m ×
1m
1.
i
0
cr
×
om
10
e
−
t
6
eo
m
rite
= 1.0 × 10
6
micrometeorites
number of micrometeorites needed to cover the moon to a depth of 1.0 m:
(1.0 × 10
6
micrometeorites)
3
= 1.0 × 10
18
micrometeorites
1.0 × 10
18
micrometeorites ×
1 micro
1
m
s
eteorite
×
36
1
0
h
0s
×
1
24
da
h
y
×
36
1
5
y
d
ea
a
r
ys
=
Note that a rougher estimate can be made by dividing the volume of the 1.0 m
3
box
by the volume of a micrometeorite.
43. V = 1.0 cm
3
1.0
1
×
.0
1
c
0
m
−3
3
kg
×
(1 ×
1
1
c
0
m
−2
3
m)
3
× 1.0 m
3
=
m = 1.0 × 10
−3
kg
1.0 × 10
3
kg
3.2 × 10
10
years
40. mass = 9.00 × 10
−7
kg
density = 918 kg/m
3
r = 41.8 cm
area = pr
2
volume =
d
m
en
a
s
s
i
s
ty
=
9.0
9
0
18
×
k
1
g
0
/
−
m
7
3
kg
= 9.80 × 10
−10
m
3
diameter =
vo
a
l
r
u
e
m
a
e
=
9.
p
80
(0
×
.4
1
1
0
8
−
m
10
)
m
2
3
=
1.79 × 10
−9
m
41. 1 cubit = 0.50 m
V
ark
= 300 cubits × 50 cubits
× 30 cubits
V
ark
= (300 cubits)(50 cubits)(30 cubits)
0
c
.5
u
0
bi
m
t
3
V
ark
=
Estimate the average size of a house to be 2000 ft
2
and 10 ft tall.
V
house
= (2000 ft
2
)(10 ft)
3.2
1
8
m
1ft
3
V
house
=
V
V
h
a
o
r
u
k
se
=
6
6
×
×
1
1
0
0
4
2
m
m
3
3
=
100
6 × 10
2
m
3
6 × 10
4
m
3
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualI Ch. 1–6
44. density = r = 1.0 × 10
3
kg/m
3
diameter = 1.0 µm
l
= 4.0 mm
diameter = 2r = 2.0 mm
density =r = 1.0 × 10
3
kg/m
3
a. V =
4
3
pr
3
=
4
3
p
1.0 × 1
2
0
−6
m
3
= 5.2 × 10
−19
m
3
m = rV = (1.0 × 10
3
kg/m
3
)(5.2 × 10
−19
m
3
)(0.9) =
b. V =
l
pr
2
= (4.0 × 10
−3
m) (p)
2.0 × 1
2
0
−3
m
2
= 1.3 × 10
−8
m
3
m = rV = (1.0 × 10
3
kg/m
3
)(1.3 × 10
−8
m
3
)(0.9) =
1 × 10
−5
kg
5 × 10
−16
kg
45. r = 6.03 × 10
7
m
m = 5.68 × 10
26
kg
a. V =
4
3
pr
3
density =
m
V
=
4
3
p
m
r
3
density =
(
4
3
p
)(
(
5
6
.
.
6
0
8
3
×
×
1
1
0
0
2
7
6
m
k
)
g
3
)
10
k
3
g
g
10
1
2
m
cm
3
density =
b. surface area = 4pr
2
= 4p(6.03 × 10
7
m)
2
surface area =
4.57 × 10
16
m
2
0.618 g/cm
3
5. 1 ly = 9 500 000 000 000 km
= 9.5 × 10
12
km
9.5 × 10
12
km ×
1
1
0
k
3
m
m
=
9.5 × 10
15
m
The Science of Physics, Standardized Test Prep
Section One—Student Edition Solutions I Ch. 2–1
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Motion In
One Dimension
Student Edition Solutions
I
1. v
avg
= 0.98 m/s east ∆x = v
avg
∆t = (0.98 m/s)(34 min)(60 s/min)
∆t = 34 min ∆x = 2.0 × 10
3
m =
2. ∆t = 15 min ∆x = v
avg
∆t = (12.5 km/h)(15 min)
v
avg
= 12.5 km/h south ∆x =
3. ∆t = 9.5 min ∆x = v
avg
∆t = (1.2 m/s) (9.5 min)(60 s/min)
v
avg
= 1.2 m/s north ∆x =
4. v
avg
= 48.0 km/h east
∆t =
v
∆
av
x
g
=
48
1
.
4
0
4
k
k
m
m
/h
=
∆x = 144 km east
5. v
avg
= 56.0 km/h east
∆t =
v
∆
av
x
g
=
56
1
.
4
0
4
k
k
m
m
/h
= 2.57 h
∆x = 144 km east
time saved = 3.00 h − 2.57 h =
0.43 h = 25.8 min
3.00 h
680 m north
3.1 km
1h
60 min
2.0 km east
Motion In One Dimension, Practice A
Givens Solutions
6. ∆x
1
= 280 km south
v
avg,1
= 88 km/h south
∆t
2
= 24 min
v
avg,2
= 0 km/h
∆x
3
= 210 km south
v
avg,3
= 75 km/h south
a. ∆t
tot
=∆t
1
+∆t
2
+∆t
3
=
v
∆
av
x
g
1
,1
+∆t
2
+
v
∆
av
x
g
3
,3
∆t
tot
=
+ (24 min)
60
1
m
h
in
+
7
2
5
10
km
km
/h
∆t
tot
= 3.2 h + 0.40 h + 2.8 h =
b. v
avg, tot
=
∆
∆
x
t
t
t
o
o
t
t
=
∆
∆
x
t
1
1
+
+
∆
∆
x
t
2
2
+
+
∆
∆
t
x
3
3
∆x
2
= v
avg,2
∆t
2
= (0 km/h)(24 min)
60
1
m
h
in
= 0 km
v
avg, tot
= =
49
6
0
.4
k
h
m
=
77 km/h south
280 km + 0 km + 210 km
6.4 h
6.4 h = 6 h 24 min
280 km
88 km/h
1. v = 3.5 mm/s ∆x = 8.4 cm
∆t =
∆
v
x
=
0.
8
3
.
5
4
c
c
m
m
/s
=
24 s
Motion In One Dimension, Section 1 Review
2. v = 1.5 m/s ∆x = 9.3 m
∆t =
∆
v
x
=
1
9
.5
.3
m
m
/s
=
6.2 s
Holt Physics Solution ManualI Ch. 2–2
Copyright © by Holt, Rinehart and Winston. All rights reserved.
I
3. ∆x
1
= 50.0 m south
∆t
1
= 20.0 s
∆x
2
= 50.0 m north
∆t
2
= 22.0 s
4. v
1
= 0.90 m/s
v
2
= 1.90 m/s
∆x = 780 m
∆t
1
−∆t
2
=
(5.50 min)(60 s/min) =
3.30 × 10
2
s
a. v
avg,1
=
∆
∆
x
t
1
1
=
5
2
0
0
.
.
0
0
m
s
=
b. v
avg,2
=
∆
∆
x
t
2
2
=
5
2
0
2
.
.
0
0
m
s
=
∆x
tot
=∆x
1
+∆x
2
= (−50.0 m) + (50.0 m) = 0.0 m
∆t
tot
=∆t
1
+∆t
2
= 20.0 s + 22.0 s = 42.0 s
v
avg
=
∆
∆
x
t
t
t
o
o
t
t
=
4
0
2
.0
.0
m
s
=
0.0 m/s
2.27 m/s north
2.50 m/s south
a. ∆t
1
=
∆
v
1
x
=
0
7
.9
8
0
0
m
m
/s
= 870 s
∆t
2
=
∆
v
2
x
=
1
7
.9
8
0
0
m
m
/s
= 410 s
∆t
1
−∆t
2
= 870 s − 410 s =
b. ∆x
1
= v
1
∆t
1
∆x
2
= v
2
∆t
2
∆x
1
=∆x
2
v
1
∆t
1
= v
2
∆t
2
v
1
[∆t
2
+ (3.30 × 10
2
s)] = v
2
∆t
2
v
1
∆t
2
+ v
1
(3.30 × 10
2
s) = v
2
∆t
2
∆t
2
(v
1
− v
2
) =−v
1
(3.30 × 10
2
s)
∆t
2
=
−v
1
(3
v
.3
1
0
−
×
v
2
10
2
s)
==
∆t
2
= 3.0 × 10
2
s
∆t
1
=∆t
2
+ (3.30 × 10
2
s) = (3.0 × 10
2
s) + (3.30 × 10
2
s) = 630 s
∆x
1
= v
1
∆t
1
= (0.90 m/s)(630 s) =
∆x
2
= v
2
∆t
2
= (1.90 m/s)(3.0 × 10
2
s) =
570 m
570 m
−(0.90 m/s)(3.30 × 10
2
s)
−1.00 m/s
−(0.90 m/s)(3.30 × 10
2
s)
0.90 m/s − 1.90 m/s
460 s
Givens Solutions
1. a
avg
=−4.1 m/s
2
∆t =
a
∆
a
v
vg
= = =
–
–
4
9
.
.
1
0
m
m
/
/
s
s
2
=
v
i
= 9.0 m/s
v
f
= 0.0 m/s
2. a
avg
= 2.5 m/s
2
∆t =
a
∆
a
v
vg
==
12.0 m
2.5
/s
m
–
/
7
s
.
2
0m/s
=
2
5
.
.
5
0
m
m
/
/
s
s
2
=
v
i
= 7.0 m/s
v
f
= 12.0 m/s
3. a
avg
=−1.2 m/s
2
∆t =
v
a
f
a
−
vg
v
i
==
−
−
1
6
.
.
2
5
m
m
/
/
s
s
2
=
v
i
= 6.5 m/s
v
f
= 0.0 m/s
5.4 s
0.0 m/s − 6.5 m/s
− 1.2 m/s
2
2.0 s
v
f
– v
i
a
avg
2.2 s
0.0 m/s – 9.0 m/s
– 4.1 m/s
2
v
f
– v
i
a
avg
Motion In One Dimension, Practice B
Section One—Student Edition Solutions I Ch. 2–3
Copyright © by Holt, Rinehart and Winston. All rights reserved.
I
4. v
i
=−1.2 m/s
a
avg
=
v
f
∆
−
t
v
i
===
v
f
=−6.5 m/s
∆t = 25 min
5. a
avg
= 4.7 × 10
−3
m/s
2
a. ∆v = a
avg
∆t = (4.7 × 10
−3
m/s
2
)(5.0 min)(60 s/min) =
∆t = 5.0 min b. v
f
=∆v + v
i
= 1.4 m/s + 1.7 m/s =
v
i
= 1.7 m/s
3.1 m/s
1.4 m/s
−3.5 × 10
−3
m/s
2
−5.3 m/s
1500 s
−6.5 m/s − (−1.2 m/s)
(25 min)(60 s/min)
Givens Solutions
1. v
i
= 0.0 m/s
∆x =
1
2
(v
i
+ v
f
)∆t =
1
2
(0.0 m/s + 6.6 m/s)(6.5 s) =
v
f
= 6.6 m/s
∆t = 6.5 s
2. v
i
= 15.0 m/s ∆x =
1
2
(v
i
+ v
f
)∆t =
1
2
(15.0 m/s + 0.0 m/s)(2.50 s) =
v
f
= 0.0 m/s
∆t = 2.50 s
3. v
i
= 21.8 m/s
∆t =
v
2
i
∆
+
x
v
f
==
∆x = 99 m
v
f
= 0.0 m/s
4. v
i
= 6.4 m/s v
f
=
2
∆
∆
t
x
− v
i
= − 6.4 m/s = 3.0 × 10
1
m/s − 6.4 m/s =
∆x = 3.2 km
∆t = 3.5 min
24 m/s
(2)(3.2 × 10
3
m)
(3.5 min)(60 s/min)
9.1 s
(2)(99 m)
21.8 m/s + 0.0 m/s
18.8 m
21 m
Motion In One Dimension, Practice C
1. v
i
= 6.5 m/s
a = 0.92 m/s
2
∆t = 3.6 s
v
f
= v
i
+ a∆t = 6.5 m/s + (0.92 m/s
2
)(3.6 s)
v
f
= 6.5 m/s + 3.3 m/s =
∆x = v
i
∆t +
1
2
a∆t
2
∆x = (6.5 m/s)(3.6 s) +
1
2
(0.92 m/s
2
)(3.6 s)
2
∆x = 23 m + 6.0 m =
29 m
9.8 m/s
Motion In One Dimension, Practice D
2. v
i
= 4.30 m/s
a = 3.00 m/s
2
∆t = 5.00 s
v
f
= v
i
+ a∆t = 4.30 m/s + (3.00 m/s
2
)(5.00 s)
v
f
= 4.30 m/s + 15.0 m/s =
∆x = v
i
∆t +
1
2
a∆t
2
∆x = (4.30 m/s)(5.00 s) +
1
2
(3.00 m/s
2
)(5.00 s)
2
∆x = 21.5 m + 37.5 m =
59.0 m
19.3 m/s
Holt Physics Solution ManualI Ch. 2–4
Copyright © by Holt, Rinehart and Winston. All rights reserved.
I
3. v
i
= 0.0 m/s v
f
= v
i
+ a∆t = 0 m/s + (−1.5 m/s
2
)(5.0 s) =
∆t = 5.0 s ∆x = v
i
∆t +
1
2
a∆t
2
= (0 m/s)(5.0 s) +
1
2
(−1.5 m/s
2
)(5.0 s)
2
=−19 m
a =−1.5 m/s
2
distance traveled =
4. v
i
= 15.0 m/s ∆t ==
10.0 m
−2
/
.
s
0
−
m
1
/
5
s
.
2
0m/s
=
−
−
5
2
.
.
0
0
s =
a =−2.0 m/s
2
∆x = v
i
∆t +
1
2
a∆t
2
v
f
= 10.0 m/s
∆x = (15.0 m/s)(2.5 s) +
1
2
(−2.0 m/s
2
)(2.5 s)
2
∆x = 38 m + (−6.2 m) = 32 m
distance traveled during braking =
32 m
2.5 s
v
f
− vi
a
19 m
−7.5 m/s
3. v
i
= 0 m/s
a = 2.3 m/s
2
∆x = 55 m
Givens Solutions
1. v
i
= 0 m/s
a = 0.500 m/s
2
∆x = 6.32 m
2. v
i
=+7.0 m/s
a =+0.80 m/s
2
∆x = 245 m
∆x = 125 m
∆x = 67 m
v
f
=
v
i
2
+ 2
a∆x
v
f
=
(0 m/s
)
2
+ (2
)(0.500
m/s
2
)(
6.32 m
)
=
6.32 m
2
/s
2
=±2.51 m/s
v
f
=
+2.51 m/s
a. v
f
=
v
i
2
+ 2
a∆x
v
f
=
(7.0 m
/s)
2
+ (
2)(0.80
m/s
2
)(
245 m)
v
f
=
49 m
2
/
s
2
+ 39
0 m
2
/s
2
=
44
0
m
2
/
s
2
=±21 m/s
v
f
=
b. v
f
=
(7
.0
m
/s
)
2
+
(
2)
(0
.8
0
m
/s
2
)
(1
25
m
)
v
f
=
49
m
2
/
s
2
+
(
2.
0
×
1
0
2
m
2
/
s
2
)
=
25
0
m
2
/
s
2
v
f
=±16 m/s =
c. v
f
=
(7
.0
m
/s
)
2
+
(
2)
(0
.8
0
m
/s
2
)
(6
7
m
)
=
49 m
2
/
s
2
+ 11
0 m
2
/s
2
v
f
=
16
0
m
2
/
s
2
=±13 m/s =
+13 m/s
+16 m/s
+21 m/s
Motion In One Dimension, Practice E
a. v
f
=
v
i
2
+
2
a
∆
x
=
(0
m
/s
)
2
+
(
2)
(2
.3
m
/s
2
)
(5
5
m
)
v
f
=
25
0
m
2
/
s
2
=±16 m/s
car speed =
b. ∆t =
v
a
f
=
2
1
.3
6
m
m
/
/
s
s
2
=
7.0 s
16 m/s
4. v
i
= 6.5 m/s
v
f
= 1.5 m/s
a =−2.7 m/s
2
∆x == =
−
−
4
5
0
.4
m
m
2
/
/
s
s
2
2
=
7.4 m
(1.5 m/s)
2
− (6.5 m/s)
2
(2)(−2.7 m/s
2
)
v
f
2
− v
i
2
2a
Section One—Student Edition Solutions I Ch. 2–5
Copyright © by Holt, Rinehart and Winston. All rights reserved.
I
5. v
i
= 0.0 m/s
v
f
= 33 m/s
∆x = 240 m
6. a = 0.85 m/s
2
v
i
= 83 km/h
v
f
= 94 km/h
v
i
= (83 km/h)(10
3
m/km)(1 h/3600 s) = 23 m/s
v
f
= (94 km/h)(10
3
m/km)(1 h/3600 s) = 26 ms
∆x ==
∆x =
∆x =
(2)
1
(
5
0
0
.8
m
5
2
m
/s
/
2
s
2
)
= 88 m
distance traveled =
88 m
680 m
2
/s
2
− 530 m
2
/s
2
(2)(0.85 m/s
2
)
(26 m/s)
2
− (23 m/s)
2
(2)(0.85 m/s
2
)
v
f
2
− v
i
2
2a
a = = =
2.3 m/s
2
(33 m/s)
2
− (0.0 m/s)
2
(2)(240 m)
v
f
2
− v
i
2
2∆x
Givens Solutions
1. a =+2.60 m/s
2
∆t =
v
f
a
− v
i
=
v
i
= 24.6 m/s
v
f
= 26.8 m/s
∆t =
2
2
.6
.2
0
m
m
/
/
s
s
2
=
3. v
i
= 0 m/s
a. a =
v
f
∆
−
t
v
i
=
12.5 m
2
/
.
s
5
−
s
0m/s
=
v
f
= 12.5 m/s
∆t = 2.5 s
b. ∆x = v
i
∆t +
1
2
a∆t
2
= (0 m/s)(2.5 s) +
1
2
(5.0 m/s
2
)(2.5 s)
2
=
c. v
avg
=
∆
∆
x
t
=
1
2
6
.5
m
s
=
+6.4 m/s
+16 m
+5.0 m/s
2
0.85 s
26.8 m/s − 24.6 m/s
2.60 m/s
2
Motion In One Dimension, Section 2 Review
1. ∆y =−239 m a. v
f
=
v
i
2
+
2
a
∆
y
=
(0
m
/s
)
2
+
(
2)
(−
3.
7
m
/s
2
)
(−
23
9
m
)
v
i
= 0 m/s
v
f
=
1.8 × 1
0
3
m
2
/
s
2
= ±42 m/s
a =−3.7 m/s
2
v
f
=
b. ∆t =
v
f
−
a
v
i
=
−42
−
m
3.
/
7
s
m
−
/
0
s
2
m/s
=
11 s
−42 m/s
Motion In One Dimension, Practice F
2. ∆y =−25.0 m
v
i
= 0 m/s
a =−9.81 m/s
2
a. v
f
=
v
i
2
+
2
a∆
y
=
(0
m
/s
)
2
+
(
2)
(−
9.
81
m
/s
2
)
(−
25
.0
m
)
v
f
=
4
.9
0
×
1
0
2
m
2
/
s
2
=
b. ∆t =
v
f
a
− v
i
=
−22
−
.1
9.
m
81
/s
m
−
/
0
s
2
m/s
=
2.25 s
−22.1 m/s
Holt Physics Solution ManualI Ch. 2–6
Copyright © by Holt, Rinehart and Winston. All rights reserved.
I
3. v
i
=+8.0 m/s
a =−9.81 m/s
2
∆y = 0 m
4. v
i
=+6.0 m/s
v
f
=+1.1 m/s
2
a =−9.81 m/s
2
∆y ==
∆y ==
−
−
1
3
9
5
.6
m
m
2
/
/
s
s
2
2
=
+1.8 m
1.2 m
2
/s
2
− 36 m
2
/s
2
−19.6 m/s
2
(1.1 m/s)
2
− (6.0 m/s)
2
(2)(−9.81 m/s
2
)
v
f
2
− v
i
2
2a
a. v
f
=
v
i
2
+ 2
ay
=
(8
.0
m
/s
)
2
+
(
2)
(−
9.
81
m
/s
2
)
(0
m
)
v
f
=
64 m
2
/
s
2
= ±8.0 m/s =
b. ∆t =
v
f
a
− v
i
=
−8.0
−
m
9.
/
8
s
1
−
m
8
/
.
s
0
2
m/s
=
−
−
9
1
.
6
8
.
1
0
m
m
/
/
s
s
2
=
1.63 s
−8.0 m/s
Givens Solutions
2. v
i
= 0 m/s ∆y = v
i
∆t +
1
2
a∆t
2
= (0 m/s)(1.5 s) +
1
2
(−9.81 m/s
2
)(1.5 s)
2
∆t = 1.5 s
∆y = 0 m + (−11 m) =−11 m
a =−9.81 m/s
2
the distance to the water’s surface =
11 m
Motion In One Dimension, Section 3 Review
7. ∆t = 0.530 h ∆x = v
avg
∆t = (19.0 km/h)(0.530 h) =
v
avg
= 19.0 km/h east
8. ∆t = 2.00 h, 9.00 min, 21.0 s ∆x = v
avg
∆t = (5.436 m/s) [(2.00 h)(3600 s/h) + (9.00 min)(60 s/min) + 21.0 s]
v
avg
= 5.436 m/s ∆x =(5.436 m/s)(7200 s + 540 s + 21.0 s) = (5.436 m/s)(7760 s)
∆x =4.22 × 10
4
m =
9. ∆t = 5.00 s a. ∆x
A
=
distance between
b. ∆x
B
= 70.0 m + 70.0 m =
poles = 70.0 m
c. v
avg,A
=
∆
∆
x
t
A
=
7
5
0
.
.
0
0
s
m
=
d. v
avg,B
=
∆
∆
x
t
B
=
1
5
4
.
0
0
m
s
=
+28 m/s
+14 m/s
+140.0 m
+70.0 m
4.22 × 10
1
km
10.1 km east
Motion In One Dimension, Chapter Review
Section One—Student Edition Solutions I Ch. 2–7
Copyright © by Holt, Rinehart and Winston. All rights reserved.
I
Givens Solutions
10. v
1
= 80.0 km/h
∆t
1
= 30.0 min
v
2
= 105 km/h
∆t
2
= 12.0 min
v
3
= 40.0 km/h
∆t
3
= 45.0 min
v
4
= 0 km/h
∆t
4
= 15.0 min
a. ∆x
1
= v
1
∆t
1
= (80.0 km/h)(30.0 min)(1 h/60 min) = 40.0 km
∆x
2
= v
2
∆t
2
= (105 km/h)(12.0 min)(1 h/60 min) = 21.0 km
∆x
3
= v
3
∆t
3
= (40.0 km/h)(45.0 min)(1 h/60 min) = 30.0 km
∆x
4
= v
4
∆t
4
= (0 km/h)(15.0 min)(1 h/60 min) = 0 km
v
avg
=
∆
∆
x
t
t
t
o
o
t
t
=
v
avg
=
v
avg
==
b. ∆x
tot
=∆x
1
+∆x
2
+∆x
3
+∆x
4
∆x
tot
= 40.0 km + 21.0 km + 30.0 km + 0 km =
91.0 km
53.5 km/h
91.0 km
(102.0 min)(1 h/60 min)
40.0 km + 21.0 km + 30.0 km + 0 km
(30.0 min + 12.0 min + 45.0 min + 15.0 min)(1 h/60 min)
∆x
1
+∆x
2
+∆x
3
+∆x
4
∆t
1
+∆t
2
+∆t
3
+∆t
4
11. v
A
= 9.0 km/h east
=+9.0 km/h
x
i, A
= 6.0 km west of
flagpole =−6.0 km
v
B
= 8.0 km/h west
=−8.0 km/h
x
i, B
= 5.0 km east of
flagpole =+5.0 km
x = distance from flagpole
to point where runners’
paths cross
∆x
A
= v
A
∆t = x − x
i, A
∆x
B
= v
B
∆t = x − x
i, B
∆x
A
−∆x
B
= (x − x
i, A
) − (x − x
i, B
) = x
i, B
− x
i, A
∆x
A
−∆x
B
= v
A
∆t − v
B
∆t = (v
A
− v
B
) ∆t
∆t =
x
i
v
,B
A
−
−
x
v
B
i, A
==
∆t = 0.647 h
∆x
A
= v
A
∆t = (9.0 km/h)(0.647 h) = 5.8 km
∆x
B
= v
B
∆t = (−8.0 km/h)(0.647 h) =−5.2 km
for runner A, x =∆x
A
+ x
i, A
= 5.8 km + (−6.0 km) =−0.2 km
x =
for runner B, x =∆x
B
+ x
i, B
=−5.2 km + (5.0 km) =−0.2 km
x =
0.2 km west of the flagpole
0.2 km west of the flagpole
11.0 km
17.0 km/h
5.0 km − (−6.0 km)
9.0 km/h − (−8.0 km/h)
Holt Physics Solution ManualI Ch. 2–8
Copyright © by Holt, Rinehart and Winston. All rights reserved.
I
16. v
i
=+5.0 m/s ∆t =
a
∆
av
v
g
=
v
a
f
a
−
vg
v
i
=
8.0 m
0.
/
7
s
5
−
m
5
/
.
s
0
2
m/s
=
0
3
.7
.0
5
m
m
/
/
s
s
2
a
avg
=+0.75 m/s
2
v
f
=+8.0 m/s ∆t =
17. For 0 s to 5.0 s: For 0 s to 5.0 s,
v
i
=−6.8 m/s
a
avg
=
v
f
∆
−
t
v
i
==
v
f
=−6.8 m/s
∆t = 5.0 s
For 5.0 s to 15.0 s: For 5.0 s to 15.0 s,
v
i
=−6.8 m/s
a
avg
=
v
f
∆
−
t
v
i
==
13
1
.
0
6
.0
m
s
/s
=
v
f
=+6.8 m/s
∆t = 10.0 s
For 0 s to 20.0 s: For 0 s to 20.0 s,
v
i
=−6.8 m/s
a
avg
=
v
f
∆
−
t
v
i
==
13
2
.
0
6
.0
m
s
/s
=
v
f
=+6.8 m/s
∆t = 20.0 s
18. v
i
= 75.0 km/h = 21.0 m/s ∆x=
1
2
(v
i
+ v
f
) ∆t =
1
2
(21.0 m/s + 0 m/s)(21.0 s) =
1
2
(21.0 m/s)(21 s)
v
f
= 0 km/h = 0 m/s
∆x=
∆t = 21 s
19. v
i
= 0 m/s ∆x =
1
2
(v
i
+ v
f
) ∆t =
1
2
(0 m/s + 18 m/s)(12 s) =
v
f
= 18 m/s
∆t = 12 s
20. v
i
=+7.0 m/s v
f
= v
i
+ a∆t = 7.0 m/s + (0.80 m/s
2
)(2.0 s) = 7.0 m/s + 1.6 m/s =
a =+0.80 m/s
2
∆t = 2.0 s
21. v
i
= 0 m/s a. v
f
= v
i
+ a∆t = 0 m/s + (−3.00 m/s
2
)(5.0 s) =
a =−3.00 m/s
2
b. ∆x = v
i
∆t +
1
2
a∆t
2
= (0 m/s)(5.0 s) +
1
2
(−3.00 m/s
2
)(5.0 s)
2
=
∆t = 5.0 s
22. v
i
= 0 m/s For the first time interval,
∆t
1
= 5.0 s v
f
= v
i
+ a
1
∆t
1
= 0 m/s + (1.5 m/s
2
)(5.0 s) =+7.5 m/s
a
1
=+1.5 m/s
2
∆x
1
= v
i
∆t
1
+
1
2
a
1
∆t
1
2
= (0 m/s)(5.0 s) +
1
2
(1.5 m/s
2
)(5.0 s)
2
=+19 m
∆t
2
= 3.0 s For the second time interval,
a
2
=−2.0 m/s
2
v
i
=+7.5 m/s
v
f
= v
i
+ a
2
∆t
2
= 7.5 m/s + (−2.0 m/s
2
)(3.0 s) = 7.5 m/s − 6.0 m/s =
∆x
2
= v
i
∆t
2
+
1
2
a
2
∆t
2
= (7.5 m/s)(3.0 s) +
1
2
(−2.0 m/s
2
)(3.0 s)
2
= 22 m − 9.0 m =+13 m
∆x
tot
=∆x
1
+∆x
2
= 19 m + 13 m =
+32 m
+1.5 m/s
−38 m
−15 m/s
+8.6 m/s
110 m
220 m
+0.680 m/s
2
6.8 m/s − (−6.8 m/s)
20.0 s
+1.36 m/s
2
6.8 m/s − (−6.8 m/s)
10.0 s
0.0 m/s
2
−6.8 m/s − (−6.8 m/s)
5.0 s
4.0 s
Givens Solutions
Section One—Student Edition Solutions I Ch. 2–9
Copyright © by Holt, Rinehart and Winston. All rights reserved.
I
23. a = 1.40 m/s
2
∆x =
v
f
2
2
−
a
v
i
2
==
4
2
9
.8
.0
0
m
m
2
/
/
s
s
2
2
=
v
i
= 0 m/s
v
f
= 7.00 m/s
17.5 m
(7.00 m/s)
2
− (0 m/s)
2
(2)(1.40 m/s
2
)
Givens Solutions
24. v
i
= 0 m/s
a = 0.21 m/s
2
∆x = 280 m
a. v
f
=
v
i
2
+
2
a∆
x
=
(0
m
/s
)
2
+
(
2)
(0
.2
1
m
/s
2
)
(2
80
m
)
=
12
0
m
2
/
s
2
=±11 m/s
b. ∆t =
v
f
a
− v
i
=
11
0
m
.2
/
1
s −
m
0
/s
m
2
/s
=
52 s
v
f
= 11 m/s
25. v
i
=+1.20 m/s
a =−0.31 m/s
2
∆x =+0.75 m
v
f
=
v
i
2
+
2
a∆
x
=
(1
.2
0
m
/s
)
2
+
(
2)
(−
0.
31
m
/s
2
)
(0
.7
5
m
)
v
f
=
1.
44
m
2
/
s
2
−
0
.4
6
m
2
/
s
2
=
0.98 m
2
/s
2
=±0.99 m/s =
+0.99 m/s
30. v
i
= 0 m/s When v
i
= 0 m/s,
∆y =−80.0 m
v
2
= 2a∆y v =
2a∆y
a =−9.81 m/s
2
v =
(2
)(
−
9.
81
m
/s
2
)
(−
80
.0
m
)
v =±
15
70
m
2
/
s
2
v =
31. v
i
= 0 m/s When v
i
= 0 m/s,
a =−9.81 m/s
2
∆t =
2∆
a
y
=
(2
−
)
9
(
.
−
8
7
1
6
m
.0
/
m
s
2
)
=
∆y =−76.0 m
3.94 s
−39.6 m/s
32. v
i, 1
=+25 m/s
v
i, 2
= 0 m/s
a =−9.81 m/s
2
y
i, 1
= 0 m
y
i, 2
= 15 m
y = distance from ground
to point where both balls
are at the same height
∆y
1
= y − y
i, 1
= v
i, 1
∆t +
1
2
a∆t
2
∆y
2
= y − y
i, 2
= v
i, 2
∆t +
1
2
a∆t
2
∆y
1
−∆y
2
= (y − y
i, 1
) − (y − y
i, 2
) = y
i, 2
− y
i, 1
∆y
1
−∆y
2
= (v
i, 1
∆t +
1
2
a∆t
2
) − (v
i, 2
∆t +
1
2
a∆t
2
) = (v
i, 1
− v
i, 2
) ∆t
∆y
1
−∆y
2
= y
i, 2
− y
i, 1
= (v
i, 1
− v
i, 2
)∆t
∆t =
v
y
i
i
,
,
2
1
−
−
y
v
i
i
,
,
1
2
=
25
15
m
m
/s
−
−
0
0
m
m/s
=
2
1
5
5
m
m
/s
=
0.60 s
33. v
avg
= 27 800 km/h circumference = 2p(r
earth
+∆x)
r
earth
= 6380 km
∆t =
circum
v
a
f
v
e
g
rence
===
∆x = 320.0 km
1.51 h
2p(6.70 × 10
3
km)
27 800 km/h
2p(6380 km + 320.0 km)
27 800 km/h
Holt Physics Solution ManualI Ch. 2–10
Copyright © by Holt, Rinehart and Winston. All rights reserved.
I
Givens Solutions
34.
a. For Δy = 0.20 m = maximum height of ball, Δt =
b. For Δy = 0.10 m = one-half maximum height of ball,
Δt =
Δt =
c. Estimating v from t = 0.04 s to t = 0.06 s:
v =
⎯
Δ
Δ
x
t
⎯
=
⎯
0
0
.1
.0
0
6
m
s
−
−
0
0
.
.
0
0
7
4
m
s
⎯
=
⎯
0
0
.
.
0
0
3
2
m
s
⎯
=
Estimating v from t = 0.09 s to t = 0.11 s:
v =
⎯
Δ
Δ
x
t
⎯
=
⎯
0
0
.1
.1
5
1
m
s
−
−
0
0
.
.
1
0
3
9
m
s
⎯
=
⎯
0
0
.
.
0
0
2
2
m
s
⎯
=
Estimating v from t = 0.14 s to t = 0.16 s:
v =
⎯
Δ
Δ
x
t
⎯
=
⎯
0
0
.1
.1
9
6
m
s
−
−
0
0
.
.
1
1
8
4
m
s
⎯
=
⎯
0
0
.
.
0
0
1
2
m
s
⎯
=
Estimating v from t = 0.19 s to t = 0.21 s:
v =
⎯
Δ
Δ
x
t
⎯
=
⎯
0
0
.2
.2
0
1
m
s
−
−
0
0
.
.
2
1
0
9
m
s
⎯
=
d. a =
⎯
Δ
Δ
v
t
⎯
=
⎯
0
0
m
.2
/
0
s −
s −
2
0
m
s
/s
⎯
=
⎯
−
0
2
.2
m
0
/
s
s
⎯
=
−10 m/s
2
0 m/s
+
0.5 m/s
+1 m/s
+
2 m/s
0.34 s as ball comes down
0.06 s as ball goes up
0.20 s
35. Δx
AB
= Δx
BC
= Δx
CD
Δt
AB
=
⎯
v
Δ
A
x
B
A
,a
B
vg
⎯
==
⎯
2Δ
v
x
B
AB
⎯
Because the train’s velocity is constant from B to C, Δt
BC
=
⎯
Δ
v
x
B
BC
⎯
.
Δt
CD
=
⎯
v
Δ
C
x
D
C
,a
D
vg
⎯
==
⎯
2Δ
v
x
B
CD
⎯
Because Δx
AB
= Δx
BC
= Δx
CD
,
⎯
Δt
2
AB
⎯
= Δt
BC
=
⎯
Δt
2
CD
⎯
,or
Δt
AB
= Δt
CD
= 2Δt
BC
.
We also know that Δt
AB
+ Δt
BC
+ Δt
CD
= 5.00 min.
Thus, the time intervals are as follows:
a. Δt
AB
=
b. Δt
BC
=
c. Δt
CD
=
2.00 min
1.00 min
2.00 min
Δx
CD
⎯
⎯
(0 +
2
v
B
)
⎯
Δx
AB
⎯
⎯
(v
B
2
+ 0)
⎯
Δt
AB
+ Δt
BC
+ Δt
CD
=
5.00 min
Section One—Student Edition Solutions I Ch. 2–11
Copyright © by Holt, Rinehart and Winston. All rights reserved.
I
Givens Solutions
∆t = 0.800 s
c. ∆y
1
= v
i,1
∆t +
1
2
a∆t
2
= (−14.7 m/s)(0.800 s) +
1
2
(−9.81 m/s
2
)(0.800 s)
2
∆y
1
=−11.8 m − 3.14 m =−14.9 m
∆y
2
= v
i,2
∆t +
1
2
a∆t
2
= (14.7 m/s)(0.800 s) +
1
2
(−9.81 m/s
2
)(0.800 s)
2
∆y
2
= 11.8 m − 3.14 m =+8.7 m
distance between balls =∆y
2
−∆y
1
= 8.7 m − (−14.9 m) =
23.6 m
36. ∆y =−19.6 m
v
i,1
=−14.7 m/s
v
i,2
=+14.7 m/s
a =−9.81 m/s
2
a. v
f,1
=
v
i
,1
2
+
2
a∆
y
=
(−
14
.7
m
/s
)
2
+
(
2)
(−
9.
81
m
/s
2
)
(−
19
.6
m
)
v
f,1
=
21
6
m
2
/
s
2
+
3
85
m
2
/
s
2
=
60
1
m
2
/
s
2
=±24.5 m/s =−24.5 m/s
v
f,2
=
v
i
,2
2
+
2
a∆
y
=
(1
4.
7
m
/s
)
2
+
(
2)
(−
9.
81
m
/s
2
)
(−
19
.6
m
)
v
f,2
=
21
6
m
2
/
s
2
+
3
85
m
2
/
s
2
=
60
1
m
2
/
s
2
=±24.5 m/s =−24.5 m/s
∆t
1
=
v
f,1
−
a
v
i,1
==
−
−
9
9
.8
.8
1
m
m
/
/
s
s
2
= 1.0 s
∆t
2
=
v
f,2
−
a
v
i,2
==
−
−
9
3
.
9
8
.
1
2
m
m
/
/
s
s
2
= 4.00 s
difference in time =∆t
2
−∆t
1
= 4.00 s − 1.0 s =
b. v
f,1
= (See a.)
v
f,2
= (See a.)
−24.5 m/s
−24.5 m/s
3.0 s
−24.5 m/s − 14.7 m/s
−9.81 m/s
2
−24.5 m/s − (−14.7 m/s)
−9.81 m/s
2
37. For the first time interval:
v
i
= 0 m/s
a =+29.4 m/s
2
∆t = 3.98 s
For the second time interval:
v
i
=+117 m/s
a =−9.81 m/s
2
v
f
= 0 m/s
While the rocket accelerates,
∆y
1
= v
1
∆t +
1
1
2
a∆t
2
= (0 m/s)(3.98 s) +
1
2
(29.4 m/s
2
)(3.98 s)
2
=+233 m
v
f
= v
i
+ a∆t = 0 m/s + (29.4 m/s
2
)(3.98 s) =+117 m/s
After the rocket runs out of fuel,
∆y
2
=
v
f
2
2
−
a
v
i
2
==+698 m
total height reached by rocket =∆y
1
+∆y
2
= 233 m + 698 m =
931 m
(0 m/s)
2
− (117 m/s)
2
(2)(−9.81 m/s
2
)
Givens Solutions
Holt Physics Solution ManualI Ch. 2–12
Copyright © by Holt, Rinehart and Winston. All rights reserved.
38. v
1
= 85 km/h
a. ∆t
1
=
∆
v
1
x
=
8
1
5
6
k
k
m
m
/h
= 0.19 h
v
2
= 115 km/h
∆x = 16 km
∆t
2
=
∆
v
2
x
=
11
1
5
6
k
k
m
m
/h
= 0.14 h
The faster car arrives ∆t
1
−∆t
2
= 0.19 h − 0.14 h = earlier.
∆t
1
−∆t
2
= 15 min b. ∆x =∆t
1
v
1
=∆t
2
v
2
= 0.25 h ∆x (v
2
− v
1
) =∆xv
2
−∆xv
1
= (∆t
1
v
1
)v
2
− (∆t
2
v
2
)v
1
∆x (v
2
− v
1
) = (∆t
1
−∆t
2
)v
2
v
1
∆x = (∆t
1
−∆t
2
)
v
2
v
2
−
v
1
v
1
= (0.25 h)
∆x = (0.25 h)
=
39. v
i
=−1.3 m/s v
f
= v
i
+ a∆t =−1.3 m/s + (−9.81 m/s
2
)(2.5 s)
a =−9.81 m/s
2
v
f
=−1.3 m/s − 25 m/s =
∆t = 2.5 s
∆x
kit
=
1
2
(v
i
+ v
f
)∆t =
1
2
(−1.3 m/s − 26 m/s)(2.5 s)
∆x
kit
=
1
2
(−27 m/s)(2.5 s) =−34 m
∆x
climber
= (−1.3 m/s)(2.5 s) =−3.2 m
The distance between the kit and the climber is ∆x
climber
−∆x
kit
.
∆x
climber
−∆x
kit
=−3.2 m − (−34 m) =
40. v
i
=+0.50 m/s a. v
f
= v
i
+ a∆t = 0.50 m/s + (−9.81 m/s
2
)(2.5 s) = 0.50 m/s − 25 m/s
∆t = 2.5 s v
f
=
a =−9.81 m/s
2
b. ∆x
fish
=
1
2
(v
i
+ v
f
)∆t =
1
2
(0.50 m/s − 24 m/s)(2.5 s)
∆x
fish
=
1
2
(−24 m/s)(2.5 s) =−30 m
∆x
pelican
= (0.50 m/s)(2.5 s) =+1.2 m
The distance between the fish and the pelican is ∆x
pelican
−∆x
fish
.
∆x
pelican
−∆x
fish
= 1.2 m − (−30 m) =
41. v
i
= 56 km/h For the time interval during which the ranger decelerates,
v
f
= 0 m/s
∆t =
v
f
−
a
v
i
==5.2 s
a =−3.0 m/s
2
∆x = v
i
∆t +
1
2
a∆t
2
= (56 × 10
3
m/h)(1 h/3600 s)(5.2 s) +
1
2
(−3.0 m/s
2
)(5.2 s)
2
∆x
tot
= 65 m
∆x = 81 m − 41 m = 4.0 × 10
1
m
maximum reaction distance =∆x
tot
−∆x = 65 m − (4.0 × 10
1
m) = 25 m
maximum reaction time =
maximum reaction time ==
1.6 s
25 m
(56 × 10
3
m/h)(1 h/3600 s)
maximum reaction distance
v
i
0 m/s − (56 × 10
3
m/h)(1 h/3600 s)
−3.0 m/s
2
31 m
−24 m/s
31 m
−26 m/s
81 km
(115 km/h)(85 km/h)
(30 km/h)
(115 km/h)(85 km/h)
(115 km/h) − (85 km/h)
0.05 h
I
Section One—Student Edition Solutions I Ch. 2–13
Copyright © by Holt, Rinehart and Winston. All rights reserved.
I
42. v
s
= 30.0 m/s a. ∆x
s
=∆x
p
v
i,p
= 0 m/s ∆x
s
= v
s
∆t
a
p
= 2.44 m/s
2
Because v
i,p
= 0 m/s,
∆x
p
=
1
2
a
p
∆t
2
v
s
∆t =
1
2
a
p
∆t
2
∆t =
2
a
v
p
s
=
(2
2
)(
.4
3
4
0.
m
0m
/s
2
/s)
=
b. ∆x
s
= v
s
∆t = (30.0 m/s)(24.6 s) =
or ∆x
p
=
1
2
a
p
∆t
2
=
1
2
(2.44 m/s
2
)(24.6 s)
2
=
738 m
738 m
24.6 s
43. For ∆t
1
:
v
i
= 0 m/s
a =+13.0 m/s
2
v
f
= v
For ∆t
2
:
a = 0 m/s
2
v = constant velocity
∆x
tot
=+5.30 × 10
3
m
∆t
tot
=∆t
1
+∆t
2
= 90.0 s
When v
i
= 0 m/s,
∆x
1
=
1
2
a∆t
1
2
∆t
2
= 90.0 s −∆t
1
∆x
2
= v∆t
2
= v(90.0 s −∆t
1
)
∆x
tot
=∆x
1
+∆x
2
=
1
2
a∆t
1
2
+ v(90.0 s −∆t
1
)
v = v
f
during the first time interval = a∆t
1
∆x
tot
=
1
2
a∆t
1
2
+ a∆t
1
(90.0 s −∆t
1
) =
1
2
a∆t
1
2
+ (90.0 s)a∆t
1
− a∆t
1
2
∆x
tot
=−
1
2
a∆t
1
2
+ (90.0 s)a∆t
1
1
2
a∆t
1
2
− (90.0 s)a∆t
1
+∆x
tot
= 0
Using the quadratic equation,
∆t
1
=
∆t
1
=
(90.0 s)(13.0 m/s
2
) ±
[−(90.0
s)(13.
0 m/s
2
)]
2
−2(
13.0 m
/s)(5.3
0 × 10
3
m)
13.0 m/s
2
(90.0 s)(a) ±
[−(90.0
s)(a)]
2
− 4
1
2
a
(∆x
tot
)
2
1
2
a
∆t
1
=
∆t
1
===
13
6
.
0
0
m
m
/
/
s
s
2
=
∆t
2
=∆t
tot
−∆t
1
= 90.0 s − 5 s =
v = a∆t
1
= (13.0 m/s
2
)(5 s) =
+60 m/s
85 s
5 s
1170 m/s ± 1110 m/s
13.0 m/s
2
1170 m/s ±
1.23 ×
10
6
m
2
/s
2
13.0 m/s
2
1170 m/s ±
(1.37 ×
10
6
m
2
/s
2
) −
(1.38
× 10
5
m
2
/s
2
)
13.0 m/s
2
Holt Physics Solution ManualI Ch. 2–14
Copyright © by Holt, Rinehart and Winston. All rights reserved.
I
44. ∆x
1
=+5800 m a. ∆x
2
=
v
f
2
2
−
a
v
i
2
==+ 300 m
a =−7.0 m/s
2
v
i
=+60 m/s (see 43.) sled’s final position = ∆x
1
+ ∆x
2
= 5800 m + 300 m =
v
f
= 0 m/s
b. ∆t =
v
f
a
− v
i
==
45. v
i
=+10.0 m/s a
avg
=
v
f
∆
−
t
v
i
=
−8.0 m
0
/
.
s
0
−
12
10
s
.0 m/s
=
v
f
=−8.0 m/s
∆t = 0.012 s
−1.5 × 10
3
m/s
2
9 s
0 m/s − 60 m/s
−7.0 m/s
2
6100 m
(0 m/s)
2
− (60 m/s)
2
(2)(−7.0 m/s
2
)
46. v
i
=−10.0 m/s
∆y =−50.0 m
a =−9.81 m/s
2
a. v
f
=
v
i
2
+ 2
ay
=
(−
10
.0
m
/s
)
2
+
(
2)
(−
9.
81
m
/s
2
)
(−
50
.0
m
)
v
f
=
1.00 ×
10
2
m
2
/s
2
+ 9
81 m
2
/
s
2
=
10
81
m
2
/
s
2
=±32.9 m/s =−32.9 m/s
∆t =
v
f
a
− v
i
==
−
−
9
2
.
2
8
.
1
9
m
m
/
/
s
s
2
=
b. v
f
= (See a.)
−32.9 m/s
2.33 s
−32.9 m/s − (−10.0 m/s)
−9.81 m/s
2
Givens Solutions
47. ∆y =−50.0 m
v
i,1
=+2.0 m/s
∆t
1
=∆t
2
+ 1.0 s
a =−9.81 m/s
2
a. v
f,1
=
v
i
,1
2
+
2
a∆
y
=
(2.0 m
/s)
2
+ (
2)(−9.8
1 m/s
2
)(−50.0
m)
v
f,1
=
4.
0
m
2
/
s
2
+
9
81
m
2
/
s
2
=
98
5
m
2
/
s
2
=±31.4 m/s =−31.4 m/s
∆t
1
=
v
f,1
−
a
v
i,1
=
−31.
−
4
9
m
.8
/
1
s −
m
2
/s
.0
2
m/s
=
−
−
9
3
.
3
8
.
1
4
m
m
/
/
s
s
2
=
b. ∆t
2
=∆t
1
− 1.0 s = 3.40 s − 1.0 s = 2.4 s
∆y = v
i,2
∆t
2
+
1
2
a∆t
2
2
v
i,2
==
v
i,2
=
−50.0
2
m
.4
+
s
28 m
=
−
2
2
.
2
4
m
s
=
c. v
f,1
= (See a.)
v
f,2
= v
i,2
+ a∆t
2
=−9.2 m/s + (−9.81 m/s
2
)(2.4 s)
v
f,2
=−9.2 m/s − 24 m/s =
−33 m/s
−31.4 m/s
−9.2 m/s
−50.0 m −
1
2
(−9.81 m/s
2
)(2.4 s)
2
2.4 s
∆y −
1
2
a∆t
2
2
∆t
2
3.40 s
Section One—Student Edition Solutions I Ch. 2–15
Copyright © by Holt, Rinehart and Winston. All rights reserved.
I
Givens Solutions
48. For the first time interval:
v
i,1
=+50.0 m/s
a
1
=+2.00 m/s
2
∆y
1
= +150 m
For the second time interval:
v
i,2
=+55.7 m/s
v
f,2
= 0 m/s
a
2
=−9.81 m/s
2
For the trip down:
∆y =−310 m
v
i
= 0 m/s
a =−9.81 m/s
2
a. v
f,1
=
v
i
,1
2
+
2
a
1
∆
y
1
=
(50.0 m
/s)
2
+ (
2)(2.00
m/s
2
)(
150 m)
v
f,1
=
(2
.5
0
×
1
0
3
m
2
/
s
2
)
+
(
6.
0
×
1
0
2
m
2
/
s
2
)
=
3.
10
×
1
0
3
m
2
/
s
2
v
f,1
=±55.7 m/s =+55.7 m/s
∆y
2
=
v
f,2
2
2
−
a
2
v
i,2
2
==+158 m
maximum height =∆y
1
+∆y
2
= 150 m + 158 m =
b. For the first time interval,
∆t
up,1
=
v
i,
2
1
∆
+
y
v
1
f,1
=
50.0
(
m
2)
/
(
s
1
+
50
55
m
.7
)
m/s
=
(
1
2
0
)(
5
1
.7
50
m
m
/s
)
= 2.8 s
For the second time interval,
∆t
up,2
=
v
i,
2
2
∆
+
y
v
2
f,2
=
55.
(
7
2
m
)(1
/s
58
+
m
0m
)
/s
= 5.67 s
∆t
up,tot
=∆t
up,1
+∆t
up,2
= 2.8 s + 5.67 s =
c. Because v
i
= 0 m/s, ∆t
down
=
2∆
a
y
==
63
s
2
= 7.9 s
∆t
tot
=∆t
up,tot
+∆t
down
= 8.5 s + 7.9 s =
16.4 s
(2)(−3
10 m)
−9.81 m/s
2
8.5 s
310 m
(0 m/s)
2
− (55.7 m/s)
2
(2)(−9.81 m/s
2
)
Holt Physics Solution ManualI Ch. 2–16
49. a
1
=+5.9 m/s
2
a
2
=+3.6 m/s
2
∆t
1
=∆t
2
− 1.0 s
Because both cars are initially at rest,
a. ∆x
1
=
1
2
a
1
∆t
1
2
∆x
2
=
1
2
a
2
∆t
2
2
∆x
1
=∆x
2
1
2
a
1
∆t
1
2
=
1
2
a
2
∆t
2
2
a
1
(∆t
2
− 1.0 s)
2
= a
2
∆t
2
2
a
1
[∆t
2
2
− (2.0 s)(∆t
2
) + 1.0 s
2
] = a
2
∆t
2
2
(a
1
)(∆t
2
)
2
− a
1
(2.0 s)∆t
2
+ a
1
(1.0 s
2
) = a
2
∆t
2
2
(a
1
− a
2
)∆t
2
2
− a
1
(2.0 s)∆t
2
+ a
1
(1.0 s
2
) = 0
Using the quadratic equation,
∆t
2
=
a
1
− a
2
= 5.9 m/s
2
− 3.6 m/s
2
= 2.3 m/s
2
∆t
2
=
∆t
2
==
∆t
2
=
1
(
2
2)
m
(2
/s
.3
±
m
9
/
m
s
2
)
/s
=
(2)(
2
2
1
.3
m
m
/s
/s
2
)
=
∆t
1
=∆t
2
− 1.0 s = 4.6 s − 1.0 s =
b. ∆x
1
=
1
2
a
1
∆t
1
2
=
1
2
(5.9 m/s
2
)(3.6 s)
2
= 38 m
or ∆x
2
=
1
2
a
2
∆t
2
2
=
1
2
(3.6 m/s
2
)(4.6 s)
2
= 38 m
distance both cars travel =
c. v
1
= a
1
∆t
1
= (5.9 m/s
2
)(3.6 s) =
v
2
= a
2
∆t
2
= (3.6 m/s
2
)(4.6 s) =
+17 m/s
+21 m/s
38 m
3.6 s
4.6 s
12 m/s ±
90 m
2
/
s
2
(2)(2.3 m/s
2
)
12 m/s ±
140 m
2
/s
2
− 5
4 m
2
/s
2
(2)(2.3 m/s
2
)
(5.9 m/s
2
)(2.0 s) ±
[−(5.9
m/s
2
)(
2.0 s)]
2
− (4)
(2.3 m
/s
2
)(5.
9 m/s
2
)(1.0 s
2
)
(2)(2.3 m/s
2
)
(a
1
)(2.0 s) ±
[−a
1
(2
.0 s)]
2
− 4(a
1
− a
2
)a
1
(1.0 s
2
)
2(a
1
− a
2
)
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
50. v
i,1
=+25 m/s
v
i,2
=+35 m/s
∆x
2
=∆x
1
+ 45 m
a
1
=−2.0 m/s
2
v
f,1
= 0 m/s
v
f,2
= 0 m/s
a. ∆t
1
=
v
f,1
a
−
1
v
i,1
=
0m
−
/
2
s
.0
−
m
25
/s
m
2
/s
=
b. ∆x
1
=
1
2
(v
i,1
+ v
f,1
)∆t
1
=
1
2
(25 m/s + 0 m/s)(13 s) =+163 m
∆x
2
=∆x
1
+ 45 m = 163 m + 45 m =+208 m
a
2
=
v
f,2
2
2
∆
−
x
v
2
i,2
2
==
c. ∆t
2
=
v
f,2
a
−
2
v
i,2
=
0m
−
/
2
s
.9
−
m
35
/s
m
2
/s
=
12 s
−2.9 m/s
2
(0 m/s)
2
− (35 m/s)
2
(2)(208 m)
13 s
Section One—Student Edition Solutions I Ch. 2–17
Copyright © by Holt, Rinehart and Winston. All rights reserved.
I
Givens Solutions
51. ∆x
1
= 20.0 m
v
1
= 4.00 m/s
∆x
2
= v
2
(0.50 s) + 20.0 m
∆t =
∆
v
x
1
1
=
4
2
.0
0
0
.0
m
m
/s
= 5.00 s
v
2
=
∆
∆
x
t
2
=
v
2
∆t = v
2
(0.50 s) + 20.0 m
v
2
(∆t − 0.50 s) = 20.0 m
v
2
=
∆t
2
−
0.
0
0
.
m
50 s
=
(5.00
20
s
.
−
0
0
m
.50 s)
=
2
4
0
.5
.0
0
m
s
=
4.44 m/s
v
2
(0.50 s) + 20.0 m
∆t
4. ∆t = 5.2 h
v
avg
= 73 km/h south
∆x = v
avg
∆t = (73 km/h)(5.2 h) =
3.8 × 10
2
km south
Motion In One Dimension, Standardized Test Prep
5. ∆t = 3.0 s
∆x = 4.0 m + (−4.0 m) + (−2.0 m) + 0.0 m =
−2.0 m
8. v
i
= 0 m/s
a = 3.3 m/s
2
∆t = 7.5 s
∆x = v
i
∆t +
1
2
a∆t
2
∆x = (0 m/s)(7.5 s) +
1
2
(3.3 m/s
2
)(7.5 s)
2
= 0 m + 93 m =
93 m
11. ∆t
1
= 10.0 min − 0 min
= 10.0 min
∆t
2
= 20.0 min − 10.0 min
= 10.0 min
∆t
3
= 30.0 min − 20.0 min
= 10.0 min
a. ∆x
1
= (2.4 × 10
3
m) − (0 × 10
3
m) =
v
1
=
∆
∆
x
t
1
1
==
b. ∆x
2
= (3.9 × 10
3
m) − (2.4 × 10
3
m) =
v
2
=
∆
∆
x
t
2
2
==
c. ∆x
3
= (4.8 × 10
3
m) − (3.9 × 10
3
m) =
v
3
=
∆
∆
x
t
3
3
==
d. ∆x
tot
=∆x
1
+∆x
2
+∆x
3
= (2.4 × 10
3
m) + (1.5 × 10
3
m) + (9 × 10
2
m)
∆x
tot
=
v
avg
=
∆
∆
x
t
t
t
o
o
t
t
=
∆
∆
x
t
1
1
+
+
∆
∆
x
t
2
2
+
+
∆
∆
t
x
3
3
=
v
avg
=
+2.7 m/s
(4.8 × 10
3
m)
(30.0 min)(60 s/min)
+4.8 × 10
3
m
+2 m/s
(9 × 10
2
m)
(10.0 min)(60 s/min)
+9 × 10
2
m
+2.5 m/s
(1.5 × 10
3
m)
(10.0 min)(60 s/min)
+1.5 × 10
3
m
+4.0 m/s
(2.4 × 10
3
m)
(10.0 min)(60 s/min)
+2.4 × 10
3
m
6. ∆x =−2.0 m (see 5.)
∆t = 3.0 s
v
avg
=
∆
∆
x
t
=
−
3
2
.
.
0
0
s
m
=
−0.67 m/s
Holt Physics Solution ManualI Ch. 2–18
Copyright © by Holt, Rinehart and Winston. All rights reserved.
I
Givens Solutions
13. v
i
=+3.0 m/s
a
1
=+0.50 m/s
2
∆t = 7.0 s
a
2
=−0.60 m/s
2
v
f
= 0 m/s
a. v
f
= a
1
∆t + v
i
= (0.50 m/s
2
)(7.0 s) + 3.0 m/s = 3.5 m/s + 3.0 m/s =
b. ∆t =
v
f
a
−
2
v
i
=
0m
−0
/s
.6
−
0
3
m
.0
/s
m
2
/s
=
5.0 s
+6.5 m/s
14. v
i
= 16 m/s east =+16 m/s
v
f
= 32 m/s east =+32 m/s
∆t = 10.0 s
a. a =
v
f
∆
−
t
v
i
=
32 m/
1
s
0
−
.0
1
s
6m/s
=
1
1
6
0.
m
0
/
s
s
=+1.6 m/s
2
=
b. ∆x =
1
2
(v
i
+ v
f
)∆t =
1
2
(16 m/s + 32 m/s)(10.0 s) =
1
2
(48 m/s)(10.0 s)
∆x =+240 m
v
avg
=
∆
∆
x
t
=
2
1
4
0
0
.0
m
s
=+24 m/s =
c. distance traveled = (See b.)
+240 m
24 m/s east
1.6 m/s
2
east
15. v
i
=+25.0 m/s
y
i
=+2.0 m/s
a =−9.81 m/s
2
For the trip up: v
f
= 0 m/s
For the trip down: v
i
= 0 m/s
∆y = (−31.9 m − 2.0 m)
∆y =−33.9 m
a. For the trip up,
∆t =
v
f
a
− v
i
=
0m
−
/
9
s
.8
−
1
2
m
5.0
/s
2
m/s
=
∆y = v
i
∆t +
1
2
a∆t
2
= (25.0 m/s)(2.55 s) +
1
2
(−9.81 m/s
2
)(2.55 s)
2
∆y = 63.8 m − 31.9 m =+31.9 m
b. For the trip down, because v
i
= 0 m/s,
∆t =
2∆
a
y
=
(2
−
)
9
(
.
−
8
3
1
3
m
.
9
/
m
s
2
)
=
6.
91
s
2
= 2.63 s
total time = 2.55 s + 2.63 s =
5.18 s
2.55 s
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 3–1
Two-Dimensional Motion
and Vectors
Student Edition Solutions
I
2. ∆x
1
= 85 m
d
2
= 45 m
q
2
= 30.0°
3. v
y, 1
= 2.50 × 10
2
km/h
v
2
= 75 km/h
q
2
=−45°
4. v
y,1
=
2.50 × 1
2
0
2
km/h
= 125 km/h
v
x,2
= 53 km/h
v
y,2
=−53 km/h
Students should use graphical techniques. Their answers can be checked using the
techniques presented in Section 2. Answers may vary.
∆x
2
= d
2
(cos q
2
) = (45 m)(cos 30.0°) = 39 m
∆y
2
= d
2
(sin q
2
) = (45 m)(sin 30.0°) = 22 m
∆x
tot
=∆x
1
+∆x
2
= 85 m + 39 m = 124 m
∆y
tot
=∆y
2
= 22 m
d =
(∆
x
t
ot
)
2
+
(
∆
y
t
ot
)
2
=
(1
24
m
)
2
+
(
22
m
)
2
d =
15
4
00
m
2
+
4
80
m
2
=
15
9
00
m
2
=
q = tan
−1
∆
∆
x
y
t
t
o
o
t
t
= tan
−1
1
2
2
2
4
m
m
= (1.0 × 10
1
)° above the horizontal
126 m
Students should use graphical techniques.
v
x,2
= v
2
(cos q
2
) = (75 km/h)[cos (−45°)] = 53 km/h
v
y,2
= v
2
(sin q
2
) = (75 km/h)[sin (−45°)] =−53 km/h
v
y,tot
= v
y,1
+ v
y, 2
= 2.50 × 10
2
km/h − 53 km/h = 197 km/h
v
x,tot
= v
s,2
= 53 km/h
v =
(v
x,
to
t
)
2
+
(
v
y
,to
t
)
2
=
(5
3
km
/h
)
2
+
(1
97
k
m
/h
)
2
v =
28
00
k
m
2
/
h
2
+
3
8
80
0
km
2
/
h
2
=
41
6
00
k
m
2
/
h
2
=
q = tan
−1
v
v
x
y,
,
t
t
o
o
t
t
= tan
−1
2
5
0
3
4
k
k
m
m
/
/
h
h
= 75° north of east
204 km/h
Students should use graphical techniques.
v
y,dr
= v
y,1
+ v
y,2
= 125 km/h − 53 km/h = 72 km/h
v
x,dr
= v
x,2
= 53 km/h
v =
(v
x,
dr
)
2
=
v
y,d
r
)
2
=
(5
3
km
/h
)
2
+
(7(7
2
km
/h
)
2
v =
28
00
k
m
2
/
h
2
+
5
20
0
km
2
/
h
2
=
8.
0
1
0
3
k
m
2
/
h
2
=
q = tan
−1
v
v
x
y
,
,
d
d
r
r
= tan
−1
7
5
2
3
k
k
m
m
/
/
h
h
= 54° north of east
89 km/h
Two-Dimensional Motion and Vectors, Section 1 Review
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualI Ch. 3–2
I
2. ∆x = 7.5 m
∆y = 45.0 m
3. ∆x = 6.0 m
∆y = 14.5 m
4. ∆x = 1.2 m
∆y = –1.4 m
d =
∆
x
2
+
∆
y
2
=
(7
.5
m
)
2
+
(
45
.0
m
)
2
d =
56
m
2
+
2
02
0
m
2
=
20
80
m
2
=
Measuring direction with respect to y (north),
q = tan
−1
∆
∆
x
y
= tan
−1
4
7
5
.5
.0
m
m
= 9.5° east of due north
45.6 m
d =
∆
x
2
+
∆
y
2
=
(6
.0
m
)
2
+
(
14
.5
m
)
2
d =
36
m
2
+
2
.1
0
×
1
0
2
m
2
=
24
6
m
2
=
Measuring direction with respect to the length of the field (down the field),
q = tan
−1
∆
∆
x
y
= tan
−1
1
6
4
.0
.5
m
m
= 22° to the side of downfield
15.7 m
d =
∆
x
2
+
∆
y
2
=
(1
.2
m
)
2
+
(
–
1.
4
m
)
2
d =
1.
4
m
2
+
2
.0
m
2
=
3.
4
m
2
=
q = tan
−1
∆
∆
x
y
= tan
−1
–
1
1
.2
.4
m
m
= –49° = 49° below the horizontal
1.8 m
Two-Dimensional Motion and Vectors, Practice A
Givens Solutions
1. v = 105 km/h v
x
= v(cos q) = (105 km/h)(cos 25°) =
q = 25°
2. v = 105 km/h v
y
= v(sin q) = (105 km/h)(sin 25°) =
q = 25°
3. v = 22 m/s v
x
= v(cos q) = (22 m/s)(cos 15°) =
q = 15° v
y
= v(sin q) = (22 m/s)(sin 15°) =
4. d = 5 m ∆x = d(cos q) = (5 m)(cos 90°) =
q = 90°∆y = d(sin q) = (5 m)(sin 90°) = 5 m
0 m
5.7 m/s
21 m/s
44 km/h
95 km/h
Two-Dimensional Motion and Vectors, Practice B
1. ∆x
1
= 8 km east
∆x
1
= 8 km
∆x
2
= 3 km west =−3km, east
∆x
2
= 3 km
∆x
3
= 12 km east
∆x
3
= 12 km
∆y = 0 km
a. d =∆x
1
+∆x
2
+∆x
3
= 8 km + 3 km + 12 km =
b. ∆x
tot
=∆x
1
+∆x
2
+∆x
3
= 8 km + (−3 km) + 12 km = 17 km east
23 km
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 3–3
I
1. d
1
= 35 m
q
1
= 0.0°
d
2
= 15 m
q
2
= 25°
2. d
1
= 2.5 km
q
1
= 35°
d
2
= 5.2 km
q
2
= 22°
∆x
1
= d
1
(cos q
1
) = (35 m)(cos 0.0°) = 35 m
∆y
1
= d
1
(sin q
1
) = (35 m)(sin 0.0°) = 0.0 m
∆x
2
= d
2
(cos q
2
) = (15 m)(cos 25°) = 14 m
∆y
2
= d
2
(sin q
2
) = (15 m)(sin 25°) = 6.3 m
∆x
tot
=∆x
1
+∆x
2
= 35 m + 14 m = 49 m
∆y
tot
=∆y
1
+∆y
2
= 0.0 m + 6.3 m = 6.3 m
d
tot
=
(∆
x
t
ot
)
2
+
(
∆
y
t
ot
)
2
=
(4
9
m
)
2
+
(
6.
3
m
)
2
d
tot
=
24
00
m
2
+
4
0
m
2
=
24
00
m
2
=
q
tot
= tan
−1
∆
∆
x
y
t
t
o
o
t
t
= tan
−1
6
4
.
9
3
m
m
= 7.3° to the right of downfield
49 m
∆x
1
= d
1
(cos q
1
) = (2.5 km)(cos 35°) = 2.0 km
∆y
1
= d
1
(sin q
1
) = (2.5 km)(sin 35°) = 1.4 km
∆x
2
= d
2
(cos q
2
) = (5.2 km)(cos 22°) = 4.8 km
∆y
2
= d
2
(sin q
2
) = (5.2 km)(sin 22°) = 1.9 km
∆x
tot
=∆x
1
+∆x
2
= 2.0 km + 4.8 km = 6.8 km
∆y
tot
=∆y
1
+∆y
2
= 1.4 km + 1.9 km = 3.3 km
d
tot
=
(∆
x
t
ot
)
2
+
(
∆
y
t
ot
)
2
=
(6
.8
k
m
)
2
+
(
3.
3
km
)
2
d
tot
=
46 km
2
11 k
m
2
=
57
k
m
2
=
q
tot
= tan
−1
∆
∆
x
y
t
t
o
o
t
t
= tan
−1
3
6
.
.
3
8
k
k
m
m
= 26° above the horizontal
7.5 km
Two-Dimensional Motion and Vectors, Practice C
Givens Solutions
3. d
1
= 8.0 m
q
1
= 90.0°
d
2
= 3.5 m
q
2
= 55°
d
3
= 5.0 m
q
3
= 0.0°
Measuring direction with respect to x = (east),
∆x
1
= d
1
(cos q
1
) = (8.0 m)(cos 90.0°) = 0.0 m
∆y
1
= d
1
(sin q
1
) = (8.0 m)(sin 90.0°) = 8.0 m
∆x
2
= d
2
(cos q
2
) = (3.5 m)(cos 55°) = 2.0 m
∆y
2
= d
2
(sin q
2
) = (3.5 m)(sin 55°) = 2.9 m
∆x
3
= d
3
(cos q
3
) = (5.0 m)(cos 0.0°) = 5.0 m
∆y
3
= d
3
(sin q
3
) = (5.0 m)(sin 0.0°) = 0.0 m
∆x
tot
=∆x
1
+∆x
2
+∆x
3
= 0.0 m + 2.0 m + 5.0 m = 7.0 m
∆y
tot
=∆y
1
+∆y
2
+∆y
3
= 8.0 m + 2.9 m + 0.0 m = 10.9 m
d
tot
=
(∆x
tot
)
2
+ (∆y
tot
)
2
=
(7
.0
m
)
2
+
(
10
.9
m
)
2
d
tot
=
49
m
2
+
1
19
m
2
=
16
8
m
2
=
q
tot
= tan
−1
∆
∆
x
y
t
t
o
o
t
t
= tan
−1
1
7
0
.
.
0
9
m
m
= 57° north of east
13.0 m
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualI Ch. 3–4
I
1. ∆y =−0.70 m
∆x = 0.25 m
a
y
=−g = −9.81 m/s
2
∆t =
2
a
∆
y
y
=
∆
v
x
x
v
x
=
2
a
∆
y
y
∆x =
(2
−
)
9
(
.
−
8
0
1
.
7
m
0
/
m
s
2
)
(0.25 m) = 0.66 m/s
Givens Solutions
2. v
x
= 3.0 m/s
v
y
= 5.0 m/s
Two-Dimensional Motion and Vectors, Section 2 Review
4. d
1
= 75 km
q
1
=−30.0°
d
2
= 155 km
q
2
= 60.0°
Measuring direction with respect to y (north),
∆x
1
= d
1
(sin q
1
) = (75 km)(sin −30.0°) =−38 km
∆y
1
= d
1
(cos q
1
) = (75 km)(cos −30.0°) = 65 km
∆x
2
= d
2
(sin q
2
) = (155 km)(sin 60.0°) = 134 km
∆y
2
= d
2
(cos q
2
) = (155 km)(cos 60.0°) = 77.5 km
∆x
tot
=∆x
1
+∆x
2
=−38 km + 134 km = 96 km
∆y
tot
=∆y
1
+∆y
2
= 65 km + 77.5 km = 142 km
d
tot
=
(∆
x
t
ot
)
2
+
(
∆
y
t
ot
)
2
=
(96 km
)
2
+ (1
42 km)
2
=
9200 k
m
2
+ 2
0 200 k
m
2
d
tot
=
29 400
km
2
=
q = tan
−1
∆
∆
x
y
t
t
o
o
t
t
= tan
−1
1
9
4
6
2
k
k
m
m
= 34° east of north
171 km
a. v =
v
x
2
+
v
y
2
=
(3
.0
m
/s
)
2
=
(
5.
0
m
/s
)
2
v =
9.
0
m
2
/
s
2
+
2
5
m
2
/
s
2
=
34
m
2
/
s
2
=
q = tan
−1
v
v
x
y
= tan
−1
5
3
.
.
0
0
m
m
/
/
s
s
= 59° downriver from its intended path
5.8 m/s
v
x
= 1.0 m/s
v
y
= 6.0 m/s
b. v =
v
x
2
+
v
y
2
=
(1
.0
m
/s
)
2
+
(
6.
0
m
/s
)
2
v =
1.
0
m
2
/
s
2
+
3
6
m
2
/
s
2
=
37
m
2
/
s
2
=
q = tan
−1
v
v
x
y
= tan
−1
1
6
.
.
0
0
m
m
/
/
s
s
= 9.5° from the direction the wave is traveling
6.1 m/s
Two-Dimensional Motion and Vectors, Practice D
2. ∆y =−1.0 m
∆x = 2.2 m
a
y
=−g = −9.81 m/s
2
∆t =
2
a
∆
y
y
=
∆
v
x
x
v
x
=
2
a
∆
y
y
∆x =
(
−
2
9
)(
.
8
−
1
1.
m
0
/
m
s
2
)
(2.2 m) = 4.9 m/s
3. d = 10.0 km
q = 45.0°
a = 2.0 m/s
2
q = 35°
a. ∆x = d(cos q) = (10.0 km)(cos 45.0°) =
∆y = d(sin q) = (10.0 km)(sin 45.0°) =
b. a
x
= a(cos q) = (2.0 m/s
2
)(cos 35°) =
a
y
= a(sin q) = (2.0 m/s
2
)(sin 35°) = 1.1 m/s
2
1.6 m/s
2
7.07 km
7.07 km
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 3–5
Givens Solutions
I
3. ∆y =−5.4 m
∆x = 8.0 m
a
y
=−g = −9.81 m/s
2
4. v
x
= 7.6 m/s
∆y =−2.7 m
a
y
=−g = −9.81 m/s
2
∆t =
2
a
∆
y
y
=
∆
v
x
x
v
x
=
2
a
∆
y
y
∆x =
(
−
2
9
)(
.
8
−
1
5.
m
4
/
m
s
2
)
(8.0 m) = 7.6 m/s
∆t =
2
a
∆
y
y
=
∆
v
x
x
∆x =
2
a
∆
y
y
v
x
=
(
−
2
9
)(
.
8
−
1
2.
m
7
/
m
s
2
)
(7.6 m/s) = 5.6 m
1. ∆x = 4.0 m
q = 15°
v
i
= 5.0 m/s
∆y
max
=−2.5 m
a
y
=−g = −9.81 m/s
2
∆x = v
i
(cos q)∆t
∆t =
v
i
(c
∆
o
x
s q)
=
(5.0 m
4
/s
.0
)(
m
cos 15°)
= 0.83 s
∆y = v
i
(sin q)∆t +
1
2
a
y
∆t
2
= (5.0 m/s)(sin 15°)(0.83 s) +
1
2
(−9.81 m/s
2
)(0.83 s)
2
∆y = 1.1 m − 3.4 m = yes−2.3 m
Two-Dimensional Motion and Vectors, Practice E
2. ∆x = 301.5 m
q = 25.0°
At ∆y
max
, v
y,f
= 0 m/s, ∆t =∆t
peak
v
y,f
= v
i
sin q + a
y
∆t
peak
= 0
∆t
peak
=
−v
i
a
s
y
in q
at ∆x
max
, ∆t
m
= 2 ∆t
p
=
−2v
i
a
s
y
in q
∆x
max
= v
i
cos q ∆t
m
= v
i
cos q
−2 v
a
i
y
sinq
=
−2 v
i
2
si
a
n
y
q cos q
v
i
=
2
−
s
a
in
y
∆
q
x
c
m
o
a
s
x
q
v
f,y
2
= v
i
2
(sin q)
2
=−2a
y
∆y
max
= 0 at peak
∆y
max
=
v
i
2
−
(s
2
in
a
y
q)
2
=
2
−
s
a
in
y
∆
q
x
c
m
o
a
s
x
q
(s
−
in
2a
q
y
)
2
=
1
4
∆x
max
tan q
∆y
max
=
1
4
(301.5 m) (tan 25.0°) = 35.1 m
3. ∆x = 42.0 m
q = 25°
v
i
= 23.0 m/s
a
y
=−g = −9.81 m/s
2
∆t =
∆
v
x
x
=
v
i
(c
∆
o
x
s q)
=
(23.0 m
42
/s
.0
)(
m
cos 25°)
=
At maximum height, v
y,f
= 0 m/s.
v
y,f
2
= v
y,i
2
+ 2a
y
∆y
max
= 0
∆y
max
= −
v
2
y
a
,i
y
2
=−
v
i
2
(
2
si
a
n
y
q)
2
= − = 4.8 m
(23.0 m/s)
2
(sin 25°)
2
(2)(−9.81 m/s
2
)
2.0 s
Givens Solutions
Holt Physics Solution ManualI Ch. 3–6
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
4. ∆x = 2.00 m
∆y = 0.55 m
q = 32.0°
a
y
=−g = −9.81 m/s
2
∆x = v
i
(cos q)∆t
∆t =
v
i
(c
∆
o
x
s q)
∆y = v
i
(sin q)∆t +
1
2
a
y
∆t
2
= v
i
(sin q)
v
i
(c
∆
o
x
s q)
+
1
2
a
y
v
i
(c
∆
o
x
s q)
2
∆y =∆x(tan q) +
2v
i
2
a
(
y
c
∆
o
x
s
2
q)
2
∆x(tan q) −∆y =
2v
i
−
2
a
(c
y
∆
os
x
2
q)
2
2v
i
2
(cos q)
2
=
∆x(t
−
a
a
n
y
∆
q)
x
2
−∆y
v
i
=
v
i
=
v
i
=
=
= 6.2 m/s
(9.81 m/s
2
)(2.00 m)
2
(2)(cos 32.0°)
2
(0.70 m)
(9.81 m/s
2
)(2.00 m)
2
(2)(cos 32.0°)
2
(1.25 − 0.55 m)
(9.81 m/s
2
)(2.00 m)
2
(2)(cos 32.0°)
2
[(2.00 m)(tan 32.0°) − 0.55 m]
−a
y
∆x
2
2(cos q)
2
[∆x(tan q) −∆y]
2. ∆y =−125 m
v
x
= 90.0 m/s
a
y
=−g = −9.81 m/s
2
∆y =
1
2
a
y
∆t
2
∆t =
2
a
∆
y
y
=
(
−
2
)
9
(
.
−
8
1
1
2
m
5
/
m
s
2
)
=
∆x = v
x
∆t = (90.0 m/s)(5.05 s) = 454 m
5.05 s
Two-Dimensional Motion and Vectors, Section 3 Review
3. v
x
= 30.0 m/s
∆y =−200.0 m
a
y
=−g = −9.81 m/s
2
v
x
= 30.0 m/s
∆y =−200.0 m
a
y
=−g = −9.81 m/s
2
∆x = 192 m
a. ∆y =
1
2
a
y
∆t
2
∆t =
2
a
∆
y
y
∆x = v
x
∆t = v
x
2
a
∆
y
y
= (30.0 m/s)
(2
−
)(
9
−
.8
2
1
00
m
.0
/s
m
2
)
=
b. v
y
=
v
y,i
2
+ 2
a
y
∆y
=
(0 m/s
)
2
+ (2
)(−9.81
m/s
2
)(
−200.0
m)
=±62.6 m/s =−62.6 m/s
v
tot
=
v
x
2
+ v
y
2
=
(30.0 m
/s)
2
+ (
−62.6 m
/s)
2
=
9.00 ×
10
2
m
2
/s
2
+ 3
.92 × 1
0
3
m
2
/
s
2
v
tot
=
4820 m
2
/s
2
=
q = tan
−1
v
v
x
y
= tan
−1
−
3
6
0
2
.0
.6
m
m
/
/
s
s
=−64.4°
q = 64.4° below the horizontal
69.4 m/s
192 m
Section One—Student Edition Solutions I Ch. 3–7
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. v
te
=+15 m/s
v
bt
=−15 m/s
v
be
= v
bt
+ v
te
=−15 m/s + 15 m/s = 0 m/s
2. v
aw
=+18.0 m/s
v
sa
=−3.5 m/s
v
sw
= v
sa
+ v
aw
=−3.5 m/s 18.0 m/s
v
sw
= 14.5 m/s in the direction that the aircraft carrier is moving
Two-Dimensional Motion and Vectors, Practice F
Givens Solutions
3. v
fw
= 2.5 m/s north
v
we
= 3.0 m/s east
v
fe
= v
fw
+ v
we
v
tot
=
v
f
w
2
+
v
w
e
2
=
(2
.5
m
/s
)
2
+
(
3.
0
m
/s
)
2
v
tot
=
6.
2
m
2
/
s
2
+
9
.0
m
2
/
s
2
=
15
.2
m
2
/
s
2
=
q = tan
−1
v
v
w
fw
e
= tan
2
3
.
.
5
0
m
m
/
/
s
s
= (4.0 × 10
1
)° north of east
3.90 m/s
4. v
tr
= 25.0 m/s north
v
dt
= 1.75 m/s at 35.0° east
of north
v
dr
= v
dt
+ v
tr
v
x,tot
= v
x,dt
= (1.75 m/s)(sin 35.0°) = 1.00 m/s
v
y,dt
= (1.75 m/s)(cos 35.0°) = 1.43 m/s
v
y,tot
= v
tr
+ v
y,dt
= 25.0 m/s + 1.43 m/s = 26.4 m/s
v
tot
=
(v
x,
to
t
)
2
+
(
v
y
,to
t
)
2
=
(1
.0
0
m
/s
)
2
+
(
26
.4
m
/s
)
2
v
tot
=
1.
00
m
2
/
s
2
+
6
97
m
2
/
s
2
=
69
8
m
2
/
s
2
=
q = tan
−1
v
v
x
y,
,
t
t
o
o
t
t
= tan
−1
1
2
.
6
0
.
0
4
m
m
/
/
s
s
= 2.17° east of north
26.4 m/s
Two-Dimensional Motion and Vectors, Section 4 Review
1. v
wg
=−9 m/s v
bw
= v
bg
v
gw
= v
bg
− v
wg
= (1 m/s) – (–9 m/s) = 1 m/s + 9 m/s
v
bg
= 1 m/s
v
bw
=
2. v
bw
= 0.15 m/s north v
be
= v
bw
+ v
we
v
we
= 1.50 m/s east
v
tot
=
v
b
w
2
+
v
w
e
2
=
(0
.1
5
m
/s
)
2
+
(
1.
50
m
/s
)
2
v
tot
=
0.
02
2
m
2
/
s
2
+
2
.2
5
m
2
/
s
2
=
2.
27
m
2
/
s
2
=
q = tan
−1
v
v
b
w
w
e
= tan
−1
0
1
.
.
1
5
5
0
m
m
/
/
s
s
= 5.7° north of east
1.51 m/s
10 m/s in the opposite direction
Copyright © by Holt, Rinehart and Winston. All rights reserved.
6. A = 3.00 units (u) Students should use graphical techniques.
B =−4.00 units (u)
a. A + B =
A
2
+
B
2
=
(3
.0
0
u
)
2
+
(
−
4.
00
u
)
2
A + B =
9.
00
u
2
+
1
6.
0
u
2
=
25
.0
u
2
=
q = tan
−1
A
B
= tan
−1
−
3
4
.0
.0
0
0
u
u
=
b. A − B =
A
2
+
(
−
B
)
2
=
(3
.0
0
u
)
2
+
(
4.
00
u
)
2
A − B =
9.
00
u
2
+
1
6.
0
u
2
=
25
.0
u
2
=
q = tan
−1
−
A
B
= tan
−1
4
3
.
.
0
0
0
0
u
u
=
c. A + 2B =
A
2
+
(
2B
)
2
=
(3
.0
0
u
)
2
+
(
−
8.
00
u
)
2
A + 2B =
9.
00
u
2
+
6
4.
0
u
2
=
73
.0
u
2
=
q = tan
−1
2
A
B
= tan
−1
−
3
8
.0
.0
0
0
u
u
=
d. B − A =
B
2
+
(
−
A
)
2
=
(−4.00
u)
2
+
(−3.00
u)
2
=
q = tan
−1
−
B
A
= tan
−1
−
−3
4
.
.
0
0
0
0
u
u
= 53.1° below the negative x-axis
or
7. A = 3.00 m Students should use graphical techniques.
B = 3.00 m A
x
= A(cos q) = (3.00 m)(cos 30.0°) = 2.60 m
q = 30.0° A
y
= A(sin q) = (3.00 m)(sin 30.0°) = 1.50 m
a. A + B =
A
x
2
+
(
A
y
+
B
)
2
=
(2
.6
0
m
)
2
+
(
4.
50
m
)
2
A + B =
6.
76
m
2
+
2
0.
2
m
2
=
27
.0
m
2
=
q = tan
−1
A
y
A
+
x
B
= tan
−1
4
2
.
.
5
6
0
0
m
m
=
b. A − B =
A
x
2
+
(
A
y
−
B
)
2
=
(2
.6
0
m
)
2
+
(
−
1.
50
m
)
2
A − B =
6.
76
m
2
+
2
.2
5
m
2
=
9.
01
m
2
=
q = tan
−1
A
y
A
−
x
B
= tan
−1
−
2
1
.6
.5
0
0
m
m
= 30.0° below the positive x-axis
3.00 m
60.0° above the positive x-axis
5.20 m
127° clockwise from the positive x-axis
5.00 units
69.4° below the positive x-axis
8.54 units
53.1° above the positive x-axis
5.00 units
53.1° below the positive x-axis
5.00 units
Two-Dimensional Motion and Vectors, Chapter Review
Givens Solutions
Holt Physics Solution ManualI Ch. 3–8
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 3–9
I
Givens Solutions
c. B − A =
(B
−
A
y
)
2
+
(
−
A
x
)
2
=
(1
.5
0
m
)
2
+
(
−
2.
60
m
)
2
B − A =
q = tan
−1
B
−
−
A
A
x
y
= tan
−1
−
1
2
.5
.6
0
0
m
m
= 30.0° above the negative x-axis
or
d. A − 2B =
A
x
2
+
(
A
y
−
2
B
)
2
=
(2.60 m
)
2
+ (−
4.50 m
)
2
=
q = tan
−1
A
y
A
−
x
2B
= tan
−1
−
2
4
.6
.5
0
0
m
m
=
8. ∆y
1
=−3.50 m Students should use graphical techniques.
d
2
= 8.20 m ∆x
2
= d
2
(cos q
2
) = (8.20 m)(cos 30.0°) = 7.10 m
q
2
= 30.0°∆y
2
= d
2
(sin q
2
) = (8.20 m)(sin 30.0°) = 4.10 m
∆x
3
=−15.0 m ∆x
tot
=∆x
2
+∆x
3
= 7.10 m − 15.0 m =−7.9 m
∆y
tot
=∆y
1
+∆y
2
=−3.50 m + 4.10 m = 0.60 m
d =
(∆
x
t
ot
)
2
+
(
∆
y
t
ot
)
2
=
(−
7.
9
m
)
2
+
(
0.
60
m
)
2
d =
62
m
2
+
0
.3
6
m
2
=
62 m
2
=
q = tan
−1
∆
∆
x
y
t
t
o
o
t
t
= tan
−1
−
0.
7
6
.
0
9
m
m
=
9. ∆x =−8.00 m Students should use graphical techniques.
∆y = 13.0 m
d =
∆
x
2
+
∆
y
2
=
(−
8.
00
m
)
2
+
(
13
.0
m
)
2
d =
64
.0
m
2
+
1
69
m
2
=
23
3
m
2
=
q = tan
−1
∆
∆
x
y
= tan
−1
−
1
8
3
.
.
0
0
0
m
m
= 58.4° south of east
15.3 m
4.3° north of west
7.9 m
60.0° below the positive x-axis
5.20 m
150° counterclockwise from the positive x-axis
3.00 m
21. ∆x
1
= 3 blocks west
=−3 blocks east
∆y = 4 blocks north
∆x
2
= 6 blocks east
a. ∆x
tot
=∆x
1
+∆x
2
=−3 blocks + 6 blocks = 3 blocks
∆y
tot
=∆y = 4 blocks
d =
(∆
x
t
ot
)
2
+
(
∆
y
t
ot
)
2
=
(3
b
lo
ck
s)
2
+
(
4
b
lo
ck
s)
2
d =
9
b
lo
ck
s
2
+
1
6
b
lo
ck
s
2
=
25
b
lo
ck
s
2
=
q = tan
−1
∆
∆
x
y
t
t
o
o
t
t
= tan
−1
4
3
b
b
l
l
o
o
c
c
k
k
s
s
=
b. distance traveled = 3 blocks + 4 blocks + 6 blocks = 13 blocks
53° north of east
5 blocks
Copyright © by Holt, Rinehart and Winston. All rights reserved.
22. ∆y
1
=−10.0 yards ∆y
tot
=∆y
1
+∆y
2
=−10.0 yards + 50.0 yards = 40.0 yards
∆x = 15.0 yards ∆x
tot
=∆x = 15.0 yards
∆y
2
= 50.0 yards d =
(∆
x
t
ot
)
2
+
(
∆
y
t
ot
)
2
=
(1
5.
0
ya
rd
s)
2
+
(
40
.0
y
ar
d
s)
2
d =
22
5
ya
rd
s
2
+
1
.6
0
×
1
0
3
y
ar
d
s
2
=
18
20
y
ar
d
s
2
=
23. ∆y
1
=−40.0 m Case 1: ∆y
tot
=∆y
1
+∆y
2
=−40.0 m − 20.0 m =−60.0 m
∆x =±15.0 m ∆x
tot
=∆x =+15.0 m
∆y
2
=±20.0 m d =
(∆
y
t
ot
)
2
+
(
∆
x
t
ot
)
2
=
(−
60
.0
m
)
2
+
(
15
.0
m
)
2
d =
3.
60
×
1
0
3
m
2
+
2
25
m
2
=
38
20
m
2
=
q = tan
−1
∆
∆
x
y
t
t
o
o
t
t
= tan
−1
−
1
6
5
0
.0
.0
m
m
=
Case 2: ∆y
tot
=∆y
1
+∆y
2
−40.0 m + 20.0 m =−20.0 m
∆x
tot
=∆x =+15.0 m
d =
(∆
y
t
ot
)
2
+
)
∆
x
t
ot
)
2
=
(−
20
.0
m
)
2
+
(
15
.0
m
)
2
d =
4.00 ×
10
2
m
2
+ 225
m
2
=
625 m
2
=
∆=tan
−1
∆
∆
y
t
t
o
o
t
t
= tan
−1
−
1
2
5
0
.0
.0
m
m
=
Case 3: ∆y
tot
=∆y
1
+∆y
2
=−40.0 m − 20.0 m =−60.0 m
∆x
tot
=∆x =−15.0 m
d =
(∆
y
t
ot
)
2
+
(
∆
x
t
ot
)
2
=
(−
60
.0
m
)
2
+
(
−
15
.0
m
)
2
d =
q = tan
−1
∆
∆
x
y
t
t
o
o
t
t
= tan
−1
−
−
6
1
0
5
.
.
0
0
m
m
=
Case 4: ∆y
tot
=∆y
1
+∆y
2
=−40.0 m + 20.0 m =−20.0 m
∆x
tot
=∆x =−15.0 m
d =
(∆
y
t
ot
)
2
+
(
∆
x
t
ot
)
2
=
(−
20
.0
m
)
2
+
(
−
15
.0
m
)
2
d =
q = tan
−1
∆
∆
x
y
t
t
o
o
t
t
= tan
−1
−
−
2
1
0
5
.
.
0
0
m
m
=
24. d = 110.0 m ∆x = d(cos q) = (110.0 m)[cos(−10.0°)] =
∆=−10.0°
∆x = d(sin q) = (110.0 m)[sin(−10.0°)] =
25. q = 25.0°∆x = d(cos q) = (3.10 km)(cos 25.0°) =
d = 3.10 km
∆y = d(sin q) = (3.10 km)(sin 25.0°) = 1.31 km north
2.81 km east
−19.1 m
108 m
53.1° south of west
25.0 m
76.0° south of west
61.8 m
53.1° south of east
25.0 m
76.0° south of east
61.8 m
42.7 yards
Givens Solutions
Holt Physics Solution ManualI Ch. 3–10
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 3–11
I
Givens Solutions
26. d
1
= 100.0 m
d
2
= 300.0 m
d
3
= 150.0 m
d
4
= 200.0 m
q
1
= 30.0°
q
2
= 60.0°
∆x
tot
= d
1
− d
3
cos q
1
− d
4
cos q
2
∆x
tot
= 100.0 m − (150.0 m)(cos 30.0°) − (200.0 m)(cos 60.0°)
∆x
tot
= 100.0 m − 1.30 × 10
2
m − 1.00 × 10
2
m =−1.30 × 10
2
m
∆y
tot
=−d
2
− d
3
sin q
1
+ d
4
sin q
2
∆y
tot
=−300.0 m − (150.0 m)(sin 30.0°) + (200.0 m)(sin 60.0°)
∆y
tot
=−300.0 m − 75.0 m + 173 m =−202 m
d =
(∆x
tot
)
2
+ (∆y
tot
)
2
=
(1.30 ×
10
2
m
)
2
+ (−
202 m)
2
d =
16 900
m
2
+ 4
0 800 m
2
=
57700
m
2
=
q = tan
−1
∆
∆
x
y
t
t
o
o
t
t
= tan
−1
−1.3
−
0
20
×
2
1
m
0
2
m
= 57.2° south of west
2.40 × 10
2
m
31. ∆y =−0.809 m
∆x = 18.3 m
a
y
=−g = −9.81 m/s
2
∆t =
∆
v
x
x
∆y =
1
2
a
y
∆t
2
=
1
2
a
y
∆
v
x
x
2
v
x
=
2
a
∆
y
y
∆x =
(2
−
)
(
9
−
.8
0
1
.8
m
0
9
/s
m
2
)
(18.3 m) = 45.1 m/s
34. v
i
= 1.70 × 10
3
m/s a. ∆y = v
i
(sin q)∆t +
1
2
a
y
∆t
2
= v
i
(sin q) +
1
2
a
y
∆t = 0
q = 55.0°
∆t = −
2v
i
(
a
si
y
n q)
=− =284 s
a
y
=−g = −9.81 m/s
2
∆x = v
i
(cos q)∆t = (1.70 × 10
3
m/s)(cos 55.0°)(284 s) =
b. ∆t = (See a.)284 s
2.77 × 10
5
m
(2)(1.70 × 10
3
m/s)(sin 55.0°)
−9.81 m/s
2
32. v
x
= 18 m/s
∆y =−52 m
a
y
=−g = −9.81 m/s
2
∆y =
1
2
a
y
∆t
2
∆t =
2
a
∆
y
y
=
(
−
2
9
)
.
(
8
−
1
5
m
2
m
/
s
2
)
=
When the stone hits the water,
v
y
= a
y
∆t = (−9.81 m/s)(3.3 s) =−32 m/s
v
tot
=
v
x
2
+
v
y
2
=
(1
8
m
/s
)
2
+
(
−
32
m
/s
)
2
v
tot
=
32
0
m
2
/
s
2
+
1
00
0
m
2
/
s
2
=
13
00
m
2
/
s
2
= 36 m/s
3.3 s
33. v
x,s
= 15 m/s
v
x,o
= 26 m/s
∆y = −5.0 m
a
y
=−g = −9.81 m/s
2
∆y =
1
2
a
y
∆t
2
∆t =
2
a
∆
y
y
=
−
2
9
(−
.
8
5
1
.0
m
m
/s
)
2
= 1.0 s
∆x
s
= v
x,s
∆t = (15 m/s)(1.0 s) = 15 m
∆x
o
= v
x,o
∆t = (26 m/s)(1.0 s) = 26 m
∆x
o
−∆x
s
= 26 m − 15 m = 11 m
Copyright © by Holt, Rinehart and Winston. All rights reserved.
35. ∆x = 36.0 m
v
i
= 20.0 m/s
q = 53°
∆y
bar
= 3.05 m
a
y
=−g = −9.81 m/s
2
a. ∆x = v
i
(cos q)∆t
∆t =
v
i
(c
∆
o
x
s q)
=
(20.0 m
36
/s
.0
)(
m
cos 53°)
= 3.0 s
∆y = v
i
(sin q)∆t +
1
2
a
y
∆t
2
= (20.0 m/s)(sin 53°)(3.0 s) +
1
2
(−9.81 m/s
2
)(3.0 s)
2
∆y = 48 m − 44 m = 4 m
∆y =∆y
bar
= 4 m − 3.05 m = 1 m
b. v
y,f
= v
i
(sin q) + a
y
∆t = (20.0 m/s)(sin 53°) + (−9.81 m/s
2
)(3.0 s)
v
x,f
= 16 m/s − 29 m/s =−13 m/s
The velocity of the ball as it passes over the crossbar is negative; therefore, the ball
is falling.
The ball clears the goal by 1 m.
Holt Physics Solution ManualI Ch. 3–12
I
Givens Solutions
36. ∆y =−1.00 m
∆x = 5.00 m
q = 45.0°
v = 2.00 m/s
∆t = 0.329 s
a
y
=−g = −9.81 m/s
2
Find the initial velocity of the water when shot at rest horizontally 1 m above the
ground.
∆y =
1
2
a
y
∆t
2
∆t =
2
a
∆
y
y
∆x = v
x
∆t
v
x
=
∆
∆
x
t
== =11.1 m/s
Find how far the water will go if it is shot horizontally 1 m above the ground while
the child is sliding down the slide.
v
x, tot
= v
x
+ v(cos q)
∆x = v
x, tot
∆t = [v
x
+ v(cos q)]∆t = [11.1 m/s + (2.00 m/s)(cos 45.0°)](0.329 s)
∆x = [11.1 m/s + 1.41 m/s](0.329 s) = (12.5 m/s)(0.329 s) = 4.11 m
5.00 m
(2
−
)
9
(
.
−
8
1
1
.
0
m
0
/
m
s
2
)
∆x
2
a
∆
y
y
37. ∆x
1
= 2.50 × 10
3
m
∆x
2
= 6.10 × 10
2
m
∆y
mountain
= 1.80 × 10
3
m
v
i
= 2.50 × 10
2
m/s
q = 75.0°
a
y
=−g = −9.81 m/s
2
For projectile’s full flight,
∆t =
v
i
(c
∆
o
x
s q)
∆y = v
i
(sin q)∆t +
1
2
a
y
∆t
2
= v
i
(sin q) +
1
2
a
y
∆t = 0
v
i
(sin q) +
1
2
a
y
v
i
(c
∆
o
x
s q)
= 0
∆x = −
2v
i
2
(sin
a
q
y
)(cos q)
=− =3190 m
Distance between projectile and ship =∆x −∆x
1
−∆x
2
= 3190 m − 2.50 × 10
3
m − 6.10 × 10
2
m =
For projectile’s flight to the mountain,
∆t′=
v
i
(c
∆
o
x
s
i
q)
∆y = v
i
(sin q)∆t′+
1
2
a
y
∆t′
2
= v
i
(sin q)
v
i
(
∆
co
x
s
1
q)
+
1
2
a
y
v
i
(
∆
co
x
s
1
q)
2
80 m
(2)(2.50 × 10
2
m/s)
2
(sin 75.0°)(cos 75.0°)
−9.81 m/s
2
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 3–13
I
Givens Solutions
∆y =∆x
1
(tan q) +
2v
i
a
2
y
(
∆
co
x
s
1
2
q)
2
∆y = (2.50 × 10
3
m)(tan 75.0°) +
∆y = 9330 m − 7320 = 2010 m
distance above peak =∆y −∆y
mountain
= 2010 m − 1.80 × 10
3
m = 210 m
(−9.81 m/s
2
)(2.50 × 10
3
m)
2
(2)(2.50 × 10
2
m/s)
2
(cos 75.0°)
2
43. v
re
= 1.50 m/s east
v
br
= 10.0 m/s north
∆x = 325 m
a. v
be
= v
br
+ v
re
v
be
v
b
r
2
v
r
e
2
=
(10.0 m
/s)
2
+ (
1.50 m
/s)
2
v
be
1.
00
×
1
0
2
m
2
/
s
2
+
2
.2
5
m
2
/
s
2
=
10
2
m
2
/
s
2
=
q = tan
−1
v
v
b
re
r
= tan
−1
1
1
.
0
5
.
0
0
m
m
/
/
s
s
=
b. ∆t =
v
∆
b
x
r
=
1
3
0
2
.0
5
m
m
/s
= 32.5 s
∆y = v
re
∆t = (1.50 m/s)(32.5 s) = 48.8 m
8.53° east of north
10.1 m/s
44. v
we
= 50.0 km/h south
v
aw
= 205 km/h
v
ae
is directed due west
a. v
aw
= v
ae
+ (−v
we
)
v
v
a
w
w
e
= sin q
q = sin
−1
v
v
a
w
w
e
= sin
−1
5
2
0
0
.
5
0
k
k
m
m
/
/
h
h
=
b. v
aw
2
= v
ae
2
+ v
we
2
v
ae
=
v
a
w
2
−
v
w
e
2
=
(2
05
k
m
/h
)
2
−
(
50
.0
k
m
/h
)
2
v
ae
=
4.
20
×
1
0
4
k
m
2
/
h
2
−
2
.5
0
×
1
0
3
k
m
2
/
h
2
v
ae
=
3.
95
×
1
0
4
k
m
2
/
h
2
= 199 km/h
14.1° north of west
45. ∆x = 1.5 km
v
re
= 5.0 km/h
v
br
= 12 km/h
The boat’s velocity in the x direction is greatest when the boat moves directly across
the river with respect to the river.
∆t
min
=
v
∆
b
x
r
= = 7.5 min
1.5 km
(12 km/h)(1 h/60 min)
46. v
re
= 3.75 m/s downstream
v
sr
= 9.50 m/s
v
se
is directed across the river
a. v
sr
= v
se
+ (−v
re
) = sin q
q = sin
−1
3
9
.
.
7
5
5
0
m
m
/
/
s
s
=
b. v
sr
2
= v
se
2
+ v
re
2
v
se
=
v
s
r
2
−
v
re
2
=
(9
.5
0
m
/s
)
2
−
(
3.
75
m
/s
)
2
v
se
=
90
.2
m
2
/
s
2
−
1
4.
1
m
2
/
s
2
=
76
.1
m
2
/
s
2
= 8.72 m/s
v
se
= 8.72 m/s directly across the river
23.2° upstream from straight across
v
re
v
sr
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualI Ch. 3–14
I
Givens Solutions
47. ∆y = 21.0 m − 1.0 m = 20.0 m
∆x = 130.0 m
q = 35.0°
a
y
=−g = −9.81 m/s
2
48. ∆x = 12 m
q = 15°
a
y
=−g = −9.81 m/s
2
a. ∆x = v
i
cos q ∆t ∆t =
v
i
c
∆
o
x
s q
∆y = v
i
sin q ∆t +
1
2
a
y
(∆t)
2
∆y = v
i
sin q
v
i
c
∆
o
x
s q
+
1
2
a
y
v
i
c
∆
o
x
s q
2
∆y =∆x tan q +
2
a
v
y
i
2
(∆
co
x
s
)
2
2
q
v
i
2
=
v
i
=
co
∆
s
x
q
2(∆y −
a
∆
y
x tan
q)
v
i
=
c
1
o
3
s
0
3
.0
5.
m
0°
v
i
=
b. ∆t ==
∆t =
c. v
y,f
= v
i
sin q + a
y
∆t = (41.7 m/s)(sin 35.0°) + (−9.81 m/s
2
)(3.81 s)
v
y,f
= 23.9 m/s − 37.4 m/s =
v
x,f
= v
i
cos q = (41.7 m/s) (cos 35.0°) =
v
f
=
1170 m
2
/s
2
+ 1
82 m
2
/
s
2
=
1350 m
2
/s
2
= 36.7 m/s
34.2 m/s
−13.5 m/s
3.81 s
130.0 m
(41.7 m/s) (cos 35.0°)
∆x
v
i
cos q
41.7 m/s
(−9.81 m/s
2
)
2[(20.0 m) − (130.0 m)(tan 35.0°)]
a
y
(∆x)
2
2 cos
2
q (∆y −∆x tan q)
a. ∆x = v
i
(cos q)∆t
∆t =
∆y = v
i
(sin q)∆t +
1
2
a
y
∆t
2
= v
i
(sin q) +
1
2
a
y
∆t = 0
v
i
(sin q) +
1
2
a
y
= 0
2v
i
2
(sin q)(cos q) = −a
y
∆x
v
i
=
=
=
b. ∆t = = = 0.83 s
v
y,f
= v
i
(sin q) + a
y
∆t = (15 m/s)(sin 15°) + (−9.81 m/s
2
)(0.83 s)
v
y,f
= 3.9 m/s − 8.1 m/s =−4.2 m/s
v
x,f
= v
x
= v
i
(cos q) = (15 m/s)(cos 15°) = 14 m/s
v
f
=
(v
x,
f
)
2
+
(
v
y
,f
)
2
=
(1
4
m
/s
)
2
+
(
−
4.
2
m
/s
)
2
v
f
=
2.
0
×
1
0
2
m
2
/
s
2
+
1
8
m
2
/
s
2
=
22
0
m
2
/
s
2
= 15 m/s
12 m
(15 m/s)(cos 15°)
∆x
v
i
(cos q)
15 m/s
(9.81 m/s
2
)(12 m)
(2)(sin 15°)(cos 15°)
−a
y
∆x
2(sin q)(cos q)
∆x
v
i
(cos q)
∆x
v
i
(cos q)
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 3–15
I
Givens Solutions
49. ∆x = 10.00 m
q = 45.0°
∆y = 3.05 m − 2.00 m
= 1.05 m
a
y
=−g = −9.81 m/s
2
See the solution to problem 47 for a derivation of the following equation.
v
i
=
=
v
i
=
=
= 10.5 m/s
(−9.81 m/s
2
)(10.00 m)
2
(2)(cos 45.0°)
2
(−8.95 m)
(−9.81 m/s
2
)(10.00 m)
2
(2)(cos 45.0°)
2
(1.05 m − 10.00 m)
(−9.81 m/s
2
)(10.00 m)
2
(2)(cos 45.0°)
2
[1.05 m − (10.00 m)(tan 45.0°)]
a
y
∆x
2
2(cos q)
2
[(∆y −∆x tan q)]
50. ∆x = 20.0 m
∆t = 50.0 s
v
pe
=±0.500 m/s
v
eg
== =0.400 m/s
v
pg
= v
pe
+ v
eg
a. Going up:
v
pg
= v
pe
+ v
eg
= 0.500 m/s + 0.400 m/s = 0.900 m/s
∆t
up
== =
b. Going down:
v
pg
=−v
pe
+ v
eg
=−0.500 m/s + 0.400 m/s =−0.100 m/s
∆t
down
== =2.00 × 10
2
s
−20.0 m
−0.100 m/s
−∆x
v
pg
22.2 s
20.0 m
0.900 m/s
∆x
v
pg
20.0 m
50.0 s
∆x
∆t
51. ∆y =−1.00 m
∆x = 1.20 m
a
y
=−g = −9.81 m/s
2
a. ∆x = v
x
∆t ∆t =
∆x
v
x
∆y =
1
2
a
y
∆t
2
=
1
2
a
y
2
=
a
2
y
v
∆
x
x
2
2
v
x
=
=
=
b. The ball’s velocity vector makes a 45° angle with the horizontal when v
x
= v
y
.
v
x
= v
y,f
= a
y
∆t ∆t =
∆y =
1
2
a
y
∆t
2
=
1
2
a
y
2
=
∆y ==−0.361 m
h = 1.00 m − 0.361 m = 0.64 m
(2.66 m/s)
2
(2)(−9.81 m/s
2
)
v
x
2
2a
y
v
x
a
y
v
x
a
y
2.66 m/s
−(9.81 m/s
2
)(1.20 m)
2
(2)(−1.00 m)
a
y
∆x
2
2∆y
∆x
v
x
52. v
1
= 40.0 km/h
v
2
= 60.0 km/h
∆x
i
= 125 m
For lead car:
∆x
tot
= v
1
∆t +∆x
i
For chasing car:
∆x
tot
= v
2
∆t
v
2
∆t = v
1
∆t +∆x
i
∆t = =
∆t = = 22.5 s
125 × 10
−3
km
(20.0 km/h)(1 h/3600 s)
(125 m)(10
−3
km/m)
(60.0 km/h − 40.0 km/h)(1 h/3600 s)
∆x
i
v
2
− v
1
Holt Physics Solution ManualI Ch. 3–16
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
53. q = 60.0°
v
1
= 41.0 km/h
v
2
= 25.0 km/h
∆t
1
= 3.00 h
∆t = 4.50 h
d
1
= v
1
∆t = (41.0 km/h)(3.00 h) = 123 km
∆x
1
= d
1
(cos q) = (123 km)(cos 60.0°) = 61.5 km
∆y
1
= d
1
(sin q) = (123 km)(sin 60.0°) = 107 km
∆t
2
=∆t −∆t
1
= 4.50 h − 3.00 h = 1.50 h
∆y
2
= v
2
∆t
2
= (25.0 km/h)(1.50 h) = 37.5 km
∆x
tot
=∆x
1
= 61.5 km
∆y
tot
=∆y
1
+∆y
2
= 107 km + 37.5 km = 144 km
d =
(∆
x
t
ot
)
2
+
(
∆
y
t
ot
)
2
=
(6
1.
5
km
)
2
+
(
14
4
km
)
2
d =
37
80
k
m
2
+
2
0
70
0
km
2
=
24
5
00
k
m
2
= 157 km
54. v
bw
=±7.5 m/s
v
we
= 1.5 m/s
∆x
d
= 250 m
∆x
u
=−250 m
v
be
= v
bw
+ v
we
Going downstream:
v
be,d
= 7.5 m/s + 1.5 m/s = 9.0 m/s
Going upstream:
v
be,u
=−7.5 m/s + 1.5 m/s =−6.0 m/s
∆t =
v
∆
b
x
e,
d
d
+
v
∆
b
x
e,
u
u
=
9
2
.
5
0
0
m
m
/s
+
−
−
6
2
.
5
0
0
m
m
/s
= 28 s + 42 s = 7.0 × 10
1
s
55. q =−24.0°
a = 4.00 m/s
2
d = 50.0 m
∆y =−30.0 m
a
y
=−g = −9.81 m/s
2
a. d =
1
2
a∆t
2
∆t
1
=
2
a
d
=
= 5.00 s
v
i
= a∆t
1
= (4.00 m/s
2
)(5.00 s) = 20.0 m/s
v
y,f
=
v
i
2
(sin
q)
2
+ 2
a
y
∆y
=
(20.0 m
/s)
2
[sin
(−24.0
°)]
2
+ (
2)(−9.8
1 m/s
2
)(−30.0
m)
v
y,f
=
66.2 m
2
/s
2
+ 5
89 m
2
/
s
2
=
65
5
m
2
/
s
2
=±25.6 m/s =−25.6 m/s
v
y,f
= v
i
(sin q) + a
y
∆t
2
∆t
2
= =
∆t
2
= = = 1.78 s
∆x = v
i
(cos q)∆t
2
= (20.0 m/s)[cos(−24.0°)](1.78 s) =
b. ∆t
2
= (See a.)1.78 s
32.5 m
−17.5 m/s
−9.81 m/s
2
−25.6 m/s + 8.13 m/s
−9.81 m/s
2
−25.6 m/s − (20.0 m/s)(sin −24.0°)
−9.81 m/s
2
v
y,f
− v
i
(sin q)
a
y
(2)(50.0 m)
4.00 m/s
2
Section One—Student Edition Solutions I Ch. 3–17
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
56. q = 34°
∆x = 240 m
a
y
=−g = −9.81 m/s
2
a. ∆x = v
i
(cos q)∆t
∆t =
v
i
(c
∆
o
x
s q)
∆y = v
i
(sin q)∆t +
1
2
a
y
∆t
2
= v
i
(sin q) +
1
2
a
y
∆t = 0
v
i
(sin q) +
1
2
a
y
v
i
(c
∆
o
x
s q)
= v
i
2
(sin q) +
2(
a
c
y
o
∆
s
x
q)
= 0
v
i
=
2(co
−
s
a
q
y
)
∆
(s
x
in q
)
=
=
b. ∆y
max
=
Because v
y,f
= 0 m/s,
∆y
max
==
∆y
max
=
v
i
(sin q)
+
1
2
a
y
2
∆y
max
= (tan q) +
8 v
i
a
2
y
(c
∆
o
x
s
2
q)
2
∆y
max
= +
∆y
max
= 81 m − 41 m = 4.0 × 10
1
m
(−9.81 m/s
2
)(240 m)
2
(8)(5.0 × 10
1
m/s)
2
(cos 34°)
(240 m)(tan 34°)
2
∆x
2
∆x
2v
i
(cos q)
∆x
2v
i
(cos q)
4.0 × 10
1
m
−(5.0 × 10
1
m/s)
2
(sin 34°)
2
(2)(−9.81 m/s
2
)
−v
i
2
(sin q)
2
2a
y
v
y,f
2
− v
y,i
2
2a
y
5.0 × 10
1
m/s
(9.81 m/s
2
)(240 m)
(2)(cos 34°)(sin 34°)
57. v
ce
= 50.0 km/h east
q = 60.0°
a. v
ce
= v
rc
(sin q)
v
rc
=
(si
v
n
ce
q)
=
(
5
s
0
in
.0
6
k
0
m
.0
/
°
h
)
= 57.7 km/h
v
rc
=
b. v
re
= v
rc
(cos q) = (57.7 km/h)(cos 60.0°) = 28.8 km/h
v
re
= 28.8 km/h straight down
57.7 km/h at 60.0° west of the vertical
58. ∆t
walk
= 30.0 s
∆t
stand
= 20.0 s
v
pe
=
∆t
w
L
alk
=
30
L
.0 s
v
eg
=
∆t
s
L
tand
=
20
L
.0 s
v
pg
= v
pe
+ v
eg
v
pg
= v
pe
+ v
eg
v
pg
=
30
L
.0 s
+
20
L
.0 s
=
2
6
L
0
+
.0
3
s
L
=
60
5
.
L
0s
∆
L
t
=
60
5
.
L
0s
∆t ==12.0 s
60.0 s
5
Holt Physics Solution ManualI Ch. 3–18
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
59. ∆x
Earth
= 3.0 m
a
y
=−g = −9.81 m/s
2
∆y = v
i
(sin q)∆t +
1
2
a
y
∆t
2
= v
i
(sin q) +
1
2
a
y
∆t = 0
∆t =−
2v
i
(
a
si
y
n q)
∆x
Earth
= v
i
(cos q)∆t = v
i
(cos q)
−
2v
i
(
a
si
y
n q)
∆x
Earth
=− =
Because v
i
and q are the same for all locations,
∆x
Earth
= , where k = 2v
i
2
(cos q)(sin q)
k = g∆x
Earth
=
∆x
moon
= (0.38g)∆x
Mars
∆x
moon
= 6∆x
Earth
= (6)(3.0 m) =
∆x
Mars
===7.9 m
3.0 m
0.38
∆x
Earth
0.38
18 m
g
6
k
g
2v
i
2
(cos q)(sin q)
g
2v
i
2
(cos q)(sin q)
a
y
60. v
x
= 10.0 m/s
q = 60.0°
a
y
=−g = −9.81 m/s
2
The observer on the ground sees the ball rise vertically, which indicates that the
x-component of the ball’s velocity is equal and opposite the velocity of the train.
v
x
= v
i
(cos q)
v
i
== =20.0 m/s
At maximum height, v
y
= 0, so
∆y
max
==
∆y
max
= = 15.3 m
−(20.0 m/s)
2
(sin 60.0°)
2
(2)(−9.81 m/s
2
)
−v
i
2
(sin q)
2
2a
y
v
y,f
2
− v
y,i
2
2a
y
10.0 m/s
(cos 60.0°)
v
x
(cos q)
61. v
i
= 18.0 m/s
q = 35.0°
∆x
i
= 18.0 m
a
y
=−g = −9.81 m/s
2
∆y = v
i
(sin q)∆t +
1
2
a
y
∆t
2
= v
i
(sin q) +
1
2
a
y
∆t = 0
∆t =
−2v
i
(
a
s
y
in q)
==2.10 s
∆x = v
i
(cos q)∆t = (18.0 m/s)(cos 35.0°)(2.10 s) = 31.0 m
∆x
run
=∆x −∆x
i
= 31.0 m − 18.0 m = 13.0 m
v
run
=
∆
∆
x
r
t
un
=
1
2
3
.1
.0
0
m
s
= 6.19 m/s downfield
−2(18.0 m/s)(sin 35.0°)
−9.81 m/s
2
62. q = 53°
v
i
= 75 m/s
∆t = 25 s
a = 25 m/s
2
a
y
= a(sin q) = (25 m/s
2
)(sin 53°) = 2.0 × 10
1
m/s
2
∆y = v
i
(sin q)∆t +
1
2
a
y
∆t
2
= (75 m/s)(sin 53°)(25 s) +
1
2
(2.0 × 10
1
m/s
2
)(25 s)
2
∆y = 1500 m + 6200 m = 7700 m
v
f
= v
i
+ a∆t = 75 m/s + (25 m/s
2
)(25 s) = 75 m/s + 620 m/s = 7.0 × 10
2
m/s
Section One—Student Edition Solutions I Ch. 3–19
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
v
i
= v
f
= 7.0 × 10
2
m/s
q = 53°
a
y
=−g =−9.81 m/s
2
v
i
= 7.0 × 10
2
m/s
q = 53°
For the motion of the rocket after the boosters quit:
v
y,f
= v
i
(sin q) + a
y
∆t = 0
∆t =
−v
i
(
a
si
y
n q)
==57 s
∆y = v
i
(sin q)∆t +
1
2
a
y
∆t
2
= (7.0 × 10
2
m/s)(sin 53°)(57 s) +
1
2
(−9.81 m/s
2
)(57 s)
2
∆y = 32 000 m − 16 000 m = 16 000 m
a. ∆y
total
= 7700 m + 16 000 m =
b. ∆y =+
1
2
a
y
∆t
2
∆t =
2
a
∆
y
y
=
= 7.0 × 10
1
s
∆t
total
= 25 s + 57 s + 7.0 × 10
1
s =
c. a
x
= a(cos q)
∆x = v
i
(cos q)∆t +
1
2
a
x
∆t
2
= v
i
(cos q)∆t +
1
2
a(cos q)∆t
2
∆x = (75 m/s)(cos 53°)(25 s) +
1
2
(25 m/s
2
)(cos 53°)(25 s)
2
∆x = (1.1 × 10
3
m) + (4.7 × 10
3
m) = 5.8 × 10
3
m
After the rockets quit:
∆t = 57 s + 7.0 × 10
1
s = 127 s
∆x = v
i
(cos q)∆t = (7.0 × 10
1
m/s)(cos 53°)(127 s) = 5.4 × 10
4
m
∆x
tot
= (5.8 × 10
3
m) + (5.4 × 10
4
m) = 6.0 × 10
4
m
152 s
(2)(−24 000 m)
−9.81 m/s
2
2.4 × 10
4
m
−(7.0 × 10
2
m/s)(sin 53°)
−9.81 m/s
2
Two-Dimensional Motion and Vectors, Standardized Test Prep
5. v
br
= 5.0 m/s east
v
re
= 5.0 m/s south
v
be
= v
br
+ v
re
v
be
=
v
b
r
2
+
v
re
2
=
(5.0 m
/s)
2
+ (
5.0 m/
s)
2
v
be
=
25 m
2
/
s
2
+ 25
m
2
/s
2
= 7.1 m/s
6. ∆x = 125 m
v
br
= 5.0 m/s
∆t =
v
∆
b
x
r
=
5
1
.
2
0
5
m
m
/s
= 25 s
7. v
ap
= 165 km/h south
=−165 km/h north
v
pe
= 145 km/h north
v
ae
= v
ap
+ v
pe
v
ae
=−165 km/h north + 145 km/h north =−20 km/h north = 20 km/h south
Holt Physics Solution ManualI Ch. 3–20
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
8. ∆x = 6.00 m
∆y =−5.40 m
d =
∆
x
2
+
∆
y
2
=
(6
.0
0
m
)
2
+
−(
5.
40
m
)
2
d =
36
.0
m
2
+
2
9.
2
m
2
=
65
.2
m
2
=
q = tan
−1
∆
∆
x
y
= tan
−1
−
6
5
.0
.4
0
0
m
m
= 42.0° south of east
8.07 m
16. v
i
= 25.0 m/s
q = 45.0°
∆x = 50.0 m
a
y
=−g = −9.81 m/s
2
∆x = v
i
(cos q)∆t
∆t =
v
i
(c
∆
o
x
s q)
∆y = v
i
(sin q)∆t +
1
2
a
y
∆t
2
= v
i
(sin q)
+
1
2
a
y
v
i
(c
∆
o
x
s q)
2
∆y =∆x(tan q) +
2v
i
2
a
(
y
c
∆
o
x
s
2
q)
2
= (50.0 m)(tan 45.0°) +
∆y = 50.0 m − 39.2 m = 10.8 m
(−9.81 m/s
2
)(50.0 m)
2
(2)(25.0 m/s)
2
(cos 45.0)
2
∆x
v
i
(cos q)
15. ∆t = 3.00 s
q = 30.0°
a
y
=−g = −9.81 m/s
2
∆y = v
i
(sin q)∆t +
1
2
a
y
∆t
2
= v
i
(sin q) +
1
2
a
y
∆t = 0
v
i
= = = 29.4 m/s
(9.81 m/s
2
)(3.00 s)
(2)(sin 30.0°)
−a
y
∆t
2(sin q)
14. d = 41.1 m
q = 40.0°
∆x = d(cos q) = (41.1 m)(cos 40.0°) =
∆y = d(sin q) = (41.1 m)(sin 40.0°) = 26.4 m
31.5 m
12. v
f,x
= v
x
= 3.0 m/s
∆y = −1.5 m
g = −9.81 m/s
2
a
y
=−g
v
f,y
=
2a
y
∆y
=
−2g∆y
=
(−2)(9
.81 m/
s
2
)(−1
.5 m)
= 5.4 m/s
2
v
f
=
v
fx
2
+ v
fy
2
=
(3.0 m
/s)
2
+ (
5.4 m/
s)
2
= 6.2 m/s
Section One—Student Edition Solutions I Ch. 4–1
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Forces and the
Laws of Motion
Student Edition Solutions
1. F = 70.0 N
q = +30.0°
2. F
y
=−2.25 N
F
x
= 1.05 N
F
x
= F(cos q) = (70.0 N)(cos 30.0°) =
F
y
= F(sin q) = (70.0 N)(sin 30.0°) = 35.0 N
60.6 N
F
net
=
F
x
2
+
F
y
2
=
(1.05 N
)
2
+ (−
2.25 N
)
2
F
net
=
1.10 N
2
+ 5.0
6N
2
=
6.16 N
2
=
q = tan
−1
F
F
x
y
= tan
−1
−
1
2
.0
.2
5
5
N
N
q = 25.0° counterclockwise from straight down
2.48 N
Forces and the Laws of Motion, Practice B
Givens Solutions
3. F
wind
= 452 N north
F
water
= 325 N west
F
x
= F
water
=−325 N
F
y
= F
wind
= 452 N
F
net
=
F
x
2
+
F
y
2
=
(−
32
5
N
)
2
+
(
45
2
N
)
2
F
net
=
1.
06
×
1
0
5
N
2
+
2
.0
4
×
1
0
5
N
2
=
3.
10
×
1
0
5
N
2
F
net
=
q = tan
−1
F
F
x
y
= tan
−1
−
4
3
5
2
2
5
N
N
=−54.3°
q = 54.3° north of west, or 35.7° west of north
557 N
Forces and the Laws of Motion, Section 2 Review
3. F
y
= 130.0 N
F
x
= 4500.0 N
F
net
=
F
x
2
+
F
y
2
=
(4
50
0.
0
N
)
2
+
(
13
0.
0
N
)
2
F
net
=
2.
02
5
×
1
0
7
N
2
+
1
.6
90
×
1
0
4
N
2
=
2.
02
7
×
1
0
7
N
2
=
q = tan
−1
F
F
x
y
= tan
−1
4
1
5
3
0
0
0
.0
.0
N
N
= 1.655° forward of the side
4502 N
1. F
net
= 7.0 N forward
m = 3.2 kg
a =
F
m
net
=
3
7
.
.
2
0
k
N
g
= 2.2 m/s
2
forward
Forces and the Laws of Motion, Practice C
2. F
net
= 390 N north
m = 270 kg
a =
F
m
net
=
2
3
7
9
0
0
k
N
g
= 1.4 m/s
2
north
Holt Physics Solution ManualI Ch. 4–2
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. m = 6.0 kg
a = 2.0 m/s
2
m = 4.0 kg
4. F
y
= 390 N, north
F
x
= 180 N, east
m = 270 kg
a. F
net
= ma = (6.0 kg)(2.0 m/s
2
) =
b. a =
F
m
net
=
4
1
.
2
0
N
kg
= 3.0 m/s
2
12 N
F
net
=
F
x
2
+
F
y
2
=
(180 N
)
2
+ (3
90 N)
2
F
net
=
3.
2
×
1
0
4
N
2
+
1
.5
×
1
0
5
N
2
=
1.
8
×
1
0
5
N
2
= 420 N
q = tan
−1
F
F
x
y
= tan
−1
3
1
9
8
0
0
N
N
q =
a =
F
m
net
=
2
4
7
2
0
0
k
N
g
= 1.6 m/s
2
65° north of east
Forces and the Laws of Motion, Section 3 Review
1. F
k
= 53 N
m = 24 kg
g = 9.81 m/s
2
m
k
=
F
F
n
k
=
m
F
k
g
=
(24 kg)
5
(
3
9.
N
81 m/s
2
)
= 0.23
Forces and the Laws of Motion, Practice D
2. m = 25 kg
F
s, max
= 165 N
F
k
= 127 N
g = 9.81 m/s
2
a. m
s
=
F
s
F
,m
n
ax
=
F
s
m
,m
g
ax
=
(25 kg
1
)(
6
9
5
.8
N
1 m/s
2
)
=
b. m
k
=
F
F
n
k
=
m
F
k
g
=
(25 kg
1
)(
2
9
7
.8
N
1 m/s
2
)
= 0.52
0.67
Forces and the Laws of Motion, Practice C
Givens Solutions
5. m = 2.0 kg
∆x = 85 cm
∆t = 0.50 s
∆x =
1
2
a(∆t)
2
a =
2
∆
∆
t
2
x
=
(2
(
)
0
(
.
0
5
.
0
85
s)
m
2
)
= 6.8 m/s
2
F
net
= ma = (2.0 kg)(6.8 m/s
2
) = 14 N
4. F
net
= 13.5 N to the right
a = 6.5 m/s
2
to the right
m =
F
n
a
et
=
F
a
net
=
6
1
.5
3.
m
5N
/s
2
= 2.1 kg
3. F
net
= 6.75 × 10
3
N east
m = 1.50 × 10
3
kg
a =
F
m
net
==4.50 m/s
2
east
6.75 × 10
3
N east
1.50 × 10
3
kg
Section One—Student Edition Solutions I Ch. 4–3
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
3. m = 145 kg
m
s
= 0.61
m
k
= 0.47
g = 9.81 m/s
2
m = 15 kg
m
s
= 0.74
m
k
= 0.57
g = 9.81 m/s
2
m = 250 kg
m
s
= 0.4
m
k
= 0.2
g = 9.81 m/s
2
m = 0.55 kg
m
s
= 0.9
m
k
= 0.4
g = 9.81 m/s
2
a. F
s,max
= m
s
F
n
= m
s
mg = (0.61)(145 kg)(9.81 m/s
2
) =
F
k
= m
k
F
n
= m
k
mg = (0.47)(145 kg)(9.81 m/s
2
) =
b. F
s,max
= m
s
F
n
= m
s
mg = (0.74)(15 kg)(9.81 m/s
2
) =
F
k
= m
k
F
n
= m
k
mg = (0.57)(15 kg)(9.81 m/s
2
) =
c. F
s,max
= m
s
F
n
= m
s
mg = (0.4)(250 kg)(9.81 m/s
2
) =
F
k
= m
k
F
n
= m
k
mg = (0.2)(250 kg)(9.81 m/s
2
) =
d. F
s,max
= m
s
F
n
= m
s
mg = (0.9)(0.55 kg)(9.81 m/s
2
) =
F
k
= m
k
F
n
= m
k
mg = (0.4)(0.55 kg)(9.81 m/s
2
) = 2 N
5 N
5 × 10
2
N
1 × 10
3
N
84 N
1.1 × 10
2
N
6.7 × 10
2
N
8.7 × 10
2
N
1. F
applied
= 185 N at 25.0° F
applied, x
= F
applied
(cos q)
above the horizontal
F
applied, y
= F
applied
(sin q)
m = 35.0 kg
F
y, net
=ΣF
y
= F
n
+ F
applied, y
− F
g
= 0
m
k
= 0.27
F
n
= F
g
− F
applied, y
= mg − F
applied
(sin q)
g = 9.81 m/s
2
F
n
= (35.0 kg)(9.81 m/s
2
) − (185 N)(sin 25.0°) = 343 N − 78.2 N = 265 N
F
k
= m
k
F
n
= (0.27)(265 N) = 72 N
F
x, net
=ΣF
x
= F
applied, x
− F
k
= F
applied
(cos q) − F
k
F
x, net
= (185 N)(cos 25.0°) − 72 N = 168 N − 72 N = 96 N
a
x
=
F
x
m
,net
=
3
9
5
6
.0
N
kg
= 2.7 m/s
2
a = a
x
=
2. q
1
= 12.0° F
g,y
= mg(cos q
1
) = (35.0 kg)(9.81 m/s
2
)(cos 12.0°) = 336 N
q
2
= 25.0° F
g,x
= mg(sin q
1
) = (35.0 kg)(9.81 m/s
2
)(sin 12.0°) = 71.4 N
F
applied
= 185 N F
applied,x
= F
applied
(cos q
2
) = (185 N)(cos 25.0°) = 168 N
m = 35.0 kg F
applied,y
= F
applied
(sin q
2
) = (185 N)(sin 25.0°) = 78.2 N
m
k
= 0.27 F
y,net
=ΣF
y
= F
n
+ F
applied,y
− F
g,y
= 0
g = 9.81 m/s
2
F
n
= F
g,y
− F
applied,y
= 336 N − 78.2 N = 258 N
F
k
= m
k
F
n
= (0.27)(258 N) = 7.0 × 10
1
N
F
x,net
=ΣF
x
= F
applied,x
− F
k
− F
g,x
= ma
x
a
x
=
F
applied,x
m
− F
k
− F
g,x
2.7 m/s
2
in the positive x direction
Forces and the Laws of Motion, Practice E
Givens Solutions
3. m = 75.0 kg a. F
x,net
= ma
x
= F
g,x
− F
k
q = 25.0 ° F
g,x
= mg(sin q)
a
x
= 3.60 m/s
2
F
k
= F
g,x
− ma
x
= mg(sin q) − ma
x
g = 9.81 m/s
2
F
k
= (75.0 kg)(9.81 m/s
2
)(sin 25.0°) − (75.0 kg)(3.60 m/s
2
)
F
k
= 311 N − 2.70 × 10
2
N = 41 N
F
n
= F
g,y
= mg(cos q) = (75.0 kg)(9.81 m/s
2
)(cos 25.0°) = 667 N
m
k
=
F
F
n
k
=
6
4
6
1
7
N
N
=
m = 175 kg b. F
x,net
= F
g,x
− F
k
= mg sin q − m
k
F
n
m
k
= 0.061 F
n
= F
g,y
= mg cosq
a
x
=
F
x
m
,net
==g sin q − m
k
g cosq
a
x
= g(sin q − m
k
cos q) = 9.81 m/s
2
[sin 25.0° − (0.061)(cos 25.0°)]
a
x
= 9.81 m/s
2
(0.423 − 0.055) = (9.81 m/s
2
)(0.368) = 3.61 m/s
2
a = a
x
= 3.61 m/s
2
down the ramp
mg sin q − m
k
mg cosq
m
0.061
Givens Solutions
Holt Physics Solution ManualI Ch. 4–4
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. m = 2.26 kg
g = 9.81 m/s
2
3. m = 2.0 kg
q = 60.0°
g = 9.81 m/s
2
a. F
g
=
1
6
mg =
1
6
(2.26 kg)(9.81 m/s
2
) =
b. F
g
= (2.64)mg = (2.64)(2.26 kg)(9.81 m/s
2
) = 58.5 N
3.70 N
a. F
x,net
= F(cos q) − mg(sin q) = 0
F =
mg
c
(
o
s
s
in
q
q)
==
b.
F
y,net
= F
n
− F(sin q) − mg(cos q) = 0
F
n
= F(sin q) + mg(cos q) = (34 N)(sin 60.0°) + (2.0 kg)(9.81 m/s
2
)(cos 60.0°)
F
n
= 29 N + 9.8 N = 39 N
34 N
(2.0 kg)(9.81 m/s
2
)(sin 60.0°)
cos 60.0°
Forces and the Laws of Motion, Section 4 Review
a
x
==
3
2
5
7
.0
N
kg
= 0.77 m/s
2
a = a
x
= 0.77 m/s
2
up the ramp
168 N − 7.0 × 10
1
N − 71.4 N
35.0 kg
4. F
g
= 325 N F
x,net
= F
applied,x
− F
k
= 0
F
applied
= 425 N F
k
= F
applied,x
= F
applied
(cos q) = (425 N)[cos(−35.2°)] = 347 N
q =−35.2° F
y,net
= F
n
+ F
applied,y
− F
g
= 0
F
n
= F
g
− F
applied,y
= F
g
− F
applied
(sin q)
F
n
= 325 N − (425 N)[sin (−35.2°)] = 325 N + 245 N = 5.70 × 10
2
N
m
k
=
F
F
n
k
=
5.70
34
×
7
1
N
0
2
N
= 0.609
Section One—Student Edition Solutions I Ch. 4–5
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
4. m = 55 kg
F
s, max
= 198 N
F
k
= 175 N
g = 9.81 m/s
2
m
s
=
F
s
F
,m
n
ax
=
F
s
m
,m
g
ax
=
(55 kg
1
)(
9
9
8
.8
N
1 m/s
2
)
=
m
k
=
F
F
n
k
=
m
F
k
g
=
(55 kg
1
)(
7
9
5
.8
N
1 m/s
2
)
= 0.32
0.37
11. F
1
+ F
2
= 334 N
−F
1
+ F
2
=−106 N
12. F = 5 N
q = 37°
20. m = 24.3 kg
F
net
= 85.5 N
b. F
1
+ F
2
= 334 N
F
2
= 114 N F
1
+ 114 N = 334 N F
1
= 220 N
F
1
=
F
2
= 114 N right for both situations
220 N right for the first situation and left for the second
+(−F
1
+ F
2
) = (−106 N)
2F
2
= 228 N
F
x
= F(cos q) = (5 N)(cos 37°) =
F
y
= F(sin q) = (5 N)(sin 37°) = 3 N
4 N
a =
F
m
net
=
2
8
4
5
.
.
3
5
k
N
g
= 3.52 m/s
2
10. F
x,1
= 950 N
F
x,2
=−1520 N
F
y,1
= 5120 N
F
y,2
=−4050 N
F
x,net
= F
x,1
+ F
x,2
= 950 N + (−1520 N) =−570 N
F
y,net
= F
y,1
+ F
y,2
= 5120 N + (−4050 N) = 1070 N
F
net
=
(F
x,net
)
2
+ (F
y
,net
)
2
=
(−570
N)
2
+ (
1070 N
)
2
F
net
=
3.
2
×
1
0
5
N
2
+
1
.1
4
×
1
0
6
N
2
=
1.
46
×
1
0
6
N
2
=
q = tan
−1
F
F
x
y,
,
n
n
e
e
t
t
= tan
−1
−
10
5
7
7
0
0
N
N
=−62°
q = 62° above the 1520 N force
1.21 × 10
3
N
21. m = 25 kg F
net
= ma = (25 kg)(2.2 m/s
2
) = 55 N
a = 2.2 m/s
2
F
net
= 55 N to the right
Forces and the Laws of Motion, Chapter Review
Givens Solutions
24. m = 0.150 kg a. F
net
=−mg =−(0.150 kg)(9.81 m/s
2
) =
v
i
= 20.0 m/s
g = 9.81 m/s
2
b. same as part a.
26. m = 5.5 kg a. F
n
= mg = (5.5 kg)(9.81 m/s
2
) =
g = 9.81 m/s
2
q = 12° b. F
n
= mg(cos q) = (5.5 kg)(9.81 m/s
2
)(cos 12°) =
q = 25° c. F
n
= mg(cos q) = (5.5 kg)(9.81 m/s
2
)(cos 25°) =
q = 45° d. F
n
= mg(cos q) = (5.5 kg)(9.81 m/s
2
)(cos 45°) =
29. m = 5.4 kg F
n
= mg(cos q) = (5.4 kg)(9.81 m/s
2
)(cos 15°) =
q = 15°
g = 9.81 m/s
2
35. m = 95 kg F
n
= F
g
= mg = (95 kg)(9.81 m/s
2
) = 930 N
F
s,max
= 650 N
m
s
=
F
s
F
,m
n
ax
=
6
9
5
3
0
0
N
N
=
F
k
= 560 N
g = 9.81 m/s
2
m
k
=
F
F
n
k
=
5
9
6
3
0
0
N
N
=
36. q = 30.0° F
n
= mg(cos q)
a = 1.20 m/s
2
mg(sin q) − F
k
= ma
x
, where F
k
= m
k
F
n
= m
k
mg(cos q)
g = 9.81 m/s
2
mg(sin q) − m
k
mg(cos q) = ma
x
m
k
=
mg(
m
si
g
n
(c
q
o
)
s
−
q)
ma
x
=
c
si
o
n
s
q
q
−
g(c
a
o
x
s q)
= tan q −
g(c
a
o
x
s q)
m
k
= (tan 30.0°) − = 0.577 − 0.141 = 0.436
1.20 m/s
2
(9.81 m/s
2
)(cos 30.0°)
0.60
0.70
51 N
38 N
49 N
53 N
54 N
−1.47 N
Givens Solutions
Holt Physics Solution ManualI Ch. 4–6
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
22. F
1
= 380 N a. F
1,x
= F
1
(sin q
1
) = (380 N)(sin 30.0°) = 190 N
q
1
= 30.0° F
1,y
= F
1
(cos q
1
) = (380 N)(cos 30.0°) = 330 N
F
2
= 450 N F
2,x
= F
2
(sin q
2
) = (450 N)[sin (−10.0°)] =−78 N
q
2
=−10.0° F
2,y
= F
2
(cos q
2
) = (450 N)[cos (−10.0°)] = 440 N
F
y,net
= F
1,y
+ F
2,y
= 330 N + 440 N = 770 N
F
x,net
= F
1,x
+ F
2,x
= 190 N − 78 N = 110 N
F
net
=
(F
x,
ne
t
)
2
+
(F
y,n
et
)
2
=
(1
10
N
)
2
+
(
77
0
N
)
2
F
net
=
1.
2
×
1
0
4
N
2
+
5
.9
×
1
0
5
N
2
=
6.
0
×
1
0
5
N
2
=
q = tan
−1
F
F
x
y,
,
n
n
e
e
t
t
= tan
−1
1
7
1
7
0
0
N
N
=
m = 3200 kg b. a =
F
m
net
=
3
7
2
7
0
0
0
N
kg
= 0.24 m/s
2
a
net
= 0.24 m/s
2
at 8.1° to the right of forward
8.1° to the right of forward
770 N
Section One—Student Edition Solutions I Ch. 4–7
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
37. m = 4.00 kg F
applied,x
= F
applied
(cos q) = (85.0 N)(cos 55.0°) = 48.8 N
F
applied
= 85.0 N F
applied,y
= F
applied
(sin q) = (85.0 N)(sin 55.0°) = 69.6 N
q = 55.0° F
n
= F
applied,y
− mg = 69.6 N − (4.00 kg)(9.81 m/s
2
) = 69.6 N − 39.2 N = 30.4 N
a
x
= 6.00 m/s
2
ma
x
= F
applied,x
− F
k
= F
applied,x
− m
k
F
n
g = 9.81 m/s
2
m
k
=
F
applied
F
,x
n
− ma
x
=
m
k
=
48.8
3
N
0.
−
4
2
N
4.0 N
=
2
3
4
0
.
.
8
4
N
N
=
38. F
applied
= 185.0 N F
applied,x
= F
applied
(cos q) = (185.0 N)(cos 25.0°) = 168 N
q = 25.0° F
applied,y
= F
applied
(sin q) = (185.0 N)(sin 25.0°) = 78.2 N
m = 35.0 kg F
y,net
= F
n
+ F
applied,y
− mg = 0
m
k
= 0.450 F
n
= mg − F
applied,y
= (35.0 kg)(9.81 m/s
2
) − 78.2 N = 343 N − 78.2 N = 265 N
g = 9.81 m/s
2
F
k
= m
k
F
n
= (0.450)(265 N) = 119 N
F
x,net
= ma
x
= F
applied,x
− F
k
a
x
=
F
x
m
,net
=
168
3
N
5.
−
0k
1
g
19 N
=
3
4
5
9
.0
N
kg
= 1.4 m/s
2
a = a
x
=
39. F
g
= 925 N F
applied,x
= F
applied
(cos q) = (325 N)(cos 25.0°) = 295 N
F
applied
= 325 N F
applied,y
= F
applied
(sin q) = (325 N)(sin 25.0°) = 137 N
q = 25.0° F
y,net
= F
n
+ F
applied,y
− F
g
= 0
m
k
= 0.25 F
n
= F
g
− F
applied,y
= 925 N − 137 N = 788 N
g = 9.81 m/s
2
F
k
= m
k
F
n
= (0.25)(788 N) = 2.0 × 10
2
N
F
x,net
= ma
x
= F
applied,x
− F
k
= 295 N − 2.0 × 10
2
N = 95 N
m =
F
g
g
=
9.
9
8
2
1
5
m
N
/s
2
= 94.3 kg
a
x
=
F
x
m
,net
=
9
9
4
5
.3
N
kg
=
40. m = 6.0 kg F
n
=
c
m
os
g
q
=
(6.0 k
c
g
o
)
s
(9
3
.
0
8
.
1
0°
m/s
2
)
=
q = 30.0°
g = 9.81 m/s
2
F = F
n
sin q = (68 N)(sin 30.0°) =
41. m = 2.0 kg Because v
i
= 0 m/s,
∆x = 8.0 × 10
−1
m ∆x =
1
2
a∆t
2
∆t = 0.50 s a =
2
∆
∆
t
2
x
=
(2
(
)
0
(
.
0
5
.
0
80
s)
m
2
)
= 6.4 m/s
2
v
i
= 0 m/s F
net
= ma = (2.0 kg)(6.4 m/s
2
) = 13 N
F
net
=
13 N down the incline
34 N
68 N
1.0 m/s
2
1.4 m/s
2
down the aisle
0.816
48.8 N − (4.00 kg)(6.00 m/s
2
)
30.4 N
Givens Solutions
42. m = 2.26 kg b. F
g
= mg = (2.26 kg)(9.81 m/s
2
) =
∆y =−1.5 m
g = 9.81 m/s
2
43. m = 5.0 kg F
T
− F
g
= ma
a = 3.0 m/s
2
F
T
= ma + F
g
= ma + mg
g = 9.81 m/s
2
F
T
= (5.0 kg)(3.0 m/s
2
) + (5.0 kg)(9.81 m/s
2
) = 15 N + 49 N = 64 N
F
T
=
44. m = 3.46 kg b. F
g
= mg = (3.46 kg)(9.81 m/s
2
) =
g = 9.81 m/s
2
45. F
1
= 2.10 × 10
3
N a. F
net
= F
1
+ F
2
= 2.10 × 10
3
N + (−1.80 × 10
3
N)
F
2
=−1.80 × 10
3
N F
net
= 3.02 × 10
2
N
m = 1200 kg
a
net
=
F
m
net
=
3.0
1
2
20
×
0
1
k
0
g
2
N
= 0.25 m/s
2
a
net
=
∆t = 12 s b. ∆x = v
i
∆t +
1
2
a∆t
2
= (0 m/s)(12 s) +
1
2
(0.25 m/s
2
)(12 s)
2
v
i
= 0 m/s ∆x =
c. v
f
= a∆t + v
i
= (0.25 m/s
2
)(12 s) + 0 m/s
v
f
=
3.0 m/s
18 m
0.25 m/s
2
forward
33.9 N
64 N upward
22.2 N
Givens Solutions
Holt Physics Solution ManualI Ch. 4–8
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
46. v
i
= 7.0 m/s
m
k
= 0.050
F
g
= 645 N
g = 9.81 m/s
2
v
f
= 0 m/s
F
k
= m
k
F
n
= (0.050)(645 N) = 32 N
m =
F
g
g
=
9.
6
8
4
1
5
m
N
/s
2
= 65.7 kg
a =
−
m
F
k
=
6
−
5
3
.7
2
k
N
g
=−0.49 m/s
2
∆x =
v
f
2
2
−
a
v
i
2
=
∆x =
5.0 × 10
1
m
(0 m/s)
2
− (7.0 m/s)
2
(2)(−0.49 m/s
2
)
Section One—Student Edition Solutions I Ch. 4–9
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
47. F
g
= 319 N a. F
applied, x
= F
applied
(cos q) = (485 N)[cos(−35°)] = 4.0 × 10
2
N
F
applied
= 485 N F
applied,y
= F
applied
(sin q) = (485 N)[sin(−35°)] =−2.8 × 10
2
N
q =−35° F
y,net
= F
n
+ F
applied,y
− F
g
= 0
m
k
= 0.57 F
n
= F
g
− F
applied,y
= 319 N − (−2.8 × 10
2
N) = 6.0 × 10
2
N
∆x = 4.00 m F
k
= m
k
F
n
= (0.57)(6.0 × 10
2
N) = 3.4 × 10
2
N
g = 9.81 m/s
2
F
x,net
= ma
x
= F
applied,x
− F
k
= 4.0 × 10
2
N − 3.4 × 10
2
N = 6 × 10
1
N
v
i
= 0 m/s
m =
F
g
g
=
9.
3
8
1
1
9
m
N
/s
2
= 32.5 kg
a
x
=
F
x
m
,net
=
6
3
×
2.
1
5
0
k
1
g
N
= 2 m/s
2
∆x = v
i
∆t +
1
2
a
x
∆t
2
Because v
i
= 0 m/s,
∆t =
2
a
∆
x
x
=
(2
)
2
(
4
m
.0
/
0
s
2
m
)
=
m
k
= 0.75 b. F
k
= m
k
F
n
= (0.75)(6.0 × 10
2
N) = 4.5 × 10
2
N
F
k
> F
applied,x
; the box will not move
2 s
48. m = 3.00 kg
q = 30.0°
∆x = 2.00 m
∆t = 1.50 s
g = 9.81 m/s
2
v
i
= 0 m/s
a. ∆x = v
i
∆t +
1
2
a∆t
2
Because v
i
= 0 m/s,
a =
2
∆
∆
t
2
x
=
(2
(
)
1
(
.
2
5
.
0
00
s)
m
2
)
=
b. F
g,x
= mg(sin q) = (3.00 kg)(9.81 m/s
2
)(sin 30.0°) = 14.7 N
F
g,y
= mg(cos q) = (3.00 kg)(9.81 m/s
2
)(cos 30.0°) = 25.5 N
F
n
= F
g,y
= 25.5 N
ma
x
= F
g,x
− F
k
= F
g,x
− m
k
F
n
m
k
=
F
g,x
F
−
n
ma
x
=
m
k
=
14.7
2
N
5.
−
5
5
N
.34 N
=
2
9
5
.4
.5
N
N
=
c. F
k
= m
k
F
n
= (0.37)(25.5 N) =
d. v
f
2
= v
i
2
+ 2a
x
∆x
v
f
=
v
i
2
+
2
a
x
∆
x
=
(0
m
/s
)
2
+
(
2)
(1
.7
8
m
/s
2
)
(2
.0
0
m
)
=
2.67 m/s
9.4 N
0.37
14.7 N − (3.00 kg)(1.78 m/s
2
)
25.5 N
1.78 m/s
2
49. v
i
= 12.0 m/s v
f
= v
i
+ a∆t
∆t = 5.00 s
a =
v
f
∆
−
t
v
i
=
6.00 m/
5
s
.0
−
0
1
s
2.0 m/s
=
−6
5
.
.
0
00
m
s
/s
v
f
= 6.00 m/s
a =
F
k
=−ma
m
k
=
F
F
n
k
=
−
m
m
g
a
=
−
g
a
=
1
9
.
.
2
8
m
m
/
/
s
s
2
2
= 0.12
−1.2 m/s
2
52. m = 3.00 kg F
s, max
= m
s
F
n
q = 35.0° mg(sin q) = m
s
[F + mg(cos q)]
m
s
= 0.300
F = =
g = 9.81 m/s
2
F =
F =
F =
53. m = 64.0 kg At t = 0.00 s, v = 0.00 m/s. At t = 0.50 s, v = 0.100 m/s.
a =
v
t
f
f
−
−
v
t
i
i
==0.20 m/s
2
F = ma = (64.0 kg)(0.20 m/s
2
) =
At t = 0.50 s, v = 0.100 m/s. At t = 1.00 s, v = 0.200 m/s.
a =
v
t
f
f
−
−
v
t
i
i
==0.20 m/s
2
F = ma = (64.0 kg)(0.20 m/s
2
) =
At t = 1.00 s, v = 0.200 m/s. At t = 1.50 s, v = 0.200 m/s.
a = 0 m/s
2
; therefore, F =
At t = 1.50 s, v = 0.200 m/s. At t = 2.00 s, v = 0.00 m/s.
a =
v
t
f
f
−
−
v
t
i
i
==−0.40 m/s
2
F = ma = (64.0 kg)(−0.40 m/s
2
) =−26 N
0.00 m/s − 0.200 m/s
2.00 s − 1.50 s
0 N
13 N
0.200 m/s − 0.100 m/s
1.00 s − 0.50 s
13 N
0.100 m/s − 0.00 m/s
0.50 s − 0.00 s
32.2 N
(3.00 kg)(9.81 m/s
2
)(0.328)
0.300
(3.00 kg)(9.81 m/s
2
)(0.574 0.246)
0.300
(3.00 kg)(9.81 m/s
2
)[sin 35.0° 0.300 (cos 35.0°)]
0.300
mg[sin q − m
s
(cos q)]
m
s
mg(sin q) − m
s
mg(cos q)
m
s
Givens Solutions
Holt Physics Solution ManualI Ch. 4–10
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
51. m
car
= 1250 kg a. F
net
= m
car
a = (1250 kg)(2.15 m/s
2
) = 2690 N
m
trailer
= 325 kg F
net
=
a = 2.15 m/s
2
b. F
net
= m
trailer
a = (325 kg)(2.15 m/s
2
) = 699 N
F
net
=
699 N forward
2690 N forward
50. F
g
= 8820 N
v
i
= 35 m/s
∆x = 1100 m
g = 9.81 m/s
2
m =
F
g
g
=
9
8
.8
8
1
20
m
N
/s
2
= 899 kg
v
f
2
= v
i
2
+ 2a∆x = 0
a =
−
2∆
v
i
x
2
=
(
−
2
(
)
3
(1
5
1
m
00
/s
m
)
2
)
= −0.56 m/s
2
F
net
= ma = (899 kg)(−0.56 m/s
2
) =
−5.0 × 10
2
N
Section One—Student Edition Solutions I Ch. 4–11
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
3. F
x,1
= 82 N
F
x,2
=−115 N
F
y,1
= 565 N
F
y,2
=−236 N
F
x,net
= F
x,1
+ F
x,2
= 82 N − 115 N =−33 N
F
y,net
= F
y,1
+ F
y,2
= 565 N − 236 N = 329 N
F
net
=
(F
x,
ne
t
)
2
+
(
F
y,n
et
)
2
=
(−
33
N
)
2
+
(
32
9
N
)
2
F
net
=
1.
09
×
1
0
3
N
2
+
1
.0
8
×
1
0
5
N
2
=
1.
09
×
1
0
5
N
2
=
q = tan
−1
F
F
x
y,
,
n
n
e
e
t
t
= tan
−1
−
32
3
9
3
N
N
=−84° above negative x-axis
q = 180.0°−84°= 96° counterclockwise from the positive x-axis
3.30 × 10
2
N
5. m = 1.5 × 10
7
kg
F
net
= 7.5 × 10
5
N
v
f
= 85 km/h
v
i
= 0 km/h
a =
F
m
net
=
1
7
.
.
5
5
×
×
1
1
0
0
7
5
k
N
g
= 5.0 × 10
−2
m/s
2
∆t =
v
f
−
a
v
i
=
∆t = 4.7 × 10
2
s
(85 km/h − 0 km/h)(10
3
m/km)(1 h/3600 s)
5.0 × 10
−2
m/s
2
6.
Apply Newton’s second law to find an expression for the acceleration of the truck.
ma = F
f
= m
k
F
n
= m
k
mg
a = m
k
g
Because the acceleration of the truck does not depend on the mass of the truck, the
stopping distance will be ∆x regardless of the mass of the truck.
7.
v
f
=
v
i
2
+
2
a∆
x
= 0
a =
−
2
v
∆
i
x
2
The acceleration will be the same regardless of the intial velocity.
a
1
= a
2
= m
k
g (see 6.)
−
2
v
∆
i,
x
1
2
=
−
2∆
v
i
x
,2
2
2
∆x
2
=
v
i
v
,2
i,
2
1
∆
2
x
where v
i,2
=
1
2
v
i,1
∆x
2
==
1
4
∆x
1
2
v
i,1
2
∆x
v
i,1
2
54. F
applied
= 3.00 × 10
2
N F
net
= F
applied
− F
g
sin q = 0
F
g
= 1.22 × 10
4
N sin q =
F
ap
F
p
g
lied
g = 9.81 m/s
2
q = sin
−1
F
ap
F
p
g
lied
= sin
−1
q = 1.41°
3.00 × 10
2
N
1.22 × 10
4
N
Givens Solutions
Forces and the Laws of Motion, Standardized Test Prep
Holt Physics Solution ManualI Ch. 4–12
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
10. m = 3.00 kg
∆y =−176.4 m
F
w
= 12.0 N
a
y
= −g =−9.81 m/s
2
Because the ball is dropped, v
i
= 0 m/s
∆y =
1
2
a
y
∆t
2
∆t =
2
a
∆
y
y
=
(2
−
)
(
9
−
.8
1
1
7
6
m
.
4
/s
m
2
)
= 6.00 s
11. m = 3.00 kg
F
w
= 23.0 N
∆t = 6.00 s (see 10.)
a
x
=
F
m
w
=
3
1
.
2
0
.
0
0
k
N
g
= 4.00 m/s
2
∆x =
1
2
a
x
∆t
2
=
1
2
(4.00 m/s
2
)(6.00 s)
2
= 72.0 m
16. m = 10.0 kg
F = 15.0 N
q = 45.0°
m
k
= 0.040
g = 9.81 m/s
2
F
net,y
= F
n
+ F sin q − mg = 0
F
n
= mg − F sin q
F
net,x
= F cos q − F
k
= F cos q − m
k
F
n
F
net,x
= F cos q − m
k
(mg − F sin q)
a
x
=
F
n
m
et,x
=
a
x
=
a
x
==
a
x
===0.71 m/s
2
a = a
x
= 0.71 m/s
2
7.1 N
10.0 kg
10.6 N − 3.5 N
10.0 kg
10.6 N − (0.040)(87.5 N)
10.0 kg
10.6 N − (0.040)(98.1 N − 10.6 N)
10.0 kg
(15.0 N)(cos 45.0°) − (0.040)[(10.0 kg)(9.81 m/s
2
) − (15.0 N)(sin 45.0°)]
10.0 kg
F cos q − m
k
(mg − F sin q)
m
12. a
y
= −g =−9.81 m/s
2
∆t = 6.00 s (see 10.)
a
x
= 4.00 m/s
2
(see 11.)
v
y
= a
y
∆t = (−9.81 m/s
2
)(6.00 s) =−58.9 m/s
v
x
= a
x
∆t = (4.00 m/s
2
)(6.00 s) = 24.0 m/s
v =
v
x
2
+
v
y
2
=
(2
4.
0
m
/s
)
2
+
(
−
58
.9
m
/s
)
2
v =
57
6
m
2
/
s
2
+
3
47
0
m
2
/
s
2
=
40
50
m
2
/
s
2
= 63.6 m/s
Section One—Student Edition Solutions I Ch. 5–1
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. F
net
= 5.00 × 10
3
N
d = 3.00 km
q = 0°
2. d = 2.00 m
q = 0°
F
net
= 350 N
3. F = 35 N
q = 25°
d = 50.0 m
W
net
= F
net
d(cos q) = (5.00 × 10
3
N)(3.00 × 10
3
m)(cos 0°) = 1.50 × 10
7
J
W
net
= F
net
d(cos q) = (350 N)(2.00 m)(cos 0°) = 7.0 × 10
2
J
W = Fd(cos q) = (35 N)(50.0 m)(cos 25°) = 1.6 × 10
3
J
Work and Energy, Practice A
Givens Solutions
3. F
g
= 1.50 × 10
3
N
F
applied
= 345 N
q = 0°
d = 24.0 m
m
k
= 0.220
4. m = 0.075 kg
F
k
= 0.350 N
g = 9.81 m/s
2
d = 1.32 m
q = 0°
a. W
1
= F
applied
d(cos q) = (345 N)(24.0 m)(cos 0°) =
b. W
2
= F
k
d(cos q) =−F
g
m
k
d(cos q)
W
2
=−(1.50 × 10
3
N)(0.220)(24.0 m)(cos 0°) =
c. W
net
= W
1
+ W
2
= 8.28 × 10
3
J + (−7.92 × 10
3
J) = 3.6 × 10
2
J
−7.92 × 10
3
J
8.28 × 10
3
J
W
net
= F
net
d(cos q) =(F
g
− F
k
)d(cos q) = (mg − F
k
)d(cos q)
W
net
= [(0.075 kg)(9.81 m/s
2
) − 0.350 N](1.33 m)(cos 0°)
W
net
= (0.74 N − 0.350 N)(1.32 m) = (0.39 N)(1.32 m) = 0.51 J
Work and Energy, Section 1 Review
1. m = 8.0 × 10
4
kg
KE = 1.1 × 10
9
J
v =
2
m
K
E
=
(2
8
)
.
(
0
1
.
×
1
1
×
0
1
4
0
k
9
g
J)
= 1.7 × 10
2
m/s
Work and Energy, Practice B
Work and Energy
Student Edition Solutions
4. W = 2.0 J
m = 180 g
g = 9.81 m/s
2
q = 0°
d =
F(c
W
os q)
=
mg(c
W
os q)
= = 1.1 m
2.0 J
(0.18 kg)(9.81 m/s
2
)(cos 0°)
Holt Physics Solution ManualI Ch. 5–2
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. m = 0.145 kg
KE = 109 J
v =
2
m
K
E
=
(
0
2
.
)
1
(
4
1
5
09
kg
J)
= 38.8 m/s
3. m
1
= 3.0 g
v
1
= 40.0 m/s
m
2
= 6.0 g
v
2
= 40.0 m/s
KE
1
=
1
2
m
1
v
1
2
=
1
2
(3.0 × 10
−3
kg)(40.0 m/s)
2
= 2.4 J
KE
2
=
1
2
m
2
v
2
2
=
1
2
(6.0 × 10
−3
kg)(40.0 m/s)
2
= 4.8 J
K
K
E
E
2
1
=
4
2
.
.
8
4
J
J
=
2
1
Givens Solutions
1. F
net
= 45 N
KE
f
= 352 J
KE
i
= 0 J
q = 0°
2. m = 2.0 × 10
3
kg
F
1
= 1140 N
F
2
= 950 N
v
f
= 2.0 m/s
v
i
= 0 m/s
q = 0°
3. m = 2.1 × 10
3
kg
q = 20.0°
F
k
= 4.0 × 10
3
N
g = 9.81 m/s
2
v
f
= 3.8 m/s
v
i
= 0 m/s
q′=0°
W
net
=∆KE = KE
f
− KE
i
W
net
= F
net
d(cos q)
d =
F
K
ne
E
t
f
(
−
co
K
s
E
q
i
)
=
(45
35
N
2
)
J
(c
−
o
0
s0
J
°)
=
3
4
5
5
2
N
J
= 7.8 m
W
net
=∆KE = KE
f
− KE
i
=
1
2
mv
f
2
−
1
2
mv
i
2
W
net
= F
net
d(cos q) = (F
1
− F
2
)d(cos q)
d ==
d = = 21 m
(2.0 × 10
3
kg)(4.0 m
2
/s
2
)
(2)(190 N)
(2.0 × 10
3
kg)[(2.0 m/s)
2
− (0 m/s)
2
]
(2)(1140 N − 950 N)(cos 0°)
1
2
m(v
f
2
− v
i
2
)
(F
1
−F
2
)(cos q)
W
net
=∆KE = KE
f
− KE
i
=
1
2
mv
f
2
−
1
2
mv
i
2
W
net
= F
net
d(cos q′)
F
net
= mg(sin q) − F
k
[mg(sin q) − F
k
]d(cos q′) =
1
2
m(v
f
2
− v
i
2
)
Simplify the equation by noting that
v
i
= 0 m/s and q′=0.
d = =
d = = = 5.1 m
(2.1 × 10
3
kg)(3.8 m/s)
2
(2)(3.0 × 10
3
N)
(2.1 × 10
3
kg)(3.8 m/s)
2
(2)(7.0 × 10
3
N − 4.0 × 10
3
N)
(2.1 × 10
3
kg)(3.8 m/s)
2
(2)[(2.1 × 10
3
kg)(9.81 m/s
2
)(sin 20.0°) − 4.0 × 10
3
N]
1
2
mv
f
2
mg(sin q) − F
k
Work and Energy, Practice C
4. m
1
= 3.0 g
v
1
= 40.0 m/s
m
2
= 3.0 g
v
2
= 80.0 m/s
KE
1
=
1
2
m
1
v
1
2
=
1
2
(3.0 × 10
−3
kg)(40.0 m/s)
2
=
KE
2
=
1
2
m
2
v
2
2
=
1
2
(3.0 × 10
−3
kg)(80.0 m/s)
2
=
K
K
E
E
1
2
=
2
9
.
.
4
6
J
J
=
1
4
9.6 J
2.4 J
5. KE = 4.32 × 10
5
J
v = 23 m/s
m =
2
v
K
2
E
=
(2)(
(
4
2
.
3
32
m
×
/s
1
)
0
2
5
J)
= 1.6 × 10
3
kg
Section One—Student Edition Solutions I Ch. 5–3
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
4. m = 75 kg
d = 4.5 m
v
f
= 6.0 m/s
v
i
= 0 m/s
q = 0°
W
net
=∆KE = KE
f
− KE
i
=
1
2
mv
f
2
−
1
2
mv
i
2
W
net
= F
net
d(cos q)
F
net
== =
F
net
= 3.0 × 10
2
N
(75 kg)(36 m
2
/s
2
)
(2)(4.5 m)
(75 kg)[(6.0 m/s)
2
− (0 m/s)
2
]
(2)(4.5 m)(cos 0°)
1
2
m(v
f
2
− v
i
2
)
d(cos q)
1. k = 5.2 N/m
x = 3.57 m − 2.45 m
= 1.12 m
2. k = 51.0 N/m
x = 0.150 m − 0.115 m
= 0.035 m
PE =
1
2
kx
2
=
1
2
(5.2 N/m)(1.12 m)
2
= 3.3 J
PE =
1
2
kx
2
=
1
2
(51.0 N/m)(0.035 m)
2
= 3.1 × 10
−2
J
Work and Energy, Practice D
3. m = 40.0 kg
h
1
= 2.00 m
g = 9.81 m/s
2
a. PE
1
= mgh
1
= (40.0 kg)(9.81 m/s
2
)(2.00 m) =
b. h
2
= (2.00 m)(1 − cos 30.0°) = (2.00 m)(1 − 0.866)
h
2
= (2.00 m)(0.134) = 0.268 m
PE
2
= mgh
2
PE
2
= (40.0 kg)(9.81 m/s
2
)(0.268 m) =
c. h
3
= 2.00 m − 2.00 m = 0.00 m
PE
3
= mgh
3
PE
3
= (40.0 kg)(9.81 m/s
2
)(0.00 m) = 0.00 J
105 J
785 J
2. m = 0.75 kg
d = 1.2 m
m
k
= 0.34
v
f
= 0 m/s
g = 9.81 m/s
2
q = 180°
W
net
=∆KE = KE
f
− KE
i
=
1
2
mv
f
2
−
1
2
mv
i
2
W
net
= F
net
d(cos q) = F
k
d (cos q) = m
k
mgd(cos q)
m
k
mgd(cos q) =
1
2
m(v
f
2
− v
i
2
)
v
i
= v
f
2
−
2
m
k
g
d(
co
s
q
)
= (0
m
/s
)
2
−
(
2)
(0
.3
4)
(9
.8
1
m
/s
2
)
(1
.2
m
)(
co
s
18
0°
)
v
i
= (2
)(
0.
34
)(
9.
81
m
/s
2
)
(1
.2
m
)
= 2.8 m/s
1. v = 42 cm/s
m = 50.0 g
KE =
1
2
mv
2
=
1
2
(50.0 × 10
−3
kg)(0.42 m/s)
2
= 4.4 × 10
−3
J
Work and Energy, Section 2 Review
Holt Physics Solution ManualI Ch. 5–4
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
3. h = 21.0 cm
g = 9.81 m/s
2
m = 30.0 g
PE
g
= mgh = (30.0 × 10
−3
kg)(9.81 m/s
2
)(0.210 m) = 6.18 × 10
−2
J
1. v
i
= 18.0 m/s
m = 2.00 kg
h
i
= 5.40 m
g = 9.81 m/s
2
PE
i
+ KE
i
= KE
f
mgh
i
+
1
2
mv
i
2
=
1
2
mv
f
2
v
f
=
2g
h
i
+
v
i
2
=
(2
)(
9.
81
m
/s
2
)
(5
.4
0
m
)
+
(
18
.0
m
/s
)
2
v
f
=
10
6
m
2
/
s
2
+
3
24
m
2
/
s
2
=
4.
30
×
1
0
2
m
2
/
s
2
= 20.7 m/s = 20.7 m/s
2. F
g
= 755 N
h
i
= 10.0 m
h
f
= 5.00 m
g = 9.81 m/s
2
PE
i
= PE
f
+ KE
f
mgh
i
= mgh
f
+
1
2
mv
f
2
v
f
=
2g
h
i
−
2
gh
f
=
(2
)(
9.
81
m
/s
2
)
(1
0.
0
m
)
−
(
2)
(9
.8
1
m
/s
2
)
(5
.0
0
m
)
v
f
=
19
6
m
2
/
s
2
−
9
8.
1
m
2
/
s
2
=
98
m
2
/
s
2
= 9.90 m/s
diver speed at 5 m = v
f
=
PE
i
= KE
f
mgh
i
=
1
2
mv
f
2
v
f
=
2g
h
i
=
(2
)(
9.
81
m
/s
2
)
(1
0.
0
m
)
= 14.0 m/s
diver speed at 0 m = v
f
= 14.0 m/s
9.9 m/s
Work and Energy, Practice E
h
f
= 0 m
3. h
i
= 10.0 m
g = 9.81 m/s
2
v
i
= 2.00 m/s
PE
i
+ KE
i
= KE
f
mgh
i
+
1
2
mv
i
2
=
1
2
mv
f
2
v
f
=
2g
h
i
+
v
i
2
=
(2
)(
9.
81
m
/s
2
)
(1
0.
0
m
)
+
(
2.
00
m
/s
)
2
v
f
=
19
6
m
2
/
s
2
+
4
.0
0
m
2
/
s
2
=
2.
00
×
1
0
2
m
2
/
s
2
= 14.1 m/s = 14.1 m/s
4. v
i
= 2.2 m/s
g = 9.81 m/s
2
KE
i
= PE
f
1
2
mv
i
2
= mgh
f
h
f
=
v
2
i
g
2
=
(2
(
)
2
(9
.2
.8
m
1
/
m
s)
/
2
s
2
)
= 0.25 m
Section One—Student Edition Solutions I Ch. 5–5
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
5. v
f
= 1.9 m/s
g = 9.81 m/s
2
PE
i
= KE
f
mgh
i
=
1
2
mv
f
2
h
i
=
v
2
f
g
2
=
(2
(
)
1
(9
.9
.8
m
1
/
m
s)
/
2
s
2
)
= 0.18 m
Givens Solutions
Work and Energy, Section 3 Review
1. x =−8.00 cm
k = 80.0 N/m
g = 9.81 m/s
2
m = 50.0 g
Taking the compressed spring as the zero level, h =−x = 8.00 cm.
PE
elastic,i
= PE
g,f
+ KE
f
1
2
kx
2
= mgh +
1
2
mv
f
2
v
f
=
k
m
x
2
−
2
gh
=
−
(
2)
(9
.8
1
m
/s
2
)
(0
.0
80
0
m
)
v
f
=
10
.2
m
2
/
s
2
−
1
.5
7
m
2
/
s
2
=
8.
6
m
2
/
s
2
= 2.93 m/s
(80.0 N/m)(−0.0800 m)
2
(50.0 × 10
−3
kg)
Work and Energy, Practice F
1. m
elevator
= 1.0 × 10
3
kg
m
load
= 800.0 kg
F
k
= 4.0 × 10
3
N
v = 3.00 m/s
g = 9.81 m/s
2
m = m
elevator
+ m
load
= 1.0 × 10
3
kg + 800.0 kg = 1.8 × 10
3
kg
P = Fv = (F
g
+ F
k
)v = (mg + F
k
)v
P = [(1.8 × 10
3
kg)(9.81 m/s
2
) + 4.0 × 10
3
N](3.00 m/s)
P = (1.8 × 10
4
N + 4.0 × 10
3
N)(3.00 m/s)
P = (2.2 × 10
4
N)(3.00 m/s) = 6.6 × 10
4
W = 66 kW
2. m = 1.50 × 10
3
kg
v
f
= 18.0 m/s
v
i
= 0 m/s
∆t = 12.0 s
F
r
= 400.0 N
For v
i
= 0 m/s,
∆x =
1
2
v
f
∆ta=
∆
v
f
t
P =
∆
W
t
=
F
∆
∆
t
x
=
(ma +
∆t
F
r
)∆x
=
+ 400.0 N
1
2
(18.0 m/s)(12.0 s)
P =
12.0 s
P =
P =
(2650 N)(
2
18.0 m/s)
= 2.38 × 10
4
W, or 23.8 kW
(2250 N + 400.0 N)(18.0 m/s)(12.0 s)
(2)(12.0 s)
(1.50 × 10
3
kg)(18.0 m/s)
12.0 s
m
∆
v
t
f
+ F
r
1
2
v
f
∆t
∆t
Holt Physics Solution ManualI Ch. 5–6
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
3. m = 2.66 × 10
7
kg
P = 2.00 kW
d = 2.00 km
g = 9.81 m/s
4. P = 19 kW
W = 6.8 × 10
7
J
∆t =
W
P
=
m
P
gd
==
or (2.61 × 10
8
s)(1 h/3600 s)(1 day/24 h)(1 year/365.25 days) = 8.27 years
2.61 × 10
8
s
(2.66 × 10
7
kg)(9.81 m/s
2
)(2.00 × 10
3
m)
2.00 × 10
3
W
∆t =
W
P
=
1
6
9
.8
×
×
1
1
0
0
3
7
W
J
=
or (3.6 × 10
3
s)(1 h/3600 s) = 1.0 h
3.6 × 10
3
s
Givens Solutions
5. m = 1.50 × 10
3
kg
v
f
= 10.0 m/s
v
i
= 0 m/s
∆t = 3.00 s
1. m = 50.0 kg
h = 5.00 m
P = 200.0 W
g = 9.81 m/s
2
a. W
net
=∆KE = KE
f
− KE
i
=
1
2
mv
f
2
−
1
2
mv
i
2
=
1
2
m (v
f
2
− v
i
2
)
W
net
=
1
2
(1.50 × 10
3
kg)[(10.0 m/s)
2
− (0 m/s)
2
]
W = W
net
=
b. P =
∆
W
t
=
7.5
3
0
.0
×
0
1
s
0
4
J
= 2.50 × 10
4
W or 25.0 kW
7.50 × 10
4
J
∆t =
W
P
=
m
P
gh
==
W = mgh = (50.0 kg)(9.81 m/s
2
)(5.00 m) = 2.45 × 10
3
J
12.3 s
(50.0 kg)(9.81 m/s
2
)(5.00 m)
200.0 W
Work and Energy, Section 4 Review
2. m = 50.0 kg
h = 5.00 m
v = 1.25 m/s
g = 9.81 m/s
P = Fv = mgv = (50.0 kg)(9.81 m/s
2
)(1.25 m/s) =
W = mgh = (50.0 kg)(9.81 m/s
2
)(5.00 m) = 2.45 × 10
3
J
613 W
7. m = 4.5 kg
d
1
= 1.2 m
d
2
= 7.3 m
g = 9.81 m/s
2
q
1
= 0°
q
2
= 90°
W
person
= F
g
[d
1
(cos q
1
) + d
2
(cos q
2
)]
W
person
= mg[d
1
(cos 0°) + d
2
(cos 90°)] = mgd
1
W
person
= (4.5 kg)(9.81 m/s
2
)(1.2 m) =
W
gravity
=−F
g
[d
1
(cos q
1
) + d
2
(cos q
2
)]
W
gravity
=−mg[d
1
(cos 0°) + d
2
(cos 90°)] =−mgd
1
W
gravity
=−(4.5 kg)(9.81 m/s
2
)(1.2 m) =−53 J
53 J
8. m = 8.0 × 10
3
kg
a
net
= 1.0 m/s
2
d = 30.0 m
q = 0°
W
net
= F
net
d(cos q) = ma
net
d(cos q) = (8.0 × 10
3
kg)(1.0 m/s
2
)(30.0 m)(cos 0°)
W = 2.4 × 10
5
J
Work and Energy, Chapter Review
Section One—Student Edition Solutions I Ch. 5–7
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
9. F = 475 N
q = 0°
d = 10.0 cm
10. F
g
= 70.0 N
F
applied
= 40.0 N
d = 253 m
q = 52.0°
14. v
1
= 5.0 m/s
v
2
= 25.0 m/s
16. Scenario 1:
v
1
= 50.0 km/h
Δx
1
= 35 m
Scenario 2:
v
2
= 100.0 km/h
W = Fd (cos q) = (475 N)(0.100 m)(cos 0°) = 47.5 J
a. W
1
= F
applied
d(cos q ) = (40.0 N)(253 m)(cos 52.0°) =
b. Because the bag’s speed is constant, F
k
= −F
applied
(cos q).
W
2
= F
k
d = −F
applied
(cos q)d = −(40.0 N)(cos 52.0°)(253 m) =
c. m
k
=
⎯
F
F
n
k
⎯
=
⎯
−
−
F
F
x,
g
ap
+
pl
F
ie
y
d
,
(
a
c
pp
o
l
s
ied
q)
⎯
==0.640
−(40.0 N)(cos 52.0°)
⎯⎯⎯
−70.0 N + (40.0 N)(sin 52.0)
−6.23 × 10
3
J
6.23 × 10
3
J
KE
1
=
⎯
1
2
⎯
mv
1
2
KE
2
=
⎯
1
2
⎯
mv
2
2
⎯
K
K
E
E
2
1
⎯
==
⎯
v
v
1
2
2
2
⎯
=
⎯
(
(
2
5
5
.0
.0
m
m
/
/
s
s
)
)
2
2
⎯
=
⎯
6
2
2
5
5
⎯
=
⎯
2
1
5
⎯
⎯
1
2
⎯
mv
1
2
⎯⎯
⎯
1
2
⎯
mv
2
2
Assuming that the cars skid to a stop, ΔKE = KE
i
KE
1
=
⎯
1
2
⎯
mv
1
2
=
⎯
1
2
⎯
m(50.0 km/h)
2
= m(1.25 × 10
3
km
2
/h
2
)
KE
2
=
⎯
1
2
⎯
mv
2
2
=
⎯
1
2
⎯
m(100.0 km/h)
2
= m(5.000 × 10
3
km
2
/h
2
)
The work done by the brakes is given by:
W
brake
= F
brake
d
Assuming that the braking force is the same for either speed:
W
1
= F
brake
(35 m)
W
2
= F
brake
Δx
2
The work required to stop the vehicle is equal to the initial Kinetic Energy
(Work—Kinetic Energy Theorem). Take the ratio of one to the other to get:
⎯
Δ
Δ
K
K
E
E
2
1
⎯
=
⎯
W
W
2
1
⎯
=
=
⎯
4
1
⎯
=
Δx
2
= 4(35 m) = 140 m
Δx
2
⎯
35 m
5.000 × 10
3
km
2
/h
2
⎯⎯
1.25 × 10
3
km
2
/h
2
F
brake
Δx
2
⎯⎯
F
brake
(35 m)
m(5.000 × 10
3
km
2
/h
2
)
⎯⎯⎯
m(1.25 × 10
3
km
2
/h
2
)
19. m = 1250 kg
v = 11 m/s
KE =
⎯
1
2
⎯
mv
2
=
⎯
1
2
⎯
(1250 kg)(11 m/s)
2
= 7.6 × 10
4
J
Givens Solutions
20. m = 0.55 g
KE = 7.6 × 10
4
J
v =
⎯
2
m
K
E
⎯
=
⎯
(
0
2
.
)
5
(
5
7
.
×
6
1
×
0
1
−
0
3
4
k
J
g
)
⎯
= 1.7 × 10
4
m/s
Holt Physics Solution ManualI Ch. 5–8
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
21. m = 50.0 kg
F
r
= 1500 N
d = 5.0 m
g = 9.81 m/s
2
KE
f
= 0 J
q = 180°
22. v
i
= 4.0 m/s
v
f
= 0 m/s
q = 25°
m = 20.0 kg
m
k
= 0.20
g = 9.81 m/s
2
q′=180°
23. h
A
= 10.0 m
m = 55 kg
h
B
= 0 m
h
A
= 0 m
h
B
=−10.0 m
h
A
= 5.0 m
h
B
=−5.0 m
W
net
=∆KE = KE
f
− KE
i
=−KE
i
The diver’s kinetic energy at the water’s surface equals the gravitational potential en-
ergy associated with the diver on the diving board relative to the water’s surface.
KE
i
= PE
g
= mgh W
net
= F
net
d(cos q) = F
r
d(cos q)
h = = = 15 m
total distance = h + d = 15 m + 5.0 m = 2.0 × 10
1
m
(1500 N)(5.0 m)(cos 180°)
−(50.0 kg)(9.81 m/s
2
)
F
r
d(cos q)
−mg
W
net
=∆KE = KE
f
− KE
i
=
1
2
mv
f
2
−
1
2
mv
i
2
W
net
= F
net
d(cos q′)
F
net
= mg(sin q) + F
k
= mg(sin q) + m
k
mg(cos q)
W
net
= mg[sin q + m
k
(cos q)]d(cos q′)
d = =
d =
d = = = 1.4 m
8.0 m
2
/s
2
(9.81 m/s
2
)(0.60)
−16 m
2
/s
2
−(2)(9.81 m/s
2
)(0.42 + 0.18)
(0 m/s)
2
− (4.0 m/s)
2
(2)(9.81 m/s
2
)[sin 25°+(0.20)(cos 25°)](cos 180°)
v
f
2
+ v
i
2
2 g[sin q + m
k
(cos q)](cos q′)
m(v
f
2
− v
i
2
)
mg[sin q + m
k
(cos q)](cos q′)
a. PE
A
= mgh
A
= (55 kg)(9.81 m/s
2
)(10.0 m) =
PE
B
= mgh
B
= (55 kg)(9.81 m/s
2
)(0 m) =
∆PE = PE
A
− PE
B
= 5400 J − 0 J =
b. PE
A
= mgh
A
= (55 kg)(9.81 m/s
2
)(0 m) =
PE
B
= mgh
B
= (55 kg)(9.81 m/s
2
)(−10.0 m) =
∆PE = PE
A
− PE
B
= 0 − (−5400 J) =
c. PE
A
= mgh
A
= (55 kg)(9.81 m/s
2
)(5.0 m) =
PE
B
= mgh
B
= (55 kg)(9.81 m/s
2
)(−5.0 m) =
∆PE = PE
A
− PE
B
= 2700 J − (−2700 J) = 5.4 × 10
3
J
−2.7 × 10
3
J
2.7 × 10
3
J
5.4 × 10
3
J
−5.4 × 10
3
J
0 J
5.4 × 10
3
J
0 J
5.4 × 10
3
J
Givens Solutions
1
2
24. m = 2.00 kg
h
1
= 1.00 m
h
2
= 3.00 m
h
3
= 0 m
a. PE = mg(−h
1
) = (2.00 kg)(9.81 m/s
2
)(−1.00 m) =
b. PE = mg(h
2
− h
1
) = (2.00 kg)(9.81 m/s
2
)(3.00 m − 1.00 m)
PE = (2.00 kg)(9.81 m/s
2
)(2.00 m) =
c. PE = mgh
3
= (2.00 kg)(9.81 m/s
2
)(0 m) = 0 J
39.2 J
−19.6 J
Section One—Student Edition Solutions I Ch. 5–9
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
25. k = 500.0 N/m
x
1
= 4.00 cm
x
2
=−3.00 cm
x
3
= 0 cm
33. m = 50.0 kg
h = 7.34 m
g = 9.81 m/s
2
34. h = 30.0 m
v
i
= 0 m/s
q = 37.0°
v
i
= 4.00 m/s
a. PE =
1
2
kx
1
2
=
1
2
(500.0 N/m)(0.0400 m)
2
=
b. PE =
1
2
kx
2
2
=
1
2
(500.0 N/m)(−0.0300 m)
2
=
c. PE =
1
2
kx
3
2
=
1
2
(500.0 N/m)(0 m)
2
= 0 J
0.225 J
0.400 J
PE
i
= KE
f
mgh =
1
2
mv
f
2
v
f
= 2g
h
= (2
)(
9.
81
m
/s
2
)
(7
.3
4
m
)
= 12.0 m/s
a. PE
i
= KE
f
mgh
i
=
1
2
mv
f
2
v
f
=
2g
h
i
=
2g
h
(1
−
c
o
s
q
)
=
(2
)(
9.
81
m
/s
2
)
(3
0.
0
m
)(
1
−
c
o
s
37
.0
°)
v
f
=
(2
)(
9.
81
m
/s
2
)
(3
0.
0
m
)(
1
−
0
.7
99
)
v
f
=
(2
)(
9.
81
m
/s
2
)
(3
0.
0
m
)(
0.
20
1)
=
b. PE
i
+ KE
i
= KE
f
mgh
i
+
1
2
mv
i
2
=
1
2
mv
f
2
v
f
=
2g
h
i
+
v
i
2
=
(2
)(
9.
81
m
/s
2
)
(3
0.
0
m
)(
0.
20
1)
+
(
4.
00
m
/s
)
2
v
f
=
11
8
m
2
/
s
2
+
1
6.
0
m
2
/
s
2
=
13
4
m
2
/
s
2
= 11.6 m/s
10.9 m/s
Givens Solutions
35. P = 50.0 hp
W = 6.40 × 10
5
J
1 hp = 746 W
∆t =
W
P
= = 17.2 s
6.40 × 10
5
J
(50.0 hp)(746 W/hp)
36. rate of flow =
∆
m
t
= 1.2 × 10
6
kg/s
d = 50.0 m
g = 9.81 m/s
2
P =
∆
W
t
=
F
∆
d
t
=
m
∆
g
t
d
=
∆
m
t
gd
P = (1.2 × 10
6
kg/s)(9.81 m/s
2
)(50.0 m) = 5.9 × 10
8
W
37. m = 215 g
h
A
= 30.0 cm
h
B
= 0 cm
h
C
=
2
3
(30.0 cm)
g = 9.81 m/s
2
a. PE
A
= mgh
A
= (215 × 10
−3
kg)(9.81 m/s
2
)(0.300 m) =
b. KE
B
= PE
A
=
c. KE
B
=
1
2
mv
2
v =
2K
m
E
B
=
=
d. PE
C
= mgh
C
= (215 × 10
−3
kg)(9.81 m/s
2
)(
2
3
)(0.300 m) =
KE
C
= KE
B
− PE
C
= 0.633 J − 0.422 J = 0.211 J
0.422 J
2.43 m/s
(2)(0.633 J)
215 × 10
−3
kg
0.633 J
0.633 J
Holt Physics Solution ManualI Ch. 5–10
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
38. F
g
= 700.0 N
d = 25.0 cm
F
upward
= (2)(355 N)
KE
i
= 0 J
g = 9.81 m/s
2
q = 0°
39. m = 50.0 kg
v
i
= 10.0 m/s
v
f
= 1.0 m/s
g = 9.81 m/s
2
40. F
g
= 80.0 N
d = 20.0 m
q = 30.0°
F
applied
= 115 N
m
k
= 0.22
g = 9.81 m/s
2
q′=0°
41. m
tot
= 130.0 kg
h
1
= 5.0 m
q = 30.0°
m
J
= 50.0 kg
g = 9.81 m/s
2
W
net
=∆KE = KE
f
− KE
i
= KE
f
=
1
2
mv
f
2
=
1
2
F
g
g
v
f
2
W
net
= F
net
d(cos q) = (F
upward
− F
g
)d(cos q)
1
2
F
g
g
v
f
2
= (F
upward
− F
g
)d(cos q)
v
f
=
v
f
=
v
f
=
v
f
=
= 0.265 m/s
(2)(9.81 m/s
2
)(1.0 × 10
1
N)(0.250 m)
700.0 N
(2)(9.81 m/s
2
)(7.10 × 10
2
N − 700.0 N)(0.250 m)
700.0 N
(2)(9.81 m/s
2
)[(2)(355 N) − 700.0 N](0.250 m)(cos 0°)
700.0 N
2g(F
upward
− F
g
)d(cos q)
F
g
KE
i
= PE
f
+ KE
f
1
2
mv
i
2
= mgh +
1
2
mv
f
2
h =
v
i
2
2
−
g
v
f
2
==
h =
(2)
9
(9
9
.8
m
1
2
m
/s
2
/s
2
)
= 5.0 m
1.00 × 10
2
m
2
/s
2
− 1.0 m
2
/s
2
(2)(9.81 m/s
2
)
(10.0 m/s)
2
− (1.0 m/s)
2
(2)(9.81 m/s
2
)
W
net
=∆KE
W
net
= F
net
d (cos q′) = F
net
d
∆KE = F
net
d = (F
applied
− F
k
− F
g,d
)d = [F
applied
− m
k
F
g
(cos q) − F
g
(sin q)]d
∆KE = [115 N − (0.22)(80.0 N)(cos 30.0°) − (80.0 N)(sin 30.0°)](20.0 m)
∆KE = (115 N − 15 N − 40.0 N)(20.0 m) = (6.0 × 10
1
N)(20.0 m)
∆KE = 1.2 × 10
3
J
For the first half of the swing,
PE
i
= KE
f
m
tot
gh =
1
2
m
tot
v
f
2
v
f
=
2g
h
=
2g
h
1
(
1
−
s
in
q
)
=
(2
)(
9.
81
m
/s
2
)
(5
.0
m
)(
1
−
s
in
3
0.
0°
)
v
f
=
(2
)(
9.
81
m
/s
2
)
(5
.0
m
)(
1
−
0
.5
00
)
=
(2
)(
9.
81
m
/s
2
)
(5
.0
m
)(
0.
50
0)
v
f
= 7.0 m/s
For the second half of the swing,
KE
T
=
1
2
m
T
v
f
2
=
1
2
(m
tot
− m
J
)v
f
2
=
1
2
(130.0 kg − 50.0 kg)(7.0 m/s)
2
KE
T
=
1
2
(80.0 kg)(7.0 m/s)
2
= 2.0 × 10
3
J
KE
T
= PE
f
= m
T
gh
f
h
f
=
m
KE
T
T
g
= = 2.5 m
2.0 × 10
3
J
(80.0 kg)(9.81 m/s
2
)
Givens Solutions
Section One—Student Edition Solutions I Ch. 5–11
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
44. m = 0.60 kg
v
A
= 2.0 m/s
KE
B
= 7.5 J
45. m = 5.0 kg
d = 2.5 m
q = 30.0°
∆t = 2.0 s
g = 9.81 m/s
2
q′=0°
v
i
= 0 m/s
q′=90°
a. W
gravity
= F
g,d
d(cos q′) = F
g,d
d = mg(sin q)d
W
gravity
= (5.0 kg)(9.81 m/s
2
)(sin 30.0°)(2.5 m) =
b. W
friction
=∆ME = KE
f
− PE
i
=
1
2
mv
f
2
− mgh
i
d =∆x =
1
2
(v
i
+ v
f
)∆t
v
f
=
2
∆
d
t
− v
i
=
2
∆
d
t
h
i
= d(sin q)
∆ME =
1
2
m
2
∆
d
t
2
− mgd(sin q)
∆ME =
1
2
(5.0 kg)
(2)
2
(2
.0
.5
s
m)
2
− (5.0 kg)(9.81 m/s
2
)(2.5 m)(sin 30.0°)
∆ME = W
friction
= 16 J − 61 J =
c. W
normal
= F
n
d(cos q′)mg(cos q)d(cos q′)
cos q′=cos 90°=0, so
W
normal
= 0 J
−45 J
61 J
Givens Solutions
42. m = 0.250 kg
k = 5.00 × 10
3
N/m
x =−0.100 m
g = 9.81 m/s
2
PE
elastic,i
= PE
g,f
1
2
kx
2
= mgh
h =
2
k
m
x
2
g
==10.2 m
(5.00 × 10
3
N/m)(−0.100 m)
2
(2)(0.250 kg)(9.81 m/s
2
)
a. KE
A
=
1
2
mv
A
2
=
1
2
(0.60 kg)(2.0 m/s)
2
=
b. KE
B
=
1
2
mv
B
2
v
B
=
2K
m
E
B
=
(2
0
)
.6
(
7
0
.
5
k
g
J
)
=
c. W
net
=∆KE = KE
B
− KE
A
= 7.5 J − 1.2 J = 6.3 J
5.0 m/s
1.2 J
Holt Physics Solution ManualI Ch. 5–12
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
47. h
1
= 50.0 m
h
2
= 10.0 m
g = 9.81 m/s
2
q = 45.0°
v
i
= 0 m/s
a. PE
i
= PE
f
+ KE
f
mgh
1
= mgh
2
+
1
2
mv
f
2
v
f
=
2g
h
1
−
2
gh
2
=
2g
(h
1
−
h
2
)
=
(2
)(
9.
81
m
/s
2
)
(5
0.
0
m
−
1
0.
0
m
)
v
f
=
(2
)(
9.
81
m
/s
2
)
(4
0.
0
m
)
=
b. At the acrobat’s highest point, v
y
= 0 m/s and v
x
= (28.0 m/s)(cos 45.0°).
PE
i
= PE
f
+ KE
f
mgh
1
= mgh
f
+
1
2
mv
f,x
2
h
f
==
h
f
==
2
9
9
.8
4
1
m
m
2
/
/
s
s
2
2
= 30.0 m above the ground
4.90 × 10
2
m
2
/s
2
− 196 m
2
/s
2
9.81 m/s
2
(9.81 m/s
2
)(50.0 m) − [(28.0 m/s)(cos 45.0°)]
2
9.81 m/s
2
gh
1
− v
f
,x
2
g
28.0 m/s
Givens Solutions
46. m = 70.0 kg
q = 35°
q′=0°
d = 60.0 m
g = 9.81 m/s
2
W = Fd(cos q′) = Fd(cos 0°) = Fd = mg(sin q)d
W = (70.0 kg)(9.81 m/s
2
)(sin 35∞)(60.0 m) = 2.4 × 10
4
J
48. m = 10.0 kg
d
1
= 3.00 m
q = 30.0°
d
2
= 5.00 m
v
i
= 0
g = 9.81 m/s
2
KE
f
= 0 J
q¢= 180°
KE
f
= 0 J
a. For slide down ramp,
PE
i
= KE
f
mgh =
1
2
mv
f
2
vf = 2g
h
= 2g
d
1
(s
in
q
)
v
f
= (2
)(
9.
81
m
/s
2
)
(3
.0
0
m
)(
si
n
3
0.
0°
)
=
b. For horizontal slide across floor,
W
net
=∆KE = KE
f
− KE
i
=−KE
i
W
net
= F
k
d
2
(cos q′)
= m
k
mgd
2
(cos q′)
KE
i
of horizontal slide equals KE
f
= PE
i
of slide down ramp.
−PE
i
=−mgd
1
(sin q) = m
k
mgd
2
(cos q′)
m
k
=
−
d
2
d
(
1
c
(
o
si
s
n
q
q
′)
)
= =
c. ∆ME = KE
f
− PE
i
=−PE
i
=−mgh =−mgd
1
(sin q)
∆ME =−(10.0 kg)(9.81 m/s
2
)(3.00 m)(sin 30.0°) =−147 J
0.300
−(3.00 m)(sin 30.0°)
(5.00 m)(cos 180°)
5.42 m/s
Section One—Student Edition Solutions I Ch. 5–13
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
50. m = 5.0 kg
q = 30.0°
q′=0°
d = 3.0 m
m
k
= 0.30
g = 9.81 m/s
2
a. Because v is constant,
F
y, net
= F(sin q) − m
k
F
n
− mg = 0
F
x, net
= F(cos q) − F
n
= 0
F
n
= F(cos q)
F(sin q) − m
k
F
n
= mg
F(sin q) − m
k
F(cos q) = mg
F =
sin q −
m
m
k
g
(cos q)
Upward component of F is parallel and in the same direction as motion, so
W = F(sin q)d =
sin
m
q
g
−
(s
m
in
k
(
q
co
)d
s q)
=
W =
=
W =
b. W
g
= F
g
d(cos q′) =−mgd =−(5.0 kg)(9.81 m/s
2
)(3.0 m) =
c. F
n
= F(cos q) =
sin q −
m
m
k
g
(cos q)
(cos q) =
F
n
= =
F
n
= 1.8 10
2
N
(5.0 kg)(9.81 m/s
2
)(cos 30.0°)
0.24
(5.0 kg)(9.81 m/s
2
)(cos 30.0°)
0.500 − 0.26
(5.0 kg)(9.81 m/s
2
)(cos 30.0°)
sin 30.0°−(0.30)(cos 30.0°)
−150 J
3.1 10
2
J
(5.0 kg)(9.81 m/s
2
)(sin 30.0°)(3.0 m)
0.24
(5.0 kg)(9.81 m/s
2
)(sin 30.0°)(3.0 m)
0.500 − 0.26
(5.0 kg)(9.81 m/s
2
)(sin 30.0°)(3.0 m)
sin 30.0°−(0.30)(cos 30.0°)
49. k = 105 N/m
m = 2.00 kg
x =−0.100 m
d = 0.250 m
g = 9.81 m/s
2
KE
f
= 0 J
q = 180°
W
net
=∆KE = KE
f
− KE
i
=−KE
i
=−PE
g
=−
1
2
kx
2
W
net
= F
k
d(cos q) = m
k
mgd(cos q) − m
k
mgd
1
2
kx
2
= m
k
mgd
m
k
=
2
k
m
x
g
2
d
==0.107
(105 N/m)(−0.100 m)
2
(2)(2.00 kg)(9.81 m/s
2
)(0.250 m)
q′=180°
a. h = L(1 − cos q) = (2.0 m)(1 − cos 30.0°) = (2.0 m)(1 − 0.866) = (2.0 m)(0.134)
PE
max
= mgh = mgL(1 − cos q) = (25 kg)(9.81 m/s
2
)(2.0 m)(0.134)
PE
max
=
b. PE
i
= KE
f
mgh =
1
2
mv
f
2
v
f
=
2g
h
=
(2
)(
9.
81
m
/s
2
)
(2
.0
m
)(
1
−
c
o
s
30
.0
°)
v
f
=
(2
)(
9.
81
m
/s
2
)
(2
.0
m
)(
0.
13
4)
=
c. ME = PE
i
+ KE
i
= 66 J + 0 J =
d. ∆ME = KE
f
− PE
i
=
1
2
mv
f
2
− PE
i
=
1
2
(25 kg)(2.00 m/s)
2
− 66 J
∆ME = (5.0 × 10
1
J) − 66 J =−16 J
66 J
2.3 m/s
66 J
Holt Physics Solution ManualI Ch. 5–14
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
52. m = 522 g
h
2
= 1.25 m
v
i
= 0 m/s
g = 9.81 m/s
2
∆x = 1.00 m
a. PE
i
= PE
f
+ KE
f
mgh = mgh
2
+
1
2
mv
2
h = h
2
+
v
2g
2
Choosing the point where the ball leaves the track as the origin of a
coordinate system,
∆x = v∆t, therefore ∆t =
∆
v
x
∆y =−
1
2
g∆t
2
At ∆y =−1.25 m (ground level),
∆y =−
1
2
g
∆
v
x
2
v =
−
2
g
∆
∆
y
x
2
=
= 1.98 m/s
h = h
2
+
v
2g
2
= 1.25 m +
(2
(
)
1
(
.
9
9
.
8
81
m
m
/s
/
)
s
2
2
)
= 1.25 m + 0.200 m
h =
b. v = (See a.)
c. KE
f
= PE
i
1
2
mv
f
2
= mgh
v
f
=
2g
h
=
(2
)(
9.
81
m
/s
2
)
(1
.4
5
m
)
= 5.33 m/s
1.98 m/s
1.45 m
−(9.81 m/s
2
)(1.00 m)
2
(2)(−1.25 m)
51. m = 25 kg
L = 2.0 m
q = 30.0°
g = 9.81 m/s
2
v
f
= 2.00 m/s
Section One—Student Edition Solutions I Ch. 5–15
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
4. m = 75 g
At ∆t = 4.5 s, KE = 350 mJ
KE =
1
2
mv
2
v =
2
m
K
E
=
(2
)
7
(
5
3
5
×
0
1
×
0
−
1
3
0
k
−
g
3
J)
= 3.1 m/s
3. ME
i
= 600 mJ
At ∆t = 6.0 s, ME
f
= 500 mJ
∆ME = ME
f
− ME
i
= 500 mJ − 600 mJ =−100 mJ
5. m = 75 g
g = 9.81 m/s
2
PE
max
= 600 mJ = mgh
max
h
max
=
PE
m
m
g
ax
==0.82 m
600 × 10
−3
J
(75 × 10
−3
kg)(9.81 m/s
2
)
6. m = 2.50 × 10
3
kg
W
net
= 5.0 kJ
d = 25.0 m
v
i
= 0 m/s
q = 0°
W
net
=∆KE = KE
f
− KE
i
Because v
i
= 0 m/s, KE
i
= 0 J, and W
net
= KE
f
=
1
2
mv
f
2
.
v
f
=
2W
m
ne
t
=
= 2.0 m/s
(2)(5.0 × 10
3
J)
2.50 × 10
3
kg
Work and Energy, Standardized Test Prep
Givens Solutions
7. m = 70.0 kg
v
i
= 4.0 m/s
v
f
= 0 m/s
∆ME = KE
f
− KE
i
∆ME =
1
2
mv
f
2
−
1
2
mv
i
2
=
1
2
m(v
f
2
− v
i
2
)
∆ME =
1
2
(70.0 kg)[(0 m/s)
2
− (4.0 m/s)
2
] =−5.6 × 10
2
J
8. m = 70.0 kg
m
k
= 0.70
g = 9.81 m/s
2
q = 180.0°
W =∆ME =−5.6 × 10
2
J
d =
F
k
(c
W
os q)
=
F
n
m
k
(
W
cos q)
=
mgm
k
W
(cos q)
d ==1.2 m
−5.6 × 10
2
J
(70.0 kg)(9.81 m/s
2
)(0.70)(cos 180°)
9. k = 250 N/m
m
p
= 0.075 kg
x
1
= 0.12 m
x
2
= 0.18 m
PE Ratio =
P
P
E
E
e
e
l
l
a
a
s
s
t
t
i
i
c
c
2
1
=
PE Ratio =
x
x
2
1
2
2
PE Ratio =
(
(
0
0
.
.
1
1
8
2
m
m
)
)
2
2
=
3
2
2
=
9
4
1
2
kx
2
2
1
2
kx
1
2
10. k = 250 N/m
m
p
= 0.075 kg
x
1
= 0.12 m
x
2
= 0.18 m
Since F
g
is negligible, and the PE
elastic
will be converted into KE. KE
2
:KE
1
will
provide the velocity ratios.
KE Ratio =
K
K
E
E
2
1
==
v
v
2
1
2
2
KE Ratio = PE Ratio =
v
v
2
1
2
2
v
v
2
1
=
PE Rat
io
=
9
4
v
v
2
1
=
3
2
1
2
mv
2
2
1
2
mv
1
2
Givens Solutions
Holt Physics Solution ManualI Ch. 5–16
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
11. m = 66.0 kg
∆t = 44.0 s
h = 14.0 m
g = 9.81 m/s2
Find PE
gained
PE = mgh = (66.0 kg)(9.81 m/s
2
)(14.0 m)
W = PE = 9.06 × 10
3
J
P =
∆
W
t
=
9.06
44
×
.0
1
s
0
3
J
= 206 W
12. m = 75.0 kg
g = 9.81 m/s
2
h = 1.00 m
PE
i
= KE
f
mgh =
1
2
mv
f
2
v
f
2
=
2m
m
gh
= 2gh
v
f
=
2gh
13. m = 75.0 kg
g = 9.81 m/s
2
h = 1.00 m
v
f
=
2gh
=
2(9.81
m/s
2
)(
1.00 m
)
=
19.6 m
2
/s
2
v
f
= 4.4 m/s
14. m = 5.0 kg
h = 25.0 m
g = 9.81 m/s
2
W
gravity
=∆PE
g
= mgh = (5.0 kg)(9.81 m/s
2
)(25.0 m) = 1.2 × 10
3
J
15.
∆KE = W
gravity
= 1.2 × 10
3
J
16. v
i
= 17 m/s
∆KE = KE
f
− KE
i
KE
f
=∆KE + KE
i
=∆KE +
1
2
mv
i
2
= 1200 J +
1
2
(5.0 kg)(17 m/s)
2
KE
f
= 1200 J + 720 J = 1.9 × 10
3
J
Section One—Student Edition Solutions I Ch. 5–17
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
17. q = 10.5°
d
1
= 200.0 m
mk = 0.075
g = 9.81 m/s
2
KE
1,i
= 0 J
KE
2,f
= 0 J
For downhill slide,
W
net,1
=∆KE
1
= KE
1,f
− KE
1,i
= KE
1,f
W
net,1
= F
net,1
d
1
(cos q′)
F
net,1
= mg(sin q) − F
k
= mg(sin q) − m
k
mg(cos q)
Because F
net,1
is parallel to and in the forward direction to d
1
, q′=0°, and
W
net,1
= mgd
1
[sin q − m
k
(cos q)]
For horizontal slide,
W
net,2
=∆KE
2
= KE
2,f
− KE
2,i
=−KE
2,i
W
net,2
= F
net,2
d
2
(cos q′) = F
k
d
2
(cos q′) = m
k
mgd
2
(cos q′)
Because F
net,2
is parallel to and in the backward direction to d
2
, q′=180°,
and W
net,2
=−m
k
mgd
2
For the entire ride,
mgd
1
[sin q − m
k
(cos q)] = KE
1,f
− m
k
mgd
2
=−KE
2,i
Because KE
1,f
= KE
2,i
, mgd
1
[sin q − m
k
(cos q)] = m
k
mgd
2
d
2
=
d
2
= =
d
2
=
(200.0
0
m
.07
)(
5
0.108)
= 290 m
(200.0 m)(0.182 − 0.074)
0.075
(200.0 m)[(sin 10.5 °) − (0.075)(cos 10.5°)]
0.075
d
1
[sin q − m
k
(cos q)]
m
k
Givens Solutions
Section One—Student Edition Solutions I Ch. 6–1
Momentum
and Collisions
Student Edition Solutions
I
1. m = 146 kg
v = 17 m/s south
2. m
1
= 21 kg
m
2
= 5.9 kg
v = 4.5 m/s to the northwest
3. m = 1210 kg
p = 5.6 × 10
4
kg
•
m/s to
the east
p = mv = (146 kg)(17 m/s south)
p = 2.5 × 10
3
kg
•
m/s to the south
a. p
tot
= m
tot
v = (m
1
+ m
2
)v = (21 kg + 5.9 kg)(4.5 m/s)
p
tot
= (27 kg)(4.5 m/s) =
b. p
1
= m
1
v = (21 kg)(4.5 m/s) =
c. p
2
= m
2
v = (5.9 kg)(4.5 m/s) = 27 kg
•
m/s to the northwest
94 kg
•
m/s to the northwest
1.2 × 10
2
kg
•
m/s to the northwest
v =
m
p
=
5.6 ×
1
1
2
0
1
4
0
k
k
g
g
•
m/s
= 46 m/s to the east
Momentum and Collisions, Practice A
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. m = 0.50 kg
v
i
= 15 m/s to the right
∆t = 0.020 s
v
f
= 0 m/s
2. m = 82 kg
∆y =−3.0 m
∆t = 0.55 s
v
i
= 0 m/s
a =−9.81 m/s
2
3. m = 0.40 kg
v
i
= 18 m/s to the north
=+18 m/s
v
f
= 22 m/s to the south
=−22 m/s
F =
mv
f
∆
−
t
mv
i
= to the right
F =−3.8 × 10
2
N to the right
F = 3.8 × 10
2
N to the left
(0.50 kg)(0 m/s) − (0.50 kg)(15 m/s)
0.020 s
v
f
=±
2a
∆
y
=±
(2
)(
−
9.
81
m
/s
2
)
(−
3.
0
m
)
=±7.7 m/s =−7.7 m/s
For the time the man is in the water,
v
i
= 7.7 m/s downward =−7.7 m/s v
f
= 0 m/s
F =
mv
f
∆
−
t
mv
i
==1.1 × 10
3
N
F = 1.1 × 10
3
N upward
(82 kg)(0 m/s) − (82 kg)(−7.7 m/s)
0.55 s
∆p = mv
f
− mv
i
= (0.40 kg)(−22 m/s) − (0.40 kg)(18 m/s)
∆p =−8.8 kg
•m/s − 7.2 kg
•
m/s =−16.0 kg
•
m/s
∆p = 16 kg
•
m/s to the south
Momentum and Collisions, Practice B
Holt Physics Solution ManualI Ch. 6–2
I
4. m = 0.50 kg
F
1
= 3.00 N to the right
∆t
1
= 1.50 s
v
i,1
= 0 m/s
F
2
= 4.00 N to the left
=−4.00 N
∆t
2
= 3.00 s
v
i,2
= 9.0 m/s to the right
a. v
f,1
=
F
1
∆t
1
m
+ mv
i,1
=
v
f,1
= 9.0 m/s =
b. v
f,2
=
F
2
∆t
2
m
+ mv
i,2
=
v
f,2
==
−7.
0
5
.5
k
0
g
k
•
m
g
/s
=−15 m/s
v
f,2
= 15 m/s to the left
−12.0 kg
•
m/s + 4.5 kg•m/s
0.50 kg
(−4.00 N)(3.00 s) + (0.50 kg)(9.0 m/s)
0.50 kg
9.0 m/s to the right
(3.00 N)(1.50 s) + (0.50 kg)(0 m/s)
0.50 kg
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. m = 2240 kg
v
i
= 20.0 m/s to the west,
v
i
=−20.0 m/s
v
f
= 0
F = 8410 N to the east,
F =+8410 N
2. m = 2500 kg
v
i
= 20.0 m/s to the north
=+20.0 m/s
F = 6250 N to the south
=−6250 N
∆t = 2.50 s
v
f
= 0 m/s
3. m = 3250 kg
v
i
= 20.0 m/s to the west
=−20.0 m/s
v
f
= 0 m/s
∆t = 5.33 s
a. ∆t =
∆
F
p
=
mv
f
F
− mv
i
∆t ==
∆t =
b. ∆x =
1
2
(v
i
+ v
f
)∆t
∆x =
1
2
(−20.0 m/s − 0)(5.33 s)
∆x =−53.3 m or 53.3 m to the west
5.33 s
44 800 kg
•
m/s
8410 kg
•
m/s
2
(2240 kg)(0) − (2240 kg)(−20.0 m/s)
(8410 N)
a. v
f
=
F∆t
m
+ mv
i
=
v
f
==
v
f
= 14 m/s =
b. ∆x =
1
2
(v
i
+ v
f
)(∆t) =
1
2
(20.0 m/s + 14 m/s)(2.50 s)
∆x =
1
2
(34 m/s)(2.50 s) =
c. ∆t =
mv
f
F
− mv
i
==8.0 s
(2500 kg)(0 m/s) − (2500 kg)(20.0 m/s)
−6250 N
42 m to the north
14 m/s to the north
3.4 × 10
4
kg
•
m/s
2500 kg
(−1.56 × 10
4
kg
•
m/s) + (5.0 × 10
4
kg
•
m/s)
2500 kg
(−6250 N)(2.50 s) + (2500 kg)(20.0 m/s)
2500 kg
a. F =
mv
f
∆
−
t
mv
i
=
F = 1.22 × 10
4
N =
b. ∆x =
1
2
(v
i
+ v
f
)(∆t) =
1
2
(−20.0 m/s + 0 m/s)(5.33 s) =−53.3 m
∆x = 53.3 m to the west
1.22 × 10
4
N to the east
(3250 kg)(0 m/s) − (3250 kg)(−20.0 m/s)
5.33 s
Momentum and Collisions, Practice C
Section One—Student Edition Solutions I Ch. 6–3
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. m
1
= 0.145 kg
m
2
= 3.00 g
v
2
= 1.50 × 10
3
m/s
3. m = 0.42 kg
v
i
= 12 m/s downfield
v
f
= 18 m/s downfield
∆t = 0.020 s
a. m
1
v
1
= m
2
v
2
v
1
=
m
m
2
v
1
2
==
b. KE
1
=
1
2
m
1
v
1
2
=
1
2
(0.145 kg)(31.0 m/s)
2
= 69.7 J
KE
2
=
1
2
m
2
v
2
2
=
1
2
(3.00 × 10
−3
kg)(1.50 × 10
3
m/s)
2
= 3380 J
The bullet has greater kinetic energy.KE
2
> KE
1
31.0 m/s
(3.00 × 10
−3
kg)(1.50 × 10
3
m/s)
(0.145 kg)
a. ∆p = mv
f
− mv
i
= (0.42 kg)(18 m/s) − (0.42 kg)(12 m/s)
∆p = 7.6 kg
•
m/s − 5.0 kg•m/s =
b. F =
∆
∆
p
t
=
2.6
0.
k
0
g
2
•
0
m
s
/s
= 1.3 × 10
2
N downfield
2.6 kg
•
m/s downfield
Momentum and Collisions, Section 1 Review
Givens Solutions
1. m
1
= 63.0 kg
m
2
= 10.0 kg
v
2,i
= 0 m/s
v
2,f
= 12.0 m/s
v
1,i
= 0 m/s
2. m
1
= 85.0 kg
m
2
= 135.0 kg
v
1,i
= 4.30 m/s to the west
=−4.30 m/s
v
2,i
= 0 m/s
3. m
1
= 0.50 kg
v
1,i
= 12.0 m/s
v
2,i
= 0 m/s
m
2
= 0.50 kg
v
1,f
= 0 m/s
v
1,f
= 2.4 m/s
a. v
2,f
=
m
1
= m
2
v
2,f
= v
1,i
+ v
2,i
− v
1,f
= 12.0 m/s + 0 m/s − 0 m/s =
b. v
2,f
= v
1,i
+ v
2,i
− v
1,f
= 12.0 m/s + 0 m/s − 2.4 m/s = 9.6 m/s
12.0 m/s
m
1
v
1,i
+ m
2
v
2,i
− m
1
v
1,f
m
2
Momentum and Collisions, Practice D
v
f
=
m
1
v
m
1,
1
i
+
+
m
m
2
2
v
2,i
=
v
f
==−1.66 m/s = 1.66 m/s to the west
(85.0 kg)(−4.30 m/s)
220.0 kg
(85.0 kg)(−4.30 m/s) + (135.0 kg)(0 m/s)
85.0 kg + 135.0 kg
v
1,f
=
v
1,f
==−1.90 m/s
astronaut speed = 1.90 m/s
(63.0 kg)(0 m/s) + (10.0 kg)(0 m/s) − (10.0 kg)(12.0 m/s)
63.0 kg
m
1
v
1,i
+ m
2
v
2,i
− m
2
v
2,f
m
1
Holt Physics Solution ManualI Ch. 6–4
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. m
1
= 44 kg m
2
= 22 kg
v
1,i
= 0 m/s
v
2,i
= 0 m/s
v
1,f
= 3.5 m/s backward
=−3.5 m/s
v
1,i
= 0 m/s
v
2,i
= 4.6 m/s to the right
=+4.6 m/s
3. m
1
= 215 g
v
1,i
= 55.0 m/s
v
2,i
= 0 m/s
m
2
= 46 g
v
1,f
= 42.0 m/s
a. v
2,f
=
v
2,f
==
c. v
f
=
m
1
v
m
1,
1
i
+
+
m
m
2
2
v
2,i
=
v
f
=
(22 kg
6
)
6
(4
k
.
g
6 m/s)
= 1.5 m/s to the right
(44 kg)(0 m/s) + (22 kg)(4.6 m/s)
44 kg + 22 kg
7.0 m/s forward
(44 kg)(0 m/s) + (22 kg)(0 m/s) − (44 kg)(−3.5 m/s)
22 kg
m
1
v
1,i
+ m
2
v
2,i
− m
1
v
1,f
m
2
v
2,f
=
v
2,f
=
v
2,f
==
2.
0
8
.0
k
4
g
6
•
m
kg
/s
= 61 m/s
11.8 kg
•
m/s − 9.03 kg
•
m/s
0.046 kg
(0.215 kg)(55.0 m/s) + (0.046 kg)(0 m/s) − (0.215 kg)(42.0 m/s)
0.046 kg
m
1
v
1,i
+ m
2
v
2,i
− m
1
v
1,f
m
2
Givens Solutions
1. m
1
= 1500 kg
v
1,i
= 15.0 m/s to the south
=−15.0 m/s
m
2
= 4500 kg
v
2,i
= 0 m/s
2. m
1
= 9.0 kg
m
2
= 18.0 kg
v
2,i
= 0 m/s
v
1,i
= 5.5 m/s
3. m
1
= 1.50 × 10
4
kg
v
1,i
= 7.00 m/s north
m
2
= m
1
= m
v
2,i
= 1.50 m/s north
v
f
==
v
f
==−3.8 m/s = 3.8 m/s to the south
(1500 kg)(−15.0 m/s)
6.0 × 10
3
kg
(1500 kg)(−15.0 m/s) + (4500 kg)(0 m/s)
1500 kg + 4500 kg
m
1
v
1,i
+ m
2
v
2,i
m
1
+ m
2
v
f
==
v
f
=
(9.0 k
2
g
7
)
.
(
0
5
k
.5
g
m/s)
= 1.8 m/s
(9.0 kg)(5.5 m/s) + (18.0 kg)(0 m/s)
9.0 kg + 18.0 kg
m
1
v
1,i
+ m
2
v
2,i
m
1
+ m
2
v
f
===
1
2
(v
1,i
+ v
2,i
)
v
f
=
1
2
(7.00 m/s north + 1.50 m/s north)
v
f
= 4.25 m/s to the north
m(v
1,i
+ v
2,i
)
2m
(m
1
v
1,i
+ m
2
v
2,i
)
m
1
+ m
2
Momentum and Collisions, Practice E
Momentum and Collisions, Section 2 Review
4. m
1
= 2.0 kg + m
b
m
2
= 8.0 kg
v
2, i
= 0 m/s
v
2, f
= 3.0 m/s
v
1, i
= 0 m/s
v
1, f
=−0.60 m/s
m
i
v
1, i
+ m
2
v
2, i
= m
1
v
1, f
+ m
2
v
2, f
(2.0 kg + m
b
)(0 m/s) + (8.0 kg)(0 m/s) = (2.0 kg + m
b
)(−0.60 m/s) + (8.0 kg)(3.0 m/s)
(2.0 kg + m
b
)(0.60 m/s) = (8.0 kg)(3.0 m/s)
m
b
= =
m
b
= 38 kg
23 kg • m/s
0.60 m/s
24 kg • m/s − 1.2 kg • m/s
0.60 m/s
Section One—Student Edition Solutions I Ch. 6–5
I
5. m
1
= 47.4 kg
v
1,i
= 4.20 m/s
v
2,i
= 0 m/s
v
f
= 3.95 m/s
v
f
= 5.00 m/s
a. m
2
=
m
1
v
v
f
2,i
−
−
m
v
1
f
v
1,i
=
m
2
===
b. v
1,i
==
v
1,i
=
(50.4 k
4
g
7
)
.
(
4
5
k
.0
g
0 m/s)
= 5.32 m/s
(47.4 kg + 3.0 kg)(5.00 m/s) − (3.0 kg)(0 m/s)
47.4 kg
(m
1
+ m
2
)v
f
− m
2
v
2,i
m
1
3.0 kg
−12 kg
•
m/s
−3.95 m/s
187 kg
•
m/s − 199 kg
•
m/s
−3.95 m/s
(47.4 kg)(3.95 m/s) − (47.4 kg)(4.20 m/s)
0 m/s − 3.95 m/s
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
4. m
1
= 22 kg
m
2
= 9.0 kg
v
2,i
= 0 m/s
v
f
= 3.0 m/s to the right
v
1,i
==
v
1,i
=
(31 kg
2
)
2
(3
k
.
g
0 m/s)
= 4.2 m/s to the right
(22 kg + 9.0 kg)(3.0 m/s) − (9.0 kg)(0 m/s)
22 kg
(m
1
+ m
2
)v
f
− m
2
v
2,i
m
1
1. m
1
= 0.25 kg
v
1,i
= 12 m/s to the west
= −12 m/s
m
2
= 6.8 kg
v
2,i
= 0 m/s
2. m
1
= 0.40 kg
v
1,i
= 8.5 m/s to the south
= −8.5 m/s
m
2
= 0.15 kg
v
2,i
= 0 m/s
a. v
f
=
m
1
v
m
1,
1
i
+
+
m
m
2
2
v
2,i
=
v
f
=
(0.25 k
7
g
.
)
0
(−
k
1
g
2 m/s)
=−0.43 m/s =
b. ∆KE = KE
f
− KE
i
KE
i
=
1
2
m
1
v
1,i
2
+
1
2
m
2
v
2,i
2
=
1
2
(0.25 kg)(−12 m/s)
2
+
1
2
(6.8 kg)(0 m/s)
2
KE
i
= 18 J + 0 J = 18 J
KE
f
=
1
2
(m
1
+ m
2
)v
f
2
=
1
2
(0.25 kg + 6.8 kg)(−0.43 m/s)
2
KE
f
=
1
2
(7.0 kg)(−0.43 m/s)
2
= 0.65 J
∆KE = KE
f
− KE
i
= 0.65 J − 18 J =−17 J
The kinetic energy decreases by .17 J
0.43 m/s to the west
(0.25 kg)(−12 m/s) + (6.8 kg)(0 m/s)
0.25 kg + 6.8 kg
a. v
f
=
m
1
v
m
1,
1
i
+
+
m
m
2
2
v
2,i
=
v
f
=
(0.40 k
0
g
.5
)(
5
−
k
8
g
.5 m/s)
=−6.2 m/s =
b. ∆KE = KE
f
− KE
i
KE
i
=
1
2
m
1
v
1,i
2
+
1
2
m
2
v
2,i
2
=
1
2
(0.40 kg)(−8.5 m/s)
2
+
1
2
(0.15 kg)(0 m/s)
2
KE
i
= 14 J + 0 J = 14 J
KE
f
=
1
2
(m
1
+ m
2
)v
f
2
=
1
2
(0.40 kg + 0.15 kg)(−6.2 m/s)
2
KE
f
=
1
2
(0.55 kg)(−6.2 m/s)
2
= 11 J
∆KE = KE
f
− KE
i
= 11 J − 14 J =−3 J
The kinetic energy decreases by .3 J
6.2 m/s to the south
(0.40 kg)(−8.5 m/s) + (0.15 kg)(0 m/s)
0.40 kg + 0.15 kg
Momentum and Collisions, Practice F
I
3. m
1
= 56 kg
v
1,i
= 4.0 m/s to the north
= +4.0 m/s
m
2
= 65 kg
v
2,i
= 12.0 m/s to the south
= −12.0 m/s
a. v
f
=
m
1
v
m
1,
1
i
+
+
m
m
2
2
v
2,i
=
v
f
===−4.6 m/s
v
f
=
b. ∆KE = KE
f
− KE
i
KE
i
=
1
2
m
1
v
1,i
2
+
1
2
m
2
v
2,i
2
=
1
2
(56 kg)(4.0 m/s)
2
+
1
2
(65 kg)(−12.0 m/s)
2
KE
i
= 450 J + 4700 J = 5200 J
KE
f
=
1
2
(m
1
+ m
2
)v
f
2
=
1
2
(56 kg + 65 kg)(−4.6 m/s)
2
KE
f
=
1
2
(121 kg)(−4.6 m/s)
2
= 1300 J
∆KE = KE
f
− KE
i
= 1300 J − 5200 J =−3900 J
The kinetic energy decreases by .3.9 × 10
3
J
4.6 m/s to the south
−560 kg
•
m/s
121 kg
220 kg
•
m/s − 780 kg
•
m/s
121 kg
(56 kg)(4.0 m/s) + (65 kg)(−12.0 m/s)
56 kg + 65 kg
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. m
1
= 0.015 kg
v
1,i
= 22.5 cm/s to the right
= +22.5 cm/s
m
2
= 0.015 kg
v
2,i
= 18.0 cm/s to the left
= −18.0 cm/s
v
1,f
= 18.0 cm/s to the left
= −18.0 cm/s
2. m
1
= 16.0 kg
v
1,i
= 12.5 m/s to the left,
v
1,i
= −12.5 m/s
m
2
= 14.0 kg
v
2,i
= 16.0 m/s to the right,
v
2,i
= 16.0 m/s
v
2,f
= 14.4 m/s to the left,
v
1,f
= −14.4 m/s
a. v
2,f
=
m
1
= m
2
v
2,f
= v
1,i
+ v
2,i
− v
1,f
= 22.5 cm/s + (−18.0 cm/s) − (−18.0 cm/s)
v
2,f
= 22.5 cm/s =
b. KE
i
=
1
2
m
1
v
1,i
2
+
1
2
m
2
v
2,i
2
KE
i
=
1
2
(0.015 kg)(0.225 m/s)
2
+
1
2
(0.015 kg)(−0.180 m/s)
2
KE
i
= 3.8 × 10
−4
J + 2.4 × 10
−4
J =
KE
f
=
1
2
m
1
v
1,f
2
+
1
2
m
2
v
2,f
2
KE
f
=
1
2
(0.015 kg)(−0.180 m/s)
2
+
1
2
(0.015 kg)(0.225 m/s)
2
KE
f
= 2.4 × 10
−4
J + 3.8 × 10
−4
J = 6.2 × 10
−4
J
6.2 × 10
−4
J
22.5 cm/s to the right
m
1
v
1,i
+ m
2
v
2,i
− m
1
v
1,f
m
2
a. v
1,f
=
v
1,f
=
v
1,f
==14.1 m/s
v
1,f
= 14.1 m/s to the right
−200 kg
•
m/s + 224 kg
•
m/s + 202 kg
•
m/s
16.0 kg
(16.0 kg)(−12.5 m/s) + (14.0 kg)(16.0 m/s) − (14.0 kg)(−14.4 m/s)
16.0 kg
(m
1
v
1,i
+ m
2
v
2,i
− m
2
v
2,f
)
m
1
Momentum and Collisions, Practice G
Holt Physics Solution ManualI Ch. 6–6
I
b. KE
i
=
1
2
m
1
v
1,i
2
+
1
2
m
2
v
2,i
2
KE
i
=
1
2
(16.0 kg)(−12.5 m/s)
2
+
1
2
(14.0 kg)(16.0 m/s)
2
KE
i
= 1.25 × 10
3
J + 1.79 × 10
3
J =
KE
f
=
1
2
m
1
v
1,f
2
+
1
2
m
2
v
2,f
2
KE
f
=
1
2
(16.0 kg)(14.1 m/s)
2
+
1
2
(14.0 kg)(−14.4 m/s)
2
KE
f
= 1.59 × 10
3
J + 1.45 × 10
3
J = 3.04 × 10
3
J
3.04 × 10
3
J
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
3. m
1
= 4.0 kg
v
1,i
= 8.0 m/s to the right
m
2
= 4.0 kg
v
2,i
= 0 m/s
v
1,f
= 0 m/s
4. m
1
= 25.0 kg
v
1, i
= 5.00 m/s to the right
m
2
= 35.0 kg
v
1, f
= 1.50 m/s to the right
v
2, f
= 4.50 m/s to the right
a. v
2, i
=
v
2, i
=
v
2, i
= =
v
2, i
= 2.0 m/s =
b. KE
i
=
1
2
m
i
v
1, i
2
+
1
2
m
2
v
2, i
2
KE
i
=
1
2
(25.0 kg)(5.00 m/s)
2
+
1
2
(35.0 kg)(2.0 m/s)
2
KE
i
= 312 J + 7.0 × 10
1
J =
KE
f
=
1
2
m
1
v
1, f
2
+
1
2
m
2
v
2, f
2
KE
f
=
1
2
(25.0 kg)(1.50 m/s)
2
+
1
2
(35.0 kg)(4.50 m/s)
2
KE
f
= 28.1 J + 354 J = 382 J
382 J
2.0 m/s to the right
7.0 × 10
1
kg
•
m/s
35.0 kg
37.5 kg
•
m/s + 158 kg
•
m/s − 125 kg
•
m/s
35.0 kg
(25.0 kg)(1.50 m/s) + (35.0 kg)(4.50 m/s) − (25.0 kg)(5.00 m/s)
35.0 kg
m
i
v
1, f
+ m
2
v
2, f
− m
1
v
1, i
m
2
a. v
2,f
=
m
1
= m
2
v
2,f
= v
1,i
+ v
2,i
− v
1,f
= 8.0 m/s + 0 m/s − 0 m/s
v
2,f
= 8.0 m/s =
b. KE
i
=
1
2
m
1
v
1,i
2
+
1
2
m
2
v
2,i
2
KE
i
=
1
2
(4.0 kg)(8.0 m/s)
2
+
1
2
(4.0 kg)(0 m/s)
2
KE
i
= 130 J + 0 J =
KE
f
=
1
2
m
1
v
1,f
2
+
1
2
m
2
v
2,f
2
KE
f
=
1
2
(4.0 kg)(0 m/s)
2
+
1
2
(4.0 kg)(8.0 m/s)
2
KE
f
= 0 J + 130 J = 1.3 × 10
2
J
1.3 × 10
2
J
8.0 m/s to the right
m
1
v
1,i
+ m
2
v
2,i
− m
1
v
1,f
m
2
Section One—Student Edition Solutions I Ch. 6–7
Holt Physics Solution ManualI Ch. 6–8
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. m
1
= 95.0 kg
v
1,i
= 5.0 m/s to the south,
v
1,i
= −5.0 m/s
m
2
= 90.0 kg
v
2,i
= 3.0 m/s to the north,
v
2,i
= 3.0 m/s
3. m
1
= m
2
= 0.40 kg
v
1,i
= 0 m/s
v
2,i
= 3.5 m/s
v
2,f
= 0 m/s
a. v
f
=
v
f
=
v
f
===−1.1 m/s
v
f
=
b. ∆KE = KE
f
− KE
i
KE
i
=
1
2
m
1
v
1,i
2
+
1
2
m
2
v
2,i
2
=
1
2
(95.0 kg)(−5.0 m/s)
2
+
1
2
(90.0 kg)(3.0 m/s)
2
KE
i
= 1200 J + 400 J = 1600 J
KE
f
=
1
2
m
f
v
1,f
2
=
1
2
(m
1
+ m
2
)v
1,f
2
=
1
2
(95.0 kg + 90.0 kg)(1.1 m/s)
2
KE
f
=
1
2
(185 kg)(1.2 m
2
/s
2
) = 220 J
∆KE = KE
f
− KE
i
= 220 J − 1600 J =−1400 J
The kinetic energy decreases by 1.4 × 10
3
J.
1.1 m/s to the south
−210 kg
•
m/s
185 kg
−480 kg
•
m/s + 270 kg
•
m/s
185 kg
(95.0 kg)(−5.0 m/s) + (90.0 kg)(3.0 m/s)
95.0 kg + 90.0 kg
(m
1
v
1,i
+ m
2
v
2,i
)
m
1
+ m
2
a. v
1,f
=
m
1
= m
2
v
1,f
= v
1,i
+ v
2,i
− v
2,f
= 0 m/s + 3.5 m/s − 0 m/s =
b. KE
1,i
=
1
2
m
1
v
1,i
2
=
1
2
(0.40 kg)(0 m/s)
2
=
c. KE
2,f
=
1
2
m
2
v
2,f
2
=
1
2
(0.40 kg)(0 m/s)
2
= 0 J
0 J
3.5 m/s
m
1
v
1,i
+ m
2
v
2,i
− m
2
v
2,f
m
1
Momentum and Collisions, Section 3 Review
Givens Solutions
11. m = 1.67 × 10
−27
kg
v = 5.00 × 10
6
m/s straight up
m = 15.0 g
v = 325 m/s to the right
m = 75.0 kg
v = 10.0 m/s southwest
m = 5.98 × 10
24
kg
v = 2.98 × 10
4
m/s forward
a. p = mv = (1.67 × 10
−27
kg)(5.00 × 10
6
m/s) =
b. p = mv = (15.0 × 10
−3
kg)(325 m/s) =
c. p = mv = (75.0 kg)(10.0 m/s) =
d. p = mv = (5.98 × 10
24
kg)(2.98 × 10
4
m/s) = 1.78 × 10
29
kg
•
m/s forward
7.50 × 10
2
kg
•
m/s to the southwest
4.88 kg
•
m/s to the right
8.35 × 10
−21
kg
•
m/s upward
Momentum and Collisions, Chapter Review
Section One—Student Edition Solutions I Ch. 6–9
I
12. m
1
= 2.5 kg
v
i
= 8.5 m/s to the left
= −8.5 m/s
v
f
= 7.5 m/s to the right
= +7.5 m/s
∆t = 0.25 s
13. m = 0.55 kg
v
i
= 0 m/s
v
f
= 8.0 m/s
∆t = 0.25 s
14. m = 0.15 kg
v
i
= 26 m/s
v
f
= 0 m/s
F =−390 N
22. m
1
= 65.0 kg
v
1,i
= 2.50 m/s forward
m
2
= 0.150 kg
v
2,i
= 2.50 m/s forward
v
2,f
= 32.0 m/s forward
m
1
= 60.0 kg
v
1,i
= 0 m/s
m
2
= 0.150 kg
v
2,i
= 32.0 m/s forward
F =
mv
f
∆
−
t
mv
i
==
F = 18 N
4.4 kg
•
m/s
0.25 s
(0.55 kg)(8.0 m/s) − (0.55 kg)(0 m/s)
0.25 s
∆t =
mv
f
−
F
mv
i
=
∆t =
−(0.15
−
k
3
g
9
)
0
(2
N
6 m/s)
=
∆x =
1
2
(v
i
+ v
f
)∆t =
1
2
(26.0 m/s + 0 m/s)(0.010 s) = 0.13 m
0.010 s
(0.15 kg)(0 m/s) − (0.15 kg)(26 m/s)
−390 N
a. v
1,f
=
v
1,f
=
v
1,f
==
v
1,f
==
b. v
f
==
v
f
==7.97 × 10
−2
m/s forward
(0.150 kg)(32.0 m/s)
60.2 kg
(60.0 kg)(0 m/s) + (0.150 kg)(32.0 m/s)
60.0 kg + 0.150 kg
m
1
v
1,i
+ m
2
v
2,i
m
1
+ m
2
2.43 m/s forward
158 kg
•
m/s
65.0 kg
162 kg
•
m/s − 4.42 kg
•
m/s
65.0 kg
162 kg
•
m/s + 0.375 kg
•
m/s − 4.80 kg
•
m/s
65.0 kg
(65.0 kg)(2.50 m/s) + (0.150 kg)(2.50 m/s) − (0.150 kg)(32.0 m/s)
65.0 kg
m
1
v
1,i
+ m
2
v
2,i
− m
2
v
2,f
m
1
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
F =
mv
f
∆
−
t
mv
i
=
F ===160 N to the right
4.0 × 10
1
kg
•
m/s
0.25 s
19 kg
•
m/s + 21 kg
•
m/s
0.25 s
(2.5 kg)(7.5 m/s) − (2.5 kg)(−8.5 m/s)
0.25 s
23. m
1
= 55 kg
m
2
= 0.057 kg
v
2,i
= 0 m/s
v
1,i
= 0 m/s
v
2,f
= 36 m/s to the north
Because the initial momentum is zero,
m
1
v
1,f
=−m
2
v
2,f
v
1,f
=
−m
m
2
v
1
2,f
==−0.037 m/s
v
1,f
= 0.037 m/s to the south
−(0.057 kg)(36 m/s)
55 kg
Holt Physics Solution ManualI Ch. 6–10
I
28. m
1
= 4.0 kg
m
2
= 3.0 kg
v
1,i
= 5.0 m/s
v
2,i
=−4.0 m/s
29. m
1
= 1.20 kg
v
1,i
= 5.00 m/s
m
2
= 0.800 kg
v
2,i
= 0 m/s
30. m
1
= 2.00 × 10
4
kg
v
1,i
= 3.00 m/s
m
2
= 2m
1
v
2,i
= 1.20 m/s
31. m
1
= 88 kg
v
1,i
= 5.0 m/s to the east
= +5.0 m/s
m
2
= 97 kg
v
2,i
= 3.0 m/s to the west
= −3.0 m/s
v
f
=
m
1
v
m
1,
1
i
+
+
m
m
2
2
v
2,i
=
v
f
=
(1.20 k
2
g
.0
)(
0
5
k
.0
g
0 m/s)
= 3.00 m/s
(1.20 kg)(5.00 m/s) + (0.800 kg)(0 m/s)
1.20 kg + 0.800 kg
a. v
f
=
m
1
v
m
1,
1
i
+
+
m
m
2
2
v
2,i
=
v
f
=
v
f
==
b. ∆KE = KE
f
− KE
i
KE
i
=
1
2
m
1
v
1,i
2
+
1
2
m
2
v
2,i
2
=
1
2
(2.00 × 10
4
kg)(3.00 m/s)
2
+
1
2
(2)(2.00 × 10
4
kg)(1.20 m/s)
2
KE
i
= 9.00 × 10
4
J + 2.88 × 10
4
J = 11.88 × 10
4
J
KE
f
=
1
2
(m
1
+ m
2
)v
f
2
=
1
2
(2.00 × 10
4
kg + 4.00 × 10
4
kg)(1.80 m/s)
2
= 9.72 × 10
4
J
∆KE = KE
f
− KE
i
= 9.72 × 10
4
J − 11.88 × 10
4
J =−2.16 × 10
4
J
The kinetic energy decreases by .2.16 × 10
4
J
1.80 m/s
10.80 × 10
4
kg
•
m/s
6.00 × 10
4
kg
6.00 × 10
4
kg
•
m/s + 4.80 × 10
4
kg
•
m/s
6.00 × 10
4
kg
(2.00 × 10
4
kg)(3.00 m/s) + (2)(2.00 × 10
4
kg)(1.20 m/s)
(2.00 × 10
4
kg) + (2)(2.00 × 10
4
kg)
a. v
f
=
m
1
v
m
1,
1
i
+
+
m
m
2
2
v
2,i
=
v
f
===
b. ∆KE = KE
f
− KE
i
KE
i
=
1
2
m
1
v
1,i
2
+
1
2
m
2
v
2,i
2
=
1
2
(88 kg)(5.0 m/s)
2
+
1
2
(97 kg)(−3.0 m/s)
2
KE
i
= 1100 J + 440 J = 1.5 × 10
3
J
KE
f
=
1
2
(m
1
+ m
2
)v
f
2
=
1
2
(88 kg + 97 kg)(0.81 m/s)
2
=
1
2
(185 kg)(0.81 m/s)
2
= 61 J
∆KE = KE
f
− KE
i
= 61 J − 1.5 × 10
3
J = −1.4 × 10
3
J
The kinetic energy decreases by .1.4 × 10
3
J
0.81 m/s to the east
150 kg
•
m/s
185 kg
440 kg
•
m/s − 290 kg
•
m/s
185 kg
(88 kg)(5.0 m/s) + (97 kg)(−3.0 m/s)
88 kg + 97 kg
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
v
f
=
m
1
v
m
1,
1
i
+
+
m
m
2
2
v
2,i
=
v
f
===1 m/s
8 kg
•
m/s
7.0 kg
2.0 × 10
1
kg
•
m/s + (−12 kg
•
m/s)
7.0 kg
(4.0 kg)(5.0 m/s) + (3.0 kg)(−4.0 m/s)
4.0 kg + 3.0 kg
Section One—Student Edition Solutions I Ch. 6–11
I
32. m
1
= 5.0 g
v
1,i
= 25.0 cm/s to the right
= +25.0 cm/s
m
2
= 15.0 g
v
2,i
= 0 m/s
v
1,f
= 12.5 cm/s to the left
= −12.5 cm/s
33. v
1,i
= 4.0 m/s
v
2,i
= 0 m/s
m
1
= m
2
v
1,f
= 0 m/s
34. m
1
= 25.0 g
v
1,i
= 20.0 cm/s to the right
m
2
= 10.0 g
v
2,i
= 15.0 cm/s to the right
v
2,f
= 22.1 cm/s to the right
a. v
2,f
=
v
2,f
=
v
2,f
===12 cm/s
v
2,f
=
b. ∆KE
2
= KE
2,f
−KE
2,i
=
1
2
m
2
v
2,f
2
−
1
2
m
2
v
2,i
2
∆KE
2
=
1
2
(15.0 × 10
−3
kg)(0.12 m/s)
2
−
1
2
(15.0 × 10
−3
kg)(0 m/s)
2
∆KE
2
= 1.1 × 10
−4
J
12 cm/s to the right
180 g
•
cm/s
15.0 g
120 g
•
cm/s + 62 g
•
cm/s
15.0 g
(5.0 g)(25.0 cm/s) + (15.0 g)(0 m/s) − (5.0 g)(−12.5 cm/s)
15.0 g
m
1
v
1,i
+ m
2
v
2,i
− m
1
v
1,f
m
2
v
2,f
=
m
1
= m
2
v
2,f
= v
1,i
+ v
2,i
− v
1,f
= 4.0 m/s + 0 m/s − 0 m/s = 4.0 m/s
m
1
v
1,i
+ m
2
v
2,i
− m
1
v
1,f
m
2
v
1,f
=
v
1,f
=
v
1,f
=
v
1,f
==17.2 cm/s to the right
429 g
•
cm/s
25.0 g
5.00 × 10
2
g
•
cm/s + 1.50 × 10
2
g
•
cm/s − 2.21 × 10
2
g
•
cm/s
25.0 g
(25.0 g)(20.0 cm/s) + (10.0 g)(15.0 cm/s) − (10.0 g)(22.1 cm/s)
25.0 g
m
1
v
1,i
+ m
2
v
2,i
− m
2
v
2,f
m
1
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
35. m = 0.147 kg
p = 6.17 kg
•
m/s toward
second base
v =
m
p
= = 42.0 m/s toward second base
6.17 kg
•
m/s
0.147 kg
36. KE = 150 J
p = 30.0 kg
•m/s
KE =
1
2
mv
2
m =
p
v
KE =
1
2
p
v
v
2
=
p
2
v
v =
2K
p
E
=
3
(
0
2
.0
)(
k
1
g
5
•
0
m
J)
/s
=
m =
p
v
==3.0 kg
30.0 kg
•
m/s
1.0 × 10
1
m/s
1.0 × 10
1
m/s
Holt Physics Solution ManualI Ch. 6–12
39. m
1
= 5.5 g
m
2
= 22.6 g
v
2,i
= 0 m/s
∆y =−1.5 m
∆x = 2.5 m
a =−9.81 m/s
2
For an initial downward speed of zero,
∆y =
1
2
a∆t
2
∆t =
2∆
a
y
v
f
=
∆
∆
x
t
== ∆x
2∆
a
y
v
f
= (2.5 m)
= 4.5 m/s
v
1, i
=
v
1, i
=
v
1, i
= = 23 m/s
(28.1 × 10
−3
kg)(4.5 m/s)
5.5 × 10
−3
kg
(5.5 g + 22.6 g)(1 kg/10
3
g)(4.5 m/s) − (22.6 × 10
−3
kg)(0 m/s)
5.5 × 10
−3
kg
(m
1
+ m
2
)v
f
− m
2
v
2, i
m
1
−9.81 m/s
2
(2)(−1.5 m)
∆x
2
∆
a
y
I
38. m
1
= 3.00 kg
v
2,i
= 0 m/s
v
f
=
1
3
v
1,i
,or v
1,i
= 3v
f
m
1
v
1,i
+ m
2
v
2,i
= m
1
v
f
+ m
2
v
f
m
2
(v
2,i
− v
f
) = m
1
v
f
− m
1
v
1,i
m
2
=
m
1
v
v
f
2,i
−
−
m
v
1
f
v
1,i
,where v
2,i
= 0 m/s
m
2
=
m
1
v
f
−
−
m
v
f
1
(3v
f
)
=−(m
1
− 3m
1
) =−m
1
+ 3m
1
m
2
= 2m
1
= (2)(3.00 kg) = 6.00 kg
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
37. m = 0.10 kg
v
i
= 15.0 m/s straight up
a =−9.81 m/s
2
a. At its maximum height, v = 0 m/s.
p = mv = (0.10 kg)(0 m/s) =
b. Halfway to its maximum height (where v
f
= 0 m/s),
∆y =
1
2
v
f
2
2
−
a
v
i
2
==5.73 m
Now let v
f
represent the velocity at ∆y = 5.73 m.
v
f
=±
v
i
2
+
2
a∆
x
=±
(1
5.
0
m
/s
)
2
+
(
2)
(−
9
.8
1
m
/s
2
)
(5
.7
3
m
)
v
f
=±
22
5
m
2
/
s
2
−
1
12
m
2
/
s
2
=±
11
3
m
2
/
s
2
= ±10.6 m/s
v
f
= 10.6 m/s upward
p = mv
f
= (0.10 kg)(10.6 m/s) = 1.1 kg
•
m/s upward
(0 m/s)
2
− (15.0 m/s)
2
(4)(−9.81 m/s
2
)
0.0 kg
•
m/s
Section One—Student Edition Solutions I Ch. 6–13
I
40. m
1
=
9.
7
8
3
1
0
m
N
/s
2
R = 5.0 m
m
2
= 2.6 kg
v
1,i
= 0 m/s
v
2,i
= 0 m/s
v
2,f
= 5.0 m/s to the north
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Because the initial momentum is zero,
v
1,f
=
−m
m
2
v
1
2,f
==−0.17 m/s = 0.17 m/s to the south
∆t =
v
∆
1
x
,f
=
v
−
1
R
,f
=
−0
−
.
5
1
.
7
0
m
m
/s
= 29 s
−(2.6 kg)(5.0 m/s)
9.
7
8
3
1
0
m
N
/s
2
41. m = 0.025 kg
v
i
= 18.0 m/s
∆t = 5.0 × 10
−4
s
v
f
= 10.0 m/s
F =
mv
f
∆
−
t
mv
i
=
F ===−4.0 × 10
2
N
magnitude of the force = 4.0 × 10
2
N
−0.20 kg
•
m/s
5.0 × 10
−4
s
0.25 kg
•
m/s − 0.45 kg
•
m/s
5.0 × 10
−4
s
(0.025 kg)(10.0 m/s) − (0.025 kg)(18.0 m/s)
5.0 × 10
−4
s
42. m
1
= 1550 kg
v
1,i
= 10.0 m/s to the south
= −10.0 m/s
m
2
= 2550 kg
v
f
= 5.22 m/s to the north
= +5.22 m/s
v
2,i
==
v
2,i
=
v
2,i
==
v
2,i
= 14.5 m/s = 14.5 m/s to the north
3.69 × 10
4
kg
•
m/s
2550 kg
2.14 × 10
4
kg
•
m/s + 1.55 × 10
4
kg
•
m/s
2550 kg
(4.10 × 10
3
kg)(5.22 m/s) − (1550 kg)(−10.0 m/s)
2550 kg
(1550 kg + 2550 kg)(5.22 m/s) − (1550 kg)(−10.0 m/s)
2550 kg
(m
1
+ m
2
)v
f
− m
1
v
1,i
m
2
43. m
1
= 52.0 g
m
2
= 153 g
v
1,i
= 0 m/s
v
2,i
= 0 m/s
v
1,f
= 2.00 m/s
g = 9.81 m/s
2
Because the initial momentum is zero,
v
2,f
=
−m
m
1
2
v
1,f
=
−(52.0 g
1
)
5
(
3
2.
g
00 m/s)
=−0.680 m/s
KE
i
= PE
f
1
2
mv
2,f
2
= mgh
h =
v
2
2
,
g
f
2
=
(
(
2
−
)
0
(
.
9
6
.
8
8
0
1
m
m
/
/
s
s
)
2
2
)
= 2.36 × 10
−2
m = 2.36 cm
44. m
1
= 85.0 kg
m
2
= 0.500 kg
v
1, i
= 0 m/s
v
2, i
= 0 m/s
v
2, f
= 20.0 m/s away from
ship =−20.0 m/s
∆x = 30.0 m
Because the initial momentum is zero,
v
1, f
== =0.118 m/s toward the ship
∆t =
v
∆
1
x
,f
=
0.
3
1
0
1
.
8
0
m
m
/s
= 254 s
−(0.500 kg)(−20.0 m/s)
85.0 kg
−m
2
v
2, f
m
1
Holt Physics Solution ManualI Ch. 6–14
45. m
1
= 2250 kg
v
1, i
= 10.0 m/s
m
2
= 2750 kg
v
2, i
= 0 m/s
d = 2.50 m
θ
= 180°
g = 9.81 m/s
2
v
f
= =
v
f
= = 4.50 m/s
From the work-kinetic energy theorem,
W
net
=∆KE = KE
f
− KE
i
=
1
2
(m
1
+ m
2
)(v
f
′)
2
−
1
2
(m
1
+ m
2
)(v
i
′)
2
where
v
i
′=4.50 m/s v
f
′=0 m/s
W
net
= W
friction
= F
k
d(cos
θ
) = (m
1
+ m
2
)g
µ
k
d(cos
θ
)
(m
1
+ m
2
)g
µ
k
d(cos
θ
) =
1
2
(m
1
+ m
2
)[(v
f
′)
2
− (v
i
′)
2
]
µ
k
= = =
µ
k
= 0.413
−(4.50 m/s)
2
−(2)(9.81 m/s
2
)(2.50 m)
(0 m/s)
2
− (4.50 m/s)
2
(2)(9.81 m/s
2
)(2.50 m)(cos 180°)
(v
f
′)
2
− (v
i
′)
2
2 gd(cos
θ
)
(2250 kg)(10.0 m/s)
5.00 × 10
3
kg
(2250 kg)(10.0 m/s) + (2750 kg)(0 m/s)
2250 kg + 2750 kg
m
i
v
1, i
+ m
2
v
2, i
m
1
+ m
2
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
46. F = 2.5 N to the right
m = 1.5 kg
∆t = 0.50 s
v
i
= 0 m/s
v
i
= 2.0 m/s to the left
= −2.0 m/s
a. v
f
=
F∆t
m
+ mv
i
=
v
f
= 0.83 m/s
b. v
f
=
F∆t
m
+ mv
i
=
v
f
===−1.2 m/s
v
f
= 1.2 m/s to the left
−1.8 kg
•
m/s
1.5 kg
1.2 N
•
s + (−3.0 kg
•
m/s)
1.5 kg
(2.5 N)(0.50 s) + (1.5 kg)(−2.0 m/s)
1.5 kg
0.83 m/s to the right
(2.5 N)(0.50 s) + (1.5 kg)(0 m/s)
1.5 kg
47. m
1
= m
2
v
1,i
= 22 cm/s
v
2,i
=−22 cm/s
Because m
1
= m
2
, v
2,f
= v
1,i
+ v
2,i
− v
1,f
.
Because kinetic energy is conserved and the two masses are equal,
1
2
v
1,i
2
+
1
2
v
2,i
2
=
1
2
v
1,f
2
+
1
2
v
2,f
2
v
1,i
2
+ v
2,i
2
= v
1,f
2
+ v
2,f
2
v
1,i
2
+ v
2,i
2
= v
1,f
2
+ (v
1,i
+ v
2,i
− v
1,f
)
2
(22 cm/s)
2
+ (−22 cm/s)
2
= v
1,f
2
+ (22 cm/s − 22 cm/s − v
1,f
)
2
480 cm
2
/s
2
+ 480 cm
2
/s
2
= 2v
1,f
2
v
1, f
=±
48
0
cm
2
/
s
2
=±22 cm/s
Because m
1
cannot pass through m
2
, it follows that v
1, f
is opposite v
1, i
.
v
1, f
=
v
2, f
= v
1, i
+ v
2, i
− v
1, f
v
2, f
= 22 cm/s + (−22 cm/s) − (−22 cm/s) = 22 cm/s
−22 cm/s
Section One—Student Edition Solutions I Ch. 6–15
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
48. m
1
= 7.50 kg
∆y =−3.00 m
m
2
= 5.98 × 10
24
kg
v
1,i
= 0 m/s
v
2,i
= 0 m/s
a =−9.81 m/s
2
a. v
1,f
=±2a
∆
y
=±
(2
)(
−
9.
81
m
/s
2
)
(−
3.
00
m
)
=±7.67 m/s =−7.67 m/s
Because the initial momentum is zero,
m
1
v
1,f
=−m
2
v
2,f
v
2,f
=
−m
m
1
2
v
1,f
==9.62 × 10
−24
m/s
−(7.50 kg)(−7.67 m/s)
5.98 × 10
24
kg
49. m = 55 kg
∆y =−5.0 m
∆t = 0.30 s
v
i
= 0 m/s
a =−9.81 m/s
2
v
i
= 9.9 m/s downward
=−9.9 m/s
v
f
= 0 m/s
a. v
f
=±2a
∆
y
=±
(2
)(
−
9.
81
m
/s
2
)
(−
5.
0
m
)
=±9.9 m/s
v
f
=−9.9 m/s =
b. F =
mv
f
∆
−
t
mv
i
=
F = 1.8 × 10
3
N = 1.8 × 10
3
N upward
(55 kg)(0 m/s) − (55 kg)(−9.9 m/s)
0.30 s
9.9 m/s downward
50. m
nuc
= 17.0 × 10
−27
kg
m
1
= 5.0 × 10
−27
kg
m
2
= 8.4 × 10
−27
kg
v
nuc,i
= 0 m/s
v
1,f
= 6.0 × 10
6
m/s along
the positive y-axis
v
2,f
= 4.0 × 10
6
m/s along
the positive x-axis
m
3
= m
nuc
− (m
1
+ m
2
) = (17.0 × 10
−27
kg) − [(5.0 × 10
−27
kg) + (8.4 × 10
−27
kg)]
m
3
= 3.6 × 10
−27
kg
p
1
= m
1
v
1,f
= (5.0 × 10
−27
kg)(6.0 × 10
6
m/s) = 3.0 × 10
−20
kg
•
m/s
p
2
= m
2
v
2,f
= (8.4 × 10
−27
kg)(4.0 × 10
6
m/s) = 3.4 × 10
−20
kg
•
m/s
Because the initial momentum is zero, the final momentum must also equal zero.
p
1
+ p
2
+ p
3
= 0 kg
•
m/s
p
3
=−(p
1
+ p
2
)
Because p
1
and p
2
are along the y-axis and the x-axis, respectively, the magnitude of
p
3
can be found by using the Pythagorean theorem.
p
3
=
p
1
2
+
p
2
2
=
(3
.0
×
1
0
−
20
k
g
•
m
/s
)
2
+
(
3.
4
×
1
0
−
20
k
g
•
m
/s
)
2
p
3
=
(9
.0
×
1
0
−
40
k
g
2
•
m
2
/
s
2
)
+
(
1.
2
×
1
0
−
39
k
g
2
•
m
2
/
s
2
)
p
3
=
(2
1
×
1
0
−
40
k
g
2
•
m
2
/
s
2
)
= 4.6 × 10
−20
kg
•
m/s
v
3,f
=
m
p
3
3
==
Because p
1,2
is between the positive x-axis and the positive y-axis and because
p
3
=−p
1,2
,p
3
must be between the negative x-axis and the negative y-axis.
tan q =
p
p
1
2
q = tan
−1
p
p
1
2
= tan
−1
3
3
.
.
0
4
= 41° below the negative x-axis
1.3 × 10
7
m/s
4.6 × 10
−20
kg
•
m/s
3.6 × 10
−27
kg
Holt Physics Solution ManualI Ch. 6–16
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
3. m = 0.148 kg
v = 35 m/s toward
home plate
p = mv = (0.148 kg)(35 m/s) = 5.2 kg
•
m/s toward home plate
4. m
1
= 1.5 kg
v
1,i
= 3.0 m/s to the right
m
2
= 1.5 kg
v
2,i
= 0 m/s
v
1,f
= 0.5 m/s to the right
a. v
2,f
=
m
1
= m
2
v
2,f
= v
1,i
+ v
2,i
− v
1,f
v
2,f
= 3.0 m/s + 0 m/s − 0.5 m/s = 2.5 m/s to the right
m
1
v
1,i
+ m
2
v
2,i
− m
1
v
1,f
m
2
8. m
1
= m
2
v
1,i
= 0 m/s
v
2,i
= 5.00 m/s to the right
v
2,f
= 0 m/s
v
1,f
=
m
1
= m
2
v
1,f
= v
1,i
+ v
2,i
− v
2,f
= 0 m/s + 5.00 m/s − 0 m/s
v
1,f
= 5.00 m/s to the right
m
1
v
1,i
+ m
2
v
2,i
− m
2
v
2,f
m
1
9. m
1
= 0.400 kg
v
1,i
= 3.50 cm/s right,
v
1,i
= 3.50 cm/s
m
2
= 0.600 kg
v
2,i
= 0
v
1,f
= 0.07 cm/s left,
v
1,f
=−0.70 cm/s
v
2,f
=
v
2,f
=
v
2,f
===2.80 cm/s
v
2,f
= 2.80 cm/s to the right
1.68 kg
•
cm/s
0.600 kg
1.40 kg
•
cm/s + 0.28 kg
•
cm/s
0.600 kg
(0.400 kg)(3.50 cm/s) + (0.600 kg)(0) − (0.400 kg)(−0.70 cm/s)
0.600 kg
m
1
v
1,i
+ m
2
v
2,i
− m
1
v
1,f
m
2
10. m
1
= 0.400 kg
v
1,f
=−0.70 × 10
−2
m/s
m
2
= 0.600 kg
v
2,f
= 2.80 × 10
−2
m/s
KE
f
=
1
2
m
1
v
1,f
2
+
1
2
m
2
v
2,f
2
KE
f
=
1
2
(0.400 kg)(−0.70 × 10
−2
m/s)
2
+
1
2
(0.600 kg)(2.80 × 10
−2
m/s)
2
KE
f
= 9.8 × 10
−6
kg
•
m
2
/s
2
+ 2.35 × 10
−4
kg
•
m
2
/s
2
KE
f
= 2.45 × 10
−4
J
13. m
1
= 8.0 g
m
2
= 2.5 kg
v
2,i
= 0 m/s
h = 6.0 cm
g = 9.81 m/s
2
KE
i
= PE
f
1
2
mv
f
2
= mgh
v
f
=
2g
h
=
(2
)(
9.
81
m
/s
2
)
(0
.0
60
m
)
= 1.1 m/s
v
1,i
==
v
1,i
=
(2.5
0
k
.0
g
0
)(
8
1
0
.1
kg
m/s)
= 340 m/s
(0.0080 kg + 2.5 kg)(1.1 m/s) − (2.5 kg)(0 m/s)
0.0080 kg
(m
1
+ m
2
)v
f
− m
2
v
2,i
m
1
Momentum and Collisions, Standardized Test Prep
Givens Solutions
5. v
1,f
= 0 m/s
v
2,f
= v
1,i
+ v
2,i
− v
1,f
= 3.0 m/s + 0 m/s − 0 m/s = 3.0 m/s to the right
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 6–17
14. m
1
= 8.0 g = 0.0080 kg
m
2
= 2.5 kg
g = 9.81 m/s
2
h = 6.0 cm = 0.060 m
KE
lowest
= KE
i
= PE
f
= mgh
KE
lowest
= (m
1
+ m
2
)gh
KE
lowest
= (0.0080 kg + 2.5 kg)(9.81 m/s
2
)(0.060m)
KE
lowest
= 1.5 J
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 7–1
Circular Motion and
Gravitation
Student Edition Solutions
Circular Motion and Gravitation, Practice A
Givens Solutions
1. a
c
= 3.0 m/s
2
r = 2.1 m
2. a
c
= 250 m/s
2
r = 0.50 m
3. r = 1.5 m
v
t
= 1.5 m/s
v
t
=
a
c
r
=
(3
.0
m
/s
2
)
(2
.1
m
)
= 2.5 m/s
v
t
=
a
c
r
=
(2
50
m
/s
2
)
(0
.5
0
m
)
= 11 m/s
a
c
=
v
r
t
2
=
(1.
1
5
.5
m
m
/s)
2
= 1.5 m/s
2
4. a
c
= 15.4 m/s
2
v
t
= 30.0 m/s
r =
v
a
t
c
2
=
(3
1
0
5
.
.
0
4
m
m
/
/
s
s
)
2
2
= 58.4 m
1. r = 2.10 m
v
t
= 2.50 m/s
F
c
= 88.0 N
2. v
t
= 13.2 m/s
F
c
= 377 N
m = 86.5 kg
3. r = 1.50 m
v
t
= 1.80 m/s
m = 18.5 kg
4. m = 905 kg
r =
3.2
2
5
p
km
F
c
= 2140 N
m = F
c
v
r
t
2
= (88.0 N)
(2
(
.
2
5
.
0
10
m
m
/s
)
)
2
= 29.6 kg
r =
m
F
v
c
t
2
==40.0 m
(86.5 kg)(13.2 m/s)
2
377 N
F
c
=
m
r
v
t
2
==40.0 N
(18.5 kg)(1.80 m/s)
2
1.50 m
v
t
=
r
m
F
c
=
3.25 ×
2
p
10
3
m
2
9
1
0
4
5
0
k
N
g
= 35.0 m/s
Circular Motion and Gravitation, Practice B
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualI Ch. 7–2
1. m
1
= m
2
= 0.800 kg
F
g
= 8.92 × 10
−11
N
G = 6.673 × 10
−11
N
k
•
g
m
2
2
r =
G
m
F
1
g
m
2
=
r = 0.692 m
6.673 × 10
−11
N
k
•
g
m
2
2
(0.800 kg)(0.800 kg)
8.92 × 10
−11
N
Circular Motion and Gravitation, Practice C
5. m = 90.0 kg
r = 11.5 m
v
t
= 13.2 m/s
F
c
=
m
r
v
t
2
==1360 N
(90.0 kg)(13.2 m/s)
2
11.5 m
3. m
1
= 66.5 kg
m
2
= 5.97 × 10
24
kg
r = 6.38 × 10
6
m
G = 6.673 × 10
−11
N
k
•
g
m
2
2
m
2
= 6.42 × 10
23
kg
r = 3.40 × 10
6
m
m
2
= 1.25 × 10
22
kg
r = 1.20 × 10
6
m
a. F
g
= G
m
r
1
m
2
2
=
6.673 × 10
−11
N
k
•
g
m
2
2
=
b. F
g
= G
m
r
1
m
2
2
=
6.673 × 10
−11
N
k
•
g
m
2
2
=
c. F
g
= G
m
r
1
m
2
2
=
6.673 × 10
−11
N
k
•
g
m
2
2
= 38.5 N
(66.5 kg)(1.25 × 10
22
kg)
(1.20 × 10
6
m)
2
246 N
(66.5 kg)(6.42 × 10
23
kg)
(3.40 × 10
6
m)
2
651 N
(66.5 kg)(5.97 × 10
24
kg)
(6.38 × 10
6
m)
2
Circular Motion and Gravitation, Section 1 Review
Givens Solutions
2. r = 12 m
a
c
= 17 m/s
2
v
t
=
a
c
r
=
(17 m/
s
2
)(12
m)
= 14 m/s
2. m
1
= 6.4 × 10
23
kg
m
2
= 9.6 × 10
15
kg
F
g
= 4.6 × 10
15
N
G = 6.673 × 10
−11
N
k
•
g
m
2
2
r =
G
m
F
1
g
m
2
=
r = 9.4 × 10
6
m = 9.4 × 10
3
km
6.673 × 10
−11
N
k
•
g
m
2
2
(6.4 × 10
23
kg)(9.6 × 10
15
kg)
4.6 × 10
15
N
Section One—Student Edition Solutions I Ch. 7–3
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
3. m
E
= 5.97 × 10
24
kg
r
E
= 6.38 × 10
6
m
m = 65.0 kg
G = 6.673 × 10
−11
N
k
•
g
m
2
2
m
E
= 5.97 × 10
24
kg
r = 7.38 × 10
6
m
m = 65.0 kg
m
S
= 5.68 × 10
26
kg
r
S
= 6.03 × 10
7
m
m = 65.0 kg
m
S
= 5.68 × 10
26
kg
r = 6.13 × 10
7
m
m = 65.0 kg
a. F
g
= G
m
r
E
m
2
E
F
g
=
6.673 × 10
−11
N
k
•
g
m
2
2
=
b. F
g
= G
m
r
m
2
E
F
g
=
6.673 × 10
−11
N
k
•
g
m
2
2
=
c. F
g
=
G
r
m
S
2
m
S
F =
6.673 × 10
−11
N
k
•
g
m
2
2
=
d. F
g
= G
m
r
m
2
S
F
g
=
6.673 × 10
−11
N
k
•
g
m
2
2
= 656 N
(65.0 kg)(5.68 × 10
26
kg)
(6.13 × 10
7
m)
2
678 N
(65.0 kg)(5.68 × 10
26
kg)
(6.03 × 10
7
m)
2
475 N
(65.0 kg)(5.97 × 10
24
kg)
(7.38 × 10
6
m)
2
636 N
(65.0 kg)(5.97 × 10
24
kg)
(6.38 × 10
6
m)
2
5. r
E
= 6.38 × 10
6
m
g = 9.81 m/s
2
G = 6.673 × 10
−11
N
k
•
g
m
2
2
g = G
m
r
E
E
2
, so m
E
=
gr
G
E
2
m
E
==5.98 × 10
24
kg
(9.81 m/s
2
)(6.38 × 10
6
m)
2
6.673 × 10
−11
N
•
m
2
/kg
2
Circular Motion and Gravitation, Section 2 Review
Givens Solutions
Holt Physics Solution ManualI Ch. 7–4
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
6.673
× 10
−1
1
N
k
•
g
m
2
2
5
6
.9
.7
7
4
×
×
1
1
0
0
2
6
4
m
kg
6.673
× 10
−1
1
N
k
•
g
m
2
2
5
6
.9
.7
7
4
×
×
1
1
0
0
2
6
4
m
kg
1. r = 3.61 × 10
5
m
m
E
= 5.97 × 10
24
kg
r
E
= 6.38 × 10
6
m
m
J
= 1.90 × 10
27
kg
r
J
= 7.15 × 10
7
m
m
m
= 7.35 × 10
22
kg
r
m
= 1.74 × 10
6
m
G = 6.673 × 10
−11
N
k
•
g
m
2
2
Above Earth:
r
1
= r + r
E
= 3.61 × 10
5
m + 6.38 × 10
6
m = 6.74 × 10
6
m
v
t
=
G
v =
6.673
× 10
−1
1
N
k
•
g
m
2
2
5
6
.9
.7
7
4
×
×
1
1
0
0
2
6
4
m
kg
=
T = 2p
G
r
m
1
3
E
T = 2p
=
Above Jupiter:
r
2
= r + r
J
= 3.61 × 10
5
m + 7.15 × 10
7
m = 7.19 × 10
7
m
v
t
=
G
m
r
2
J
v
t
=
6.673 × 10
−11
=
T = 2p
G
r
2
m
3
J
T = 2p
=
Above Earth’s moon:
r
3
= r + r
m
= 3.61 × 10
5
m + 1.74 × 10
6
m = 2.10 × 10
6
m
v
t
=
G
m
r
3
m
v
t
=
6.673 × 10
−11
N
k
•
g
m
2
2
=
T = 2p
G
r
m
3
3
m
T = 2p
= 8.63 × 10
3
s
(2.10 × 10
6
m)
3
6.673 × 10
−11
N
k
•
g
m
2
2
(7.35 × 10
22
kg)
1.53 × 10
3
m/s
7.35 × 10
22
kg
2.10 × 10
6
m
1.08 × 10
4
s
(7.19 × 10
7
m)
3
6.673 × 10
−11
N
k
•
g
m
2
2
(1.90 × 10
27
kg)
4.20 × 10
4
m/s
1.90 × 10
27
kg
7.19 × 10
7
m
N
•m
2
kg
2
5.51 × 10
3
s
(6.74 × 10
6
m)
3
6.673 × 10
−11
N
k
•
g
m
2
2
(5.97 × 10
24
kg)
7.69 × 10
3
m/s
m
E
r
1
Circular Motion and Gravitation, Practice D
Givens Solutions
Section One—Student Edition Solutions I Ch. 7–5
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
2. T = 125 min
r
E
= 6.38 × 10
6
m
m
E
= 5.97 × 10
24
kg
G = 6.673 × 10
−11
N
k
•
g
m
2
2
T
2
=
4
G
p
m
2
r
E
3
r
3
=
T
2
4
G
p
m
2
E
r =
3
r = 8.28 × 10
6
m
height above Earth = r − r
E
= 8.28 × 10
6
m − 6.38 × 10
6
m = 1.90 × 10
6
m
[(125 min)(60 s/min)]
2
(6.673 × 10
−11
N
•
m
2
/kg
2
)(5.97 × 10
24
kg)
4p
2
6.673
× 10
−1
1
N
k
•
g
m
2
2
5
6
.9
.7
7
4
×
×
1
1
0
0
2
6
4
m
kg
5. r = 3.84 × 10
8
m
m
E
= 5.97 × 10
24
kg
G = 6.673 × 10
−11
N
k
•
g
m
2
2
v
t
=
G
m
r
E
v
t
=
6.673 × 10
−11
N
k
•
g
m
2
2
=
T = 2p
G
r
m
3
E
T = 2p
= 2.37 × 10
6
s
(3.84 × 10
8
m)
3
6.673 × 10
−11
N
k
•
g
m
2
2
(5.97 × 10
24
kg)
1.02 × 10
3
m/s
5.97 × 10
24
kg
3.84 × 10
8
m
Circular Motion and Gravitation, Section 3 Review
1. F = 3.0 N
d = 0.25 m
q = 90.0°
2. m = 3.0 kg
d = 2.0 m
q
1
= 5.0°
g = 9.81 m/s
2
q
2
= 15.0°
3. t = 40.0 N
•
m
d = 30.0 cm
t = Fd(sin q) = (3.0 N)(0.25 m)(sin 90.0°) = 0.75 N
•
m
a. t = Fd(sin q
1
) = mgd(sin q
1
)
t = (3.0 kg)(9.81 m/s
2
)(2.0 m)(sin 5.0°) =
b. t = mgd(sin q
2
) = (3.0 kg)(9.81 m/s
2
)(2.0 m)(sin 15.0°) = 15 N
•
m
5.1 N
•
m
For a given torque, the minimum force must be applied perpendicular to the lever
arm, or sin q = 1. Therefore,
F =
d
t
=
4
0
0
.
.
3
0
0
N
0
•
m
m
= 133 N
Circular Motion and Gravitation, Practice E
Holt Physics Solution ManualI Ch. 7–6
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
9. a
c
= 28 m/s
2
r = 27 cm
10. v
t
= 20.0 m/s
F
n
= 2.06 × 10
4
N
r
1
= 10.0 m
g = 9.81 m/s
2
v
t
=
ra
c
=
(2
7
×
1
0
−
2
m
)(
28
m
/s
2
)
= 2.7 m/s
a. F
net
= F
n
− F
g
= F
n
− mg
F
net
= F
c
=
m
r
v
1
t
2
F
n
− mg =
m
r
v
1
t
2
mv
t
2
= r
1
(F
n
− mg)
m(v
t
2
+ r
1
g) = r
1
F
n
m ==
m ==
m = 414 kg
2.06 × 10
5
N
•
m
498 m
2
/s
2
2.06 × 10
5
N
•
m
4.00 × 10
2
m
2
/s
2
+ 98.1 m
2
/s
2
(10.0 m)(2.06 × 10
4
N)
(20.0 m/s)
2
+ (10.0 m)(9.81 m/s
2
)
r
1
F
n
v
t
2
+ r
1
g
Circular Motion and Gravitation, Section 4 Review
Givens Solutions
8. F
30
= 30.0 N
q
30
= 45°
d
30
= 0 m
F
25
= 25.0 N
q
25
= 59°
d
25
= 2.0 m
F
10
= 10.0 N
q
10
= 23°
d
10
= 4.0 m
t
30
= F
30
d
30
(sin q
30
) = (30.0 N)(0 m)(sin 45°) =
t
25
= F
25
d
25
(sin q
25
) = (25.0 N)(2.0 m)(sin 59°) =
t
10
= F
10
d
10
(sin q
10
) = (−10.0 N)(4.0 m)(sin 23°) =
The bar will rotate counterclockwise because t
net
is positive
(43 N
•
m − 16 N
•
m = +27 N
•
m).
−16 N
•
m
43 N
•
m
0 N
•
m
5. eff = 0.73
d
in
= 18.0 m
d
out
= 3.0 m
m = 58 kg
g = 9.81 m/s
2
eff =
W
W
o
i
u
n
t
eff =
F
F
ou
in
t
d
d
i
o
n
ut
where F
out
= mg
F
in
=
m
ef
g
f
d
d
o
in
ut
==1.3 × 10
2
N
(58 kg)(9.81 m/s
2
)(3.0 m)
(0.73)(18.0 m)
6. F
g
= 950 N
F
applied
= 350 N
MA =
F
F
o
i
u
n
t
=
F
ap
F
p
g
lied
=
9
3
5
5
0
0
N
N
= 2.7
8. a
c
= 145 m/s
2
r = 0.34 m
v
t
=
ra
c
=
(0
.3
4
m
)(
14
5
m
/s
2
)
= 7.0 m/s
Circular Motion and Gravitation, Chapter Review
6.673
× 10
−1
1
N
k
•
g
m
2
2
5
6
.9
.7
7
4
×
×
1
1
0
0
2
6
4
m
kg
Section One—Student Edition Solutions I Ch. 7–7
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
11. r = 10.0 m
v
t
= 8.0 m/s
F
rope, max
= 1.0 × 10
3
N
g = 9.81 m/s
2
F
total
= F
c
+ F
g
=
m
r
v
t
2
+ mg
F
total
≤ F
rope, max
F
rope, max
= m
max
v
r
t
2
+ g
m
max
= =
m
max
= =
m
max
= 62 kg
1.0 × 10
3
N
16.2 m/s
2
1.0 × 10
3
N
6.4 m/s
2
+ 9.81 m/s
2
1.0 × 10
3
N
(8
1
.0
0.
m
0m
/s)
2
+ 9.81 m/s
2
F
rope, max
v
r
t
2
+ g
18. F
g
= 3.20 × 10
−8
N
m
1
= 50.0 kg
m
2
= 60.0 kg
G = 6.673 × 10
−11
N
•
m
2
/kg
2
r =
G
m
F
1
g
m
2
=
r = 2.50 m
(6.673 × 10
−11
N
•
m
2
/kg
2
)(50.0 kg)(60. kg)
3.20 × 10
−8
N
19. m
1
= 9.11 × 10
−31
kg
m
2
= 1.67 × 10
−27
kg
F
g
= 1.0 × 10
−47
N
G = 6.673 × 10
−11
N
•
m
2
/kg
2
r =
G
m
F
1
g
m
2
=
r = 1.0 × 10
−10
m = 0.10 nm
(6.673 × 10
−11
N
•
m
2
/kg
3
)(9.11 × 10
−31
kg)(1.67 × 10
−27
kg)
1.0 × 10
−47
N
27. r = 1.44 × 10
8
m
r
E
= 6.38 × 10
6
m
m
E
= 5.97 × 10
24
kg
G = 6.673 × 10
−11
N
k
•
g
m
2
2
r
1
= r + r
E
= 1.44 × 10
8
m + 6.38 × 10
6
m = 1.50 × 10
8
m
v
t
=
G
m
r
1
E
v
t
=
6.673 × 10
−11
N
k
•
g
m
2
2
=
T = 2p
G
r
m
1
3
E
T = 2p
= 5.78 × 10
5
s
(1.50 × 10
8
m)
3
6.673 × 10
−11
N
k
•
g
m
2
2
(5.97 × 10
24
kg)
1630 m/s
5.97 × 10
24
kg
1.50 × 10
8
m
b. F
c
= mg
m
r
v
2
t
2
= mg
v
t
=
gr
2
=
(9
.8
1
m
/s
2
)
(1
5.
0
m
)
= 12.1 m/s
r
2
= 15.0 m
Holt Physics Solution ManualI Ch. 7–8
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
39. m = 2.00 × 10
3
kg
r = 20.0 m
m
k
= 0.70
g = 9.81 m/s
2
F
k
= m
k
F
n
= m
k
mg
F
c
= m
⎯
v
r
t
2
⎯
F
k
= F
c
m
k
mg = m
⎯
v
r
t
2
⎯
v
t
=
rm
k
g
=
(2
0.
0
m
)(
0.
70
)(
9.
81
m
/s
2
)
v
t
= 12 m/s
28. T = 24.0 h
r
E
= 6.38 × 10
6
m
m
E
= 5.97 × 10
24
kg
G = 6.673 × 10
−11
⎯
N
k
•
g
m
2
2
⎯
T = 2p
T
2
= 4p
2
⎯
G
r
m
1
3
E
⎯
r
1
=
3
r
1
=
3
r
1
= 4.22 × 10
7
m (from Earth’s center)
r = r
1
− r
E
= 4.22 × 10
7
m − 6.38 × 10
6
m = 3.58 × 10
7
m
(24.0 h)
3600
⎯
h
s
⎯
2
6.673 × 10
−11
⎯
N
k
•
g
m
2
2
⎯
(5.97 × 10
24
kg)
⎯
⎯⎯
⎯⎯⎯
⎯
4p
2
T
2
Gm
E
⎯
4p
2
r
1
3
⎯
Gm
E
29. r = 2.0 × 10
8
m
T = 5.0 × 10
4
s
G = 6.673 × 10
−11
⎯
N
k
•
g
m
2
2
⎯
T = 2p
T
2
= 4p
2
⎯
G
r
m
3
⎯
m =
⎯
4
T
p
2
2
G
r
3
⎯
=
m = 1.9 × 10
27
kg
4p
2
(2.0 × 10
8
m)
3
⎯⎯⎯⎯⎯
(5.0 × 10
4
s)
2
6.673 × 10
−11
⎯
N
k
•
g
m
2
2
⎯
r
3
⎯
Gm
37. m = 54 kg
r = 0.050 m
g = 9.81 m/s
2
q = 90°
38. q = 90.0° − 8.0°=82.0°
m = 1130 kg
d = 3.05 m − 1.12 m −
0.40 m = 1.53 m
g = 9.81 m/s
2
t = Fd(sin q) = mgr(sin q)
t = (54 kg)(9.81 m/s
2
)(0.050 m)(sin 90°) = 26 N
•
m
t
net
= t
g
+ t
jack
= 0
mgd(sin q) + t
jack
= 0
t
jack
= −mgd(sin q) = −(1130 kg)(9.81 m/s
2
)(1.53 m)(sin 82.0°)
magnitude of t
jack
= 1.68 × 10
4
N
•
m
Section One—Student Edition Solutions I Ch. 7–9
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
40. m
m
= 7.35 × 10
22
kg
m
s
= 1.99 × 10
30
kg
G = 6.673 × 10
−11
N
k
•
g
m
2
2
r = 3.84 × 10
8
m
m
E
= 5.97 × 10
24
kg
m
m
= 7.35 × 10
22
kg
m
E
= 5.97 × 10
24
kg
m
s
= 1.99 × 10
30
kg
r = 1.50 × 10
11
m
r = 1.50 × 10
11
m − 0.00384 × 10
11
m = 1.50 × 10
11
m
a. F
g
= G
m
m
r
2
m
s
F
g
=
6.673 × 10
−11
N
k
•
g
m
2
2
=
b. F
g
= G
m
E
r
m
2
m
F
g
=
6.673 × 10
−11
N
k
•
g
m
2
2
=
c. F
g
= G
m
r
E
2
m
s
F
g
=
6.673 × 10
−11
N
k
•
g
m
2
2
= 3.52 × 10
22
N
(5.97 × 10
24
kg)(1.99 × 10
30
kg)
(1.50 × 10
11
m)
2
1.99 × 10
20
N
(5.97 × 10
24
kg)(7.35 × 10
22
kg)
(3.84 × 10
8
m)
2
4.34 × 10
20
N
(7.35 × 10
22
kg)(1.99 × 10
30
kg)
(1.50 × 10
11
m)
2
41. m = 75 kg
r = 0.075 m
d = 0.25 m
g = 9.81 m/s
2
For a force perpendicular to d, t = Fd.
F =
d
t
=
m
d
gr
==2.2 × 10
2
N
(75 kg)(9.81 m/s
2
)(0.075 m)
0.25 m
42. t = 58 N
•
m
d = 0.35 m
q = 56°
t = Fd(sin q)
F =
d(si
t
n q)
==2.0 × 10
2
N
58 N
•
m
(0.35 m)(sin 56°)
43. d = 1.4 m
F = 1600 N
q = 53.5°
t = Fd(sin q) = (1600 N)(1.4 m)(sin 53.5°) = 1800 N
•
m
Consider the total mass of each hand to be at the midpoint of that hand.
t
net
=−m
h
g
(sin q
h
) − m
m
g
(sin q
m
)
t
net
=−(60.0 kg)(9.81 m/s
2
)
2.7
2
m
(sin 20.0°) − (100.0 kg)(9.81 m/s
2
)
4.5
2
m
(sin 60.0°)
t
net
=−2.7 × 10
2
N
•
m − 1.9 × 10
3
N
•
m =−2.2 × 10
3
N
•
m
L
m
2
L
h
2
44. L
h
= 2.7 m
L
m
= 4.5 m
m
h
= 60.0 kg
m
m
= 100.0 kg
q
h
= 20.0° from 6:00
q
m
= 60.0° from 6:00
g = 9.81 m/s
2
45. eff = 0.64
m = 78 kg
d
out
= 4.0 m
d
in
= 24 m
g = 9.81 m/s
2
eff =
W
W
o
i
u
n
t
=
F
F
ou
in
t
d
d
i
o
n
ut
F
in
=
F
d
o
in
u
(
t
e
d
f
o
f
u
)
t
=
d
m
in
g
(
d
e
o
ff
ut
)
=
F
in
= 2.0 × 10
2
N
(78 kg)(9.81 m/s
2
)(4.0 m)
(24 m)(0.64)
6.673
× 10
−1
1
N
k
•
g
m
2
2
5
6
.9
.7
7
4
×
×
1
1
0
0
2
6
4
m
kg
Holt Physics Solution ManualI Ch. 7–10
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
46. d = 2.0 m
q = 15°
m
k
= 0.160
W
out
= F
g
d(sin q)
W
in
= (F
f
+ F
g,x
)d = [m
k
F
g
(cos q) + F
g
(sin q)]d
W
in
= F
g
d[m
k
(cos q) + (sin q)]
eff =
W
W
o
i
u
n
t
==
eff ==
0.15
0.
+
26
0.26
eff =
0
0
.
.
2
4
6
1
= 0.63 = 63%
sin 15°
(0.160)(cos 15°) + (sin 15°)
sin q
m
k
(cos q) + (sin q)
F
g
d(sin q)
F
g
d[m
k
(cos q) + (sin q)]
47. d
out
= 3.0 m
F
in
= 2200 N
d
in
= 14 m
m = 750 kg
g = 9.81 m/s
2
eff =
W
W
o
i
u
n
t
=
F
F
ou
in
t
d
d
i
o
n
ut
=
m
F
i
g
n
d
d
o
i
u
n
t
eff ==0.72 = 72%
(750 kg)(9.81 m/s
2
)(3.0 m)
(2200 N)(14 m)
48. eff = 0.875
F
in
= 648 N
m = 150 kg
d
out
= 2.46 m
g = 9.81 m/s
2
eff =
W
W
o
i
u
n
t
=
F
F
ou
in
t
d
d
i
o
n
ut
=
m
F
i
g
n
d
d
o
i
u
n
t
d
in
=
F
m
in
g
(
d
e
o
ff
ut
)
==6.4 m
(150 kg)(9.81 m/s
2
)(2.46 m)
(648 N)(0.875)
49. r
Io
= 1.82 × 10
6
m
d = 4.22 × 10
8
m
r
J
= 7.15 × 10
7
m
m
J
= 1.90 × 10
27
kg
G = 6.673 × 10
−11
N
k
•
g
m
2
2
a. r = r
Io
+ d + r
J
r = 1.82 × 10
6
m + 4.22 × 10
8
m + 7.15 × 10
7
m
r = 4.95 × 10
8
m
T = 2p
= 2p
T = (1.94 × 10
5
s)(1 h/3600 s)(1 day/24 h) =
b. r = 4.95 × 10
8
m (see part a.)
v
t
=
G
v
t
=
6.673 × 10
−11
N
k
•
g
m
2
2
= 1.60 × 10
4
m/s
1.90 × 10
27
kg
4.95 × 10
8
m
m
J
r
2.25 days
(4.95 × 10
8
m)
3
6.673 × 10
−11
N
k
•
g
m
2
2
(1.90 × 10
27
kg)
r
3
Gm
J
Section One—Student Edition Solutions I Ch. 7–11
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
50. F
g
= 13 500 N
r = 2.00 × 10
2
m
v
t
= 50.0 km/h
g = 9.81 m/s
2
a. a
c
=
v
r
t
2
==
b. F
c
= ma
c
=
F
g
g
a
c
=
9
1
.
3
81
50
m
0
/
N
s
2
(0.965 m/s
2
) =
c. F
c
= F
k
= m
k
F
n
=µ
k
F
g
m
k
=
F
F
g
c
=
1
1
3
3
5
3
0
0
0
N
N
= 0.0985
1.33 × 10
3
N
0.965 m/s
2
(50.0 × 10
3
m/h)
2
(1 h/3600 s)
2
2.00 × 10
2
m
51. d = 15.0 m
q
1
= 90.0°−20.0°=70.0°
F
g,max
= 450 N
q
2
= 90.0°−40.0°=50.0°
a. t
max
= F
g,max
d(sin q
1
) = (450 N)(15.0 m)(sin 70.0°) =
b. F
g
=
d(
t
si
m
n
a
q
x
2
)
==5.5 × 10
2
N
6.3 × 10
3
N
•
m
(15.0 m)(sin 50.0°)
6.3 × 10
3
N
•
m
52. m
1
= 5.00 kg
m
2
= 1.99 × 10
30
kg
F
g
= 1370 N
G = 6.673 × 10
−11
N
k
•
g
m
2
2
F
g
= G
m
r
1
m
2
2
r =
Gm
F
1
g
m
2
r =
= 6.96 × 10
8
m
6.673 × 10
−11
N
k
•
g
m
2
2
(5.00 kg)(1.99 × 10
30
kg)
1370 N
53. v
t
= 55.0 km/h
r = 40.0 m
m = 1350 kg
m
k
= 0.500
g = 9.81 m/s
2
F
f
= m
k
F
n
= m
k
mg = (0.500)(1350 kg)(9.81 m/s
2
) =
F
c
=
m
r
v
t
2
==
Because F
c
> F
f
, the frictional force is not large enough to maintain the circular
motion.
7880 N
(1350 kg)[(55.0 × 10
3
m/h)(1 h/3600 s)]
2
40.0 m
6620 N
54. q = 60.0°
d = 0.35 m
t = 2.0 N
•
m
F =
d s
t
inq
==
t
max
is produced when q = 90.0°
t
max
= Fd sinq = (6.6 N)(0.35 m)(sin 90.0°) = 2.3 N
•
m
6.6 N
2.0 N
•
m
(0.35 m)(sin 60.0°)
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualI Ch. 7–12
Circular Motion and Gravitation, Standardized Test Prep
Givens Solutions
2. v
t
= 15 m/s
r = 25 m
a
c
=
v
r
t
2
==9.0 m/s
2
(15 m/s)
2
25 m
4. m
E
= 5.97 × 10
24
kg
m
s
= 1.99 × 10
30
kg
r = 1.50 × 10
11
m
G = 6.673 × 10
−11
N
k
•
g
m
2
2
F
g
= G
m
r
E
2
m
s
F
g
=
6.673 × 10
−11
F
g
= 3.52 × 10
22
N
(5.97 × 10
24
kg)(1.99 × 10
30
kg)
(1.50 × 10
11
m)
2
N•m
2
kg
2
9. F
1
= 6.0 N
F
2
= 6.0 N
F
3
= 6.0 N
q
1
= 90.0°
q
2
= 90.0°−60.0°=30.0°
q
3
= 0.0°
d = 1.0 m
t
net
= t
1
+ t
2
+ t
3
t
net
= F
1
d sinq
1
+ F
2
d sinq
2
+ F
3
d sinq
3
t
net
= (6.0 N)(1.0 m)(sin 90.0°) + (6.0 N)(1.0 m)(sin 30.0°) + (6.0 N)(1.0 m)(sin 0.0°)
t
net
= 6.0 N
•
m + 3.0 N
•
m + 0.0 N
•
m = 9.0 N
•
m
10. F
in
= 75 N
F
out
= 225 N
MA =
F
F
o
i
u
n
t
=
2
7
2
5
5
N
N
= 3
17. m
s
= 1.99 × 10
30
kg
r = 2.28 × 10
11
m
G = 6.673 × 10
−11
N
k
•
g
m
2
2
T = 2p
T =
2p
T = 687 days
1 day
24 h
1 h
3600 s
(2.28 × 10
11
m)
3
6.673 × 10
−11
N
k
•
g
m
2
2
(1.99 × 10
30
kg)
r
3
Gm
s
11. eff = 87.5% = 0.875
F
out
= 1320 N
d
out
= 1.50 m
eff ==
W
in
== =2260 J
(1320 N)(1.50 m)
0.875
F
out
d
out
eff
F
out
d
out
W
in
W
out
W
in
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 8–1
1. F
g
= 50.0 N
apparent weight in water
= 36.0 N
r
water
= 1.00 × 10
3
kg/m
3
apparent weight in liquid
= 41.0 N
r
metal
= 3.57 × 10
3
kg/m
3
2. m = 2.8 kg
l
= 2.00 m
w = 0.500 m
h = 0.100 m
r
water
= 1.00 × 10
3
kg/m
3
g = 9.81 m/s
2
3. w = 4.0 m
l
= 6.0 m
h = 4.00 cm
r
water
= 1.00 × 10
3
kg/m
3
g = 9.81 m/s
2
4. m
balloon
= 0.0120 kg
r
helium
= 0.179 kg/m
3
r = 0.500 m
r
air
= 1.29 kg/m
3
g = 9.81 m/s
2
F
B
= F
g
r
water
Vg = (m + M)g
M = r
water
V − m = r
water
(
l
wh) − m
M = (1.00 × 10
3
kg/m
3
)(2.00 m)(0.500 m)(0.100 m) − 2.8 kg = 1.00 × 10
2
kg − 2.8 kg
M = 97 kg
F
g
= F
B
mg = r
water
Vg = r
water
(w
l
h)g
F
g
= (1.00 × 10
3
kg/m
3
)(4.0 m)(6.0 m)(0.0400 m)(9.81 m/s
2
) = 9.4 × 10
3
N
a. F
B
= r
air
Vg = r
air
4
3
pr
3
g
F
B
==
b. m
helium
= r
helium
V = r
helium
4
3
pr
3
m
helium
==0.0937 kg
F
g
= (m
balloon
+ m
helium
)g = (0.0120 kg + 0.0937 kg)(9.81 m/s
2
)
F
g
= (0.1057 kg)(9.81 m/s
2
) = 1.04 N
F
net
= F
B
− F
g
= 6.63 N − 1.04 N = 5.59 N
(0.179 kg/m
3
)(4p)(0.500 m)
3
3
6.63 N
(1.29 kg/m
3
)(4p)(0.500 m)
3
(9.81 m/s
2
)
3
Fluid Mechanics, Practice A
Givens Solutions
a. F
B
= F
g
− apparent weight = 50.0 N − 36.0 N = 14.0 N
r
metal
=
F
F
B
g
r
water
=
r
metal
=
b. F
B
= F
g
− apparent weight = 50.0 N − 41.0 N = 9.0 N
r
liquid
=
F
F
B
g
r
metal
=
r
liquid
= 6.4 × 10
2
kg/m
3
(9.0 N)(3.57 × 10
3
kg/m
3
)
50.0 N
3.57 × 10
3
kg/m
3
(50.0 N)(1.00 × 10
3
kg/m
3
)
14.0 N
Fluid Mechanics
Student Edition Solutions
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualI Ch. 8–2
3. m
balloon
= 650 kg
m
pack
= 4600 kg
r
air
= 1.29 kg/m
3
r
helium
= 0.179 kg/m
3
4. a = 0.325 m/s
2
r
sw
= 1.025 × 10
3
kg/m
3
g = 9.81 m/s
2
F
B
= r
air
Vg
F
g
= (m
balloon
+ m
pack
+ m
helium
)g
m
helium
= r
helium
V
F
B
= F
g
r
air
Vg =(m
balloon
+ m
pack
+ r
helium
V )g
V =
m
r
b
a
a
i
l
r
lo
−
on
r
+
he
m
liu
p
m
ack
=
V =
1.
5
1
2
1
0
k
0
g
k
/m
g
3
= 4.7 × 10
3
m
3
650 kg + 4600 kg
1.29 kg/m
3
− 0.179 kg/m
3
Use Newton’s second law.
m
s
a = F
B
− F
g
= m
sw
g − m
s
g
r
s
Va = r
sw
Vg − r
s
Vg
r
s
(a + g) = r
sw
g
r
s
= r
sw
a +
g
g
= (1.025 × 10
3
kg/m
3
)
r
s
= (1.025 × 10
3
kg/m
3
)
1
9
0
.8
.1
1
4
m
m
/
/
s
s
2
2
= 9.92 × 10
2
kg/m
3
9.81 m/s
2
0.325 m/s
2
+ 9.81 m/s
2
Fluid Mechanics, Section 1 Review
Givens Solutions
1. r
1
= 5.00 cm
r
2
= 15.0 cm
F
2
= 1.33 × 10
4
N
2. F
g
= 1025 N
w = 1.5 m
l
= 2.5 m
3. r = 0.40 cm
P
b
= 1.010 × 10
5
Pa
P
t
= 0.998 × 10
5
Pa
a.
A
F
1
1
=
A
F
2
2
F
1
=
F
A
2
A
2
1
=
F
p
2
p
r
2
r
2
1
2
=
F
r
2
2
r
2
1
2
F
1
==
b. P =
A
F
2
2
=
p
F
r
2
2
2
=
(
1
p
.
)
3
(
3
0.
×
15
1
0
0
4
m
N
)
2
= 1.88 × 10
5
Pa
1.48 × 10
3
N
(1.33 × 10
4
N)(0.0500 m)
2
(0.150 m)
2
P =
A
F
==
(1.5
1
m
02
)
5
(2
N
.5 m)
= 2.7 × 10
2
Pa
F
g
w
l
a. P
net
= P
b
− P
t
= 1.010 × 10
5
Pa − 0.998 × 10
5
Pa =
b. F
net
= P
net
A = P
net
pr
2
F
net
= (1.2 × 10
3
Pa)(p)(4.0 × 10
−3
m)
2
= 6.0 × 10
−2
N
1.2 × 10
3
Pa
Fluid Mechanics, Practice B
Section One—Student Edition Solutions I Ch. 8–3
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Fluid Mechanics, Section 2 Review
Givens Solutions
1. F
g
= 25 N
w = 1.5 m
F
g
= 15 N
r = 1.0 m
F
g
= 25 N
w = 2.0 m
F
g
= 25 N
r = 1.0 m
a. P =
A
F
=
w
F
g
2
P =
(1
2
.5
5
m
N
)
2
= 11 Pa
b. P =
A
F
=
p
F
r
g
2
P =
(p)(
1
1
5
.0
N
m)
2
= 4.8 Pa
c. P =
A
F
=
w
F
g
2
P =
(2
2
.0
5
m
N
)
2
= 6.2 Pa
d. P =
A
F
=
p
F
r
g
2
P =
(p)(
2
1
5
.0
N
m)
2
= 8.0 Pa
a is the largest pressure
3. h = 5.0 × 10
2
m
P
o
= 1.01 × 10
5
Pa
r = 1.025 × 10
3
kg/m
3
g = 9.81 m/s
2
P = P
o
+ rgh= 1.01 × 10
5
Pa + (1.025 × 10
3
kg/m
3
)(9.81 m/s
2
)(5.0 × 10
2
m)
P = 1.01 × 10
5
Pa + 5.0 × 10
6
Pa =
N =
P
P
o
=
1
5
.
.
0
1
1
×
×
1
1
0
0
6
5
P
P
a
a
= 5.0 × 10
1
5.1 × 10
6
Pa
2. h = 366 m
r = 1.00 × 10
3
kg/m
3
g = 9.81 m/s
2
P = rgh
P = (1.00 × 10
3
kg/m
3
)(9.81 m/s
2
)(366 m) = 3.59 × 10
6
Pa
1. P
1
= 3.00 × 10
5
Pa
v
1
= 1.00 m/s
r
2
=
1
4
r
1
A
1
v
1
= A
2
v
2
v
2
=
A
A
1
2
v
1
=
p
p
r
1
r
2
2
2
v
1
==16v
1
v
2
= (16)(1.00 m/s) = 16.0 m/s
r
1
2
v
1
1
4
r
1
2
Fluid Mechanics, Section 3 Review
4. P = 3 P
o
P
o
= 1.01 × 10
5
Pa
r = 1.025 × 10
3
kg/m
3
g = 9.81 m/s
2
P = P
0
+ rgh
h =
P
r
−
g
P
o
=
3P
o
r
−
g
P
o
=
2
r
P
g
o
h = = 20.1 m
(2)(1.01 × 10
5
Pa)
(1.025 × 10
3
kg/m
3
)(9.81 m/s
2
)
Holt Physics Solution ManualI Ch. 8–4
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
2. r =
2.0
2
cm
= 1.0 cm
r = 1.00 × 10
3
kg/m
3
V = 2.5 × 10
−2
m
3
∆t = 30.0 s
flow rate = Av
v =
flow
A
rate
==
pr
V
2
∆t
v ==2.7 m/s
2.5 × 10
−2
m
3
(p)(0.010 m)
2
(30.0 s)
∆
V
t
A
8. F
g
= 315 N
apparent weight in water
= 265 N
r
water
= 1.00 × 10
3
kg/m
3
apparent weight in oil
= 269 N
r
o
= 6.3 × 10
3
kg/m
3
9. F
g
= 300.0 N
apparent weight = 200.0 N
r
alcohol
= 0.70 × 10
3
kg/m
3
a. F
B
= F
g
− apparent weight = 315 N − 265 N = 5.0 × 10
1
N
r
o
=
F
F
B
g
r
water
=
r
o
=
b. F
B
= F
g
− apparent weight = 315 N − 269 N = 46 N
r
oil
=
F
F
B
g
r
o
=
r
oil
= 9.2 × 10
2
kg/m
3
(46 N)(6.3 × 10
3
kg/m
3
)
315 N
6.3 × 10
3
kg/m
3
(315 N)(1.00 × 10
3
kg/m
3
)
5.0 × 10
1
N
F
B
= F
g
− apparent weight = 300.0 N − 200.0 N = 100.0 N
r
o
=
F
F
B
g
r
alcohol
=
r
o
= 2.1 × 10
3
kg/m
3
(300.0 N)(0.70 × 10
3
kg/m
3
)
100.0 N
Fluid Mechanics, Chapter Review
14. P = 2.0 × 10
5
Pa
A = 0.024 m
2
F
g
= 4PA = (4)(2.0 × 10
5
Pa)(0.024 m
2
) = 1.9 × 10
4
N
15. P = 5.00 × 10
5
Pa
r =
4.00
2
mm
= 2.00 mm
F = PA = P(pr
2
)
F = (5.00 × 10
5
Pa)(p)(2.00 × 10
−3
m)
2
= 6.28 N
16. r
A
=
0.64
2
cm
= 0.32 cm
r
B
=
3.8
2
cm
= 1.9 cm
F
g,B
= 500.0 N
A
F
A
A
=
F
A
g
B
,B
F
A
=
F
g
A
,B
B
A
A
=
F
g,B
p
(
r
p
B
r
2
A
2
)
=
F
g
r
,B
B
r
2
A
2
F
A
==14 N
F = 14 N downward
(500.0 N)(0.0032 m)
2
(0.019 m)
2
Section One—Student Edition Solutions I Ch. 8–5
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
20. F
g
= 4.5 N
r = 13.6 × 10
3
kg/m
3
g = 9.81 m/s
2
21. A = 1.00 km
2
P = 1.01 × 10
5
Pa
22. m
m
= 70.0 kg
m
c
= 5.0 kg
r = 1.0 cm
g = 9.81 m/s
2
V =
m
r
==
g
F
r
g
V ==3.4 × 10
−5
m
3
4.5 N
(9.81 m/s
2
)(13.6 × 10
3
kg/m
3
)
F
g
g
r
F = PA = (1.01 × 10
5
Pa)(1.00 km
2
)(10
6
m
2
/km
2
) = 1.01 × 10
11
Pa
F
g
= PA = P(4pr
2
)
P =
4p
F
g
v
2
=
(m
m
4p
+
r
m
2
c
)g
=
P ==5.9 × 10
5
Pa
(75.0 kg)(9.81 m/s
2
)
(4p)(0.010 m)
2
(70.0 kg + 5.0 kg)(9.81 m/s
2
)
(4p)(0.010 m)
2
23. r = 1.35 × 10
3
kg/m
3
r = 6.00 cm
m = rV = r
1
2
4
3
pr
3
=
2
3
rpr
3
m ==6.11 × 10
–1
kg
(2)(1.35 × 10
3
kg/m
3
)(π)(6.00 × 10
–2
m)
3
3
25. m = 1.0 kg + 2.0 kg = 3.0 kg
r
f
= 916 kg/m
3
m
b
= 2.0 kg
r
b
= 7.86 × 10
3
kg/m
3
g = 9.81 m/s
2
For the spring scale, apparent weight of block = F
g,b
− F
B
= F
g,b
− F
g,b
r
r
b
f
= m
b
g
1 −
r
r
b
f
apparent weight of block = (2.0 kg)(9.81 m/s
2
)
1 −
7.86
91
×
6
1
k
0
g
3
/m
kg
3
/m
3
= (2.0 kg)(9.81 m/s
2
)(1 − 0.117)
apparent weight of block = (2.0 kg)(9.81 m/s
2
)(0.883) =
For the lower scale, the measured weight equals the weight of the beaker and oil, plus
a force equal to and opposite in direction to the buoyant force on the block. Therefore,
apparent weight = mg + F
B
= mg + F
g,b
r
r
b
f
=
m +
m
r
b
b
r
f
g
apparent weight =
3.0 kg +
(2
7
.0
.8
k
6
g
×
)(
1
9
0
1
3
6
k
k
g
g
/
/
m
m
3
3
)
(9.81 m/s
2
)
= (3.0 kg + 0.23 kg)(9.81 m/s
2
)
apparent weight = (3.2 kg)(9.81 m/s
2
) = 31 N
17 N
24. F
g
= 1.0 × 10
6
N
h = 2.5 cm
r = 1.025 × 10
3
kg/m
3
g = 9.81 m/s
2
F
g
= mg = rVg = rAhg
A =
r
F
h
g
g
=
A = 4.0 × 10
3
m
2
1.0 × 10
6
N
(1.025 × 10
3
kg/m
3
)(2.5 × 10
–2
m)(9.81 m/s
2
)
Holt Physics Solution ManualI Ch. 8–6
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
26. rv = 600.0 kg/m
3
A = 5.7 m
2
V
r
= 0.60 m
3
r
water
=1.0 × 10
3
kg/m
3
g = 9.81 m/s
2
F
B
= F
g,r
F
B
=r
water
V
water
g = r
water
(Ah)g
F
g,r
= m
r
g = rrV
r
g
r
water
Ahg =r
r
V
r
g
h =
r
r
w
r
at
V
er
r
A
= = 6.3 × 10
–2
m = 6.3 cm
(600.0 kg/m
3
)(0.60 m
3
)
(1.0 × 10
3
kg/m
3
)(5.7 m
2
)
27. h
=
26 cm
w
=
21 cm
y
=
3.5 cm
F
g
=
19 N
g
=
9.81 m/s
2
a. r =
m
V
==
hw
F
g
yg
r ==
b. P =
F
A
g
=
h
F
w
g
=
(0.26 m
19
)(
N
0.21 m)
=
c. P =
F
A
g
=
h
F
y
g
=
(0.26 m
1
)
9
(0
N
.035 m)
= 2.1 × 10
3
Pa
3.5 × 10
2
Pa
1.0 × 10
3
kg/m
3
19 N
(0.26 m)(0.21 m)(0.035 m)(9.81 m/s
2
)
F
g
g
hwy
28. r =
0.25
2
0m
= 0.125 m
flow rate = 1.55 m
3
/s
flow rate = Av = pr
2
v
v =
flo
p
w
r
r
2
ate
=
(p
1
)(
.5
0
5
.1
m
25
3
/
m
s
)
2
= 31.6 m/s
29. h = 2.0 cm = 0.020 m
y
water
= 1.5 cm = 0.015 m
r
oil
= 900.0 kg/m
3
r
water
= 1.00 × 10
3
kg/m
3
In water:
F
g,b
= F
B,water
= r
water
Vg = r
water
Ay
water
g
In oil:
F
g,b
= F
B,oil
= r
oil
Vg = r
oil
Ay
oil
g
r
water
Ay
water
g = r
oil
Ay
oil
g
r
water
y
water
= r
oil
y
oil
y
oil
=
y
oil
=
y
oil
= 0.017 m = 1.7 × 10
−2
m
1.00 × 10
3
kg/m
3
× 0.015 m
900.0 kg/m
3
r
water
× y
water
r
oil
Section One—Student Edition Solutions I Ch. 8–7
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
31. k = 90.0 N/m
m
b
= 2.00 g
V = 5.00 m
3
g = 9.81 m/s
2
r
air
= 1.29 kg/m
3
r
hel
= 0.179 kg/m
3
F
net
= F
B
− F
g,b
− F
g,hel
− F
spring
= 0
r
air
Vg − m
b
g − r
hel
Vg − k∆x = 0
∆x =
∆x =
∆x =
∆x ==0.605 m
(9.81 m/s
2
)(5.55 kg)
90.0 N/m
(9.81 m/s
2
)(6.45 kg − 2.00 × 10
−3
kg − 0.895 kg)
90.0 N/m
(9.81 m/s
2
)[(1.29 kg/m
3
)(5.00 m
3
) − 2.00 × 10
−3
kg − (0.179 kg/m
3
)(5.00 m
3
)]
90.0 N/m
g(r
air
V − m
b
− r
hel
V)
k
32. A = 2.0 cm
2
r = 1.0 g/cm
3
v = 42 cm/s
A
2
= 3.0 × 10
3
cm
2
a. flow rate = Av = (2.0 cm
2
)(42 cm/s) = 84 cm
3
/s
In g/s:
flow rate = (84 cm
3
/s)(1.0 g/cm
3
) =
b. Use the continuity equation.
v
2
=
A
A
1
v
2
1
=
(2.0
3.
c
0
m
×
2
1
)(
0
4
3
2
cm
cm
2
/s)
= 0.028 cm/s = 2.8 × 10
−4
m/s
84 g/s
33. m = 1.0 kg
r = 0.10 m
h = 2.0 m
r
water
= 1.00 × 10
3
kg/m
3
g = 9.81 m/s
2
r
air
= 1.29 kg/m
3
F
net
= (m + m
air
)a = F
B
− F
g,b
− F
g,a
(m + m
air
)a = r
water
Vg − g(m + m
air
)
a =
m
r
w
+
ate
m
r
V
ai
g
r
− g =−g =
3m
r
w
+
ate
r
r
(
a
4
ir
p
(
r
4
3
p
)g
r
3
)
− g
a =−9.81 m/s
2
a =−9.81 m/s
2
a =− 9.81 m/s
2
a = 41 m/s
2
− 9.81 m/s
2
= 31 m/s
2
Use the following equation to find the speed of the ball as it exits the water.
Note that v
i
= 0.
v
f
2
= v
i
2
+ 2ah = 2ah
Use the following equation to find the maximum height of the ball above the water.
Note that v
i
= v
f
for the ball leaving the water.
v
f
2
= v
i
2
− 2g∆y = 0
∆y =
v
2
i
g
2
=
2
2
a
g
h
=
a
g
h
∆y =
(31
9
m
.8
/s
1
2
m
)(2
/s
.0
2
m)
= 6.3 m
(1.00 × 10
3
kg/m
3
)(4π)(0.10 m
3
)(9.81 m/s
2
)
3.0 kg
(1.00 × 10
3
kg/m
3
)(4p)(0.10 m)
3
(9.81 m/s
2
)
3.0 kg + 0.016 kg
(1.00 × 10
3
kg/m
3
)(4p)(0.10 m)
3
(9.81 m/s
2
)
(3)(1.0 kg) + (1.29 kg/m
3
)(4p)(0.10 m)
3
r
water
4
3
pr
3
g
m + r
air
4
3
pr
3
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualI Ch. 8–8
34. ∆t = 1.00 min
N = 150
m = 8.0 g
v = 400.0 m/s
A = 0.75 m
2
For one bullet:
P =
A
F
=
A
∆
∆
p
t
=
mv
A
f
−
∆t
mv
i
In a perfect elastic collision with the wall, v
i
=− v
f
.
P =
2
A
m
∆
v
t
For all the bullets:
P = N
2
A
m
∆
v
t
==21 Pa
(150)(2)(8.0 × 10
−3
kg)(400.0 m/s)
(0.75 m
2
)(1.00 min)(60 s/min)
35. m = 4.00 kg
r =
0.20
2
0m
= 0.100 m
h = 4.00 m
r
water
= 1.00 × 10
3
kg/m
3
g = 9.81 m/s
2
a. Assume that the mass of the helium in the sphere is not significant compared with
the 4.00 kg mass of the sphere.
F
net
= ma = F
B
− F
g
ma = r
water
Vg − mg
a =
a =
a =
41.1
4
N
.0
−
0k
3
g
9.2 N
=
4
1
.0
.9
0
N
kg
=
b. Noting that v
i
= 0,
∆y = v
i
∆t +
1
2
a∆t
2
=
1
2
a∆t
2
∆t =
2∆
a
y
=
2(
h
a
−
2
r)
∆t =
=
(2
0
)
.4
(
3
8
.
8
m
0
/
m
s
2
)
= 4.0 s
(2)(4.00 m − 0.200 m)
0.48 m/s
2
0.48 m/s
2
(1.00 × 10
3
kg/m
3
)
4
3
(p)(0.100 m)
3
(9.81 m/s
2
) − (4.00 kg)(9.81 m/s
2
)
4.00 kg
r
water
4
3
pr
3
g − mg
m
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 8–9
Givens Solutions
37. k = 16.0 N/m
m
b
= 5.00 × 10
−3
kg
r
b
= 650.0 kg/m
3
r
water
= 1.00 × 10
3
kg/m
3
g = 9.81 m/s
2
F
net
= F
B
− F
g
− F
spring
= 0
r
water
Vg − m
b
g − k∆x = 0
r
water
m
r
b
b
g − m
b
g − k∆x = 0
∆x =
∆x =
∆x =
∆x =
∆x ==1.7 × 10
−3
m
(0.54)(5.00 × 10
−3
kg)(9.81 m/s
2
)
16.0 N/m
(1.54 − 1)(5.00 × 10
–3
kg)(9.81 m/s
2
)
16.0 N/m
1.0
6
0
50
×
.0
10
k
3
g
k
/m
g/
3
m
3
− 1
(5.00 × 10
−3
kg)(9.81 m/s
2
)
16.0 N/m
r
w
r
a
b
ter
− 1
m
b
g
k
r
water
m
r
b
b
g − m
b
g
k
2.
A
A
a
l
p
if
p
t
l
e
i
d
ed
=
1
7
A
F
a
a
p
p
p
p
l
l
i
i
e
e
d
d
=
A
F
l
l
i
i
f
f
t
t
e
e
d
d
F
applied
=
F
lifted
A
×
lif
A
ted
applied
F
applied
=
1
7
F
lifted
Fluid Mechanics, Standardized Test Prep
7. v
top
= v
i
= 0 m/s
v
f
2
= v
i
2
+ 2g(h
top
− h
bottom
)
v
bottom
2
= 2g(h
top
− h
bottom
)
v
bottom
=
2g(h
top
− h
bott
om
)
8. A
2
= 0.5 A
1
A
1
v
1
= A
2
v
2
v
2
=
A
A
1
v
2
1
v
2
=
A
A
1
v
2
1
=
0
A
.5
1
v
A
1
1
v
2
=
0
v
.
1
5
v
2
= 2v
1
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualI Ch. 8–10
11. A
m
= 6.40 cm
2
A
b
= 1.75 cm
2
m
k
= 0.50
F
p
= 44 N
A
F
1
1
=
A
F
2
2
F
b
=
A
A
m
b
F
p
=
1
6
.
.
7
4
5
0
c
c
m
m
2
2
(44 N) = 12 N
F
b
is the normal force exerted on the brake shoe. F
k
is given as follows:
F
k
= m
k
F
n
= (0.50)(12 N) = 6.0 N
12.
F
B
= F
g
F
B,oil
+ F
B,water
= F
g,block
14. r
oil
= 930 kg/m
3
h = 4.00 cm
r
block
= 960 kg/m
3
r
water
= 1.00 × 10
3
kg/m
3
g = 9.81 m/s
2
y =
(
(
r
r
b
w
lo
a
c
t
k
er
−
−
r
r
o
o
il
i
)
l
)
h
=
y ==1.71 × 10
−2
m = 1.71 cm
(0.0400 m)(30 kg/m
3
)
70 kg/m
3
(0.0400 m)(960 kg/m
3
− 930 kg/m
3
)
1.00 × 10
3
kg/m
3
− 930 kg/m
3
13.
F
B,oil
+ F
B,water
= F
g,block
m
oil
g + m
water
g = m
block
g
r
oil
V
oil
+ r
water
V
water
= r
block
V
block
r
oil
A(h − y) + r
water
Ay = r
block
Ah
r
oil
(h − y) + r
water
y = r
block
h
r
oil
h − r
oil
y + r
water
y = r
block
h
y(r
water
− r
oil
) = h(r
block
− r
oil
)
y =
(
(
r
r
b
w
lo
a
c
t
k
er
−
−
r
r
o
o
il
i
)
l
)
h
10. r
a
=
1.6
2
cm
= 0.80 cm
r
c
=
1.0 × 1
2
0
−6
m
= 0.50 × 10
−6
m
v
a
= 1.0 m/s
v
c
= 1.0 cm/s
Use the continuity equation.
A
c
=
A
v
a
c
v
a
,where A
c
is the total capillary cross section needed.
A
c
=
pr
v
a
c
2
v
a
==2.0 × 10
−2
m
2
A
c
= NA
N =
A
A
c
=
p
A
r
c
c
2
==2.5 × 10
10
capillaries
2.0 × 10
−2
m
2
(p)(0.50 × 10
−6
m)
2
(p)(8.0 × 10
−3
m)
2
(1.0 m/s)
0.010 m/s
Section One—Student Edition Solutions I Ch. 9–1
Heat
Student Edition Solutions
I
1. T
F
=−128.6°F
3. T
F,1
= 98.6°F
T
F,2
= 102°F
4. T
C,i
= 23°C
T
C,f
= 78°C
5. T = 77.34 K
T
C
=
5
9
(T
F
− 32.0) =
5
9
(−128.6 − 32.0)°C =
5
9
(−160.6)°C
T
C
=
T = T
C
+ 273.15 = (−89.22 + 273.15) K = 183.93 K
−89.22°C
T
C,1
=
5
9
(T
F,1
− 32.0) =
5
9
(98.6 − 32.0)°C =
5
9
(66.6)°C
T
C,1
=
T
C,2
=
5
9
(T
F,2
− 32.0) =
5
9
(102°−32.0)°C =
5
9
(7.0 × 10
1
)°C
T
C,2
= 39°C
37.0°C
T = T
C
+ 273.15
T
i
= T
C,i
+ 273.15 = (23 + 273.15) K = 296 K
T
f
= T
C,f
+ 273.15 = (78 + 273.15) K = 351 K
∆T = T
f
− T
i
= 351 K − 296 K =
Alternatively, because a degree Celsius equals a kelvin,
∆T =∆T
C
= T
C,f
− T
C,i
= 78°C − 23°C
∆T = 55°C =
∆T
F
=
9
5
(78 − 23)°F =
9
5
(55)°F = 99°F
55 K
55 K
T
C
= T − 273.15 = (77.34 − 273.15)°C =
T
F
=
9
5
T
C
+ 32.0 =
9
5
(−195.81)°F + 32.0°F = (−352.46 + 32.0)°F
T
F
=−320.5°F
−195.81°C
Heat, Practice A
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. T
F,1
= 105°F
T
F,2
=−25°F
T
C,1
=
5
9
(T
F,1
− 32.0) =
5
9
(105 − 32.0)°C =
5
9
(73)°C
T
C,1
=
T = (T
C
+ 273.15)K
T
1
= (41 + 273.15)K =
T
C,2
=
5
9
(T
F,2
− 32.0) =
5
9
(−25 − 32.0)°C =
5
9
(−57)°C
T
C,2
=
T
2
= (−32 + 273.15)K = 241 K
−32°C
314 K
41°C
Holt Physics Solution ManualI Ch. 9–2
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. T = 90.2 K
3. boiling point = 444.6°C
melting point = 586.1°F
below boiling point
T
C
= T − 273.15 = (90.2 − 273.15)°C =
T
F
=
9
5
(T
C
) + 32.0 =
9
5
(−183.0)°F + 32.0°F = (−329.4 + 32.0)°F
T
F
=−297.4°F
−183.0°C
a. ∆T
C
=
5
9
(∆T
F
) =
5
9
(586.1)°C = 325.6°C
melting point = 444.6°C − 325.6°C =
b. T
F,1
=
9
5
(T
C,1
) + 32.0 =
9
5
(119.0)°F + 32.0°F = (214.2 + 32.0)°F
T
F,1
=
T
F,2
=
9
5
(T
C,2
) + 32.0 =
9
5
(444.6)°F + 32.0°F = (800.3 + 32.0)°F
T
F,2
=
c. T
1
= T
C,1
+ 273.15 = (119.0 + 273.15) K =
T
2
= T
C,2
+ 273.15 = (444.6 + 273.15) K = 717.8 K
392.2 K
832.3°F
246.2°F
119.0°C
Heat, Section 1 Review
Givens Solutions
1. m = 11.5 kg
g = 9.81 m/s
2
h = 6.69 m
2. m
s
= 0.500 kg
m
h
= 2.50 kg
v
h
= 65.0 m/s
3. m = 3.0 × 10
−3
kg
h = 50.0 m
4. ∆U = 209.3 J
m = 0.25 kg
∆U = mgh = (11.5 kg)(9.81 m/s
2
)(6.69 m) = 755 J
∆U =
1
3
(KE
h
) =
1
3
1
2
m
h
v
h
2
=
1
6
(2.50 kg)(65.0 m/s)
2
∆U = 1.76 × 10
3
J
∆U = (0.65)(PE
i
) = (0.65)(mgh) = (0.65)(3.0 × 10
−3
kg)(9.81 m/s
2
)(50.0 m)
∆U = 0.96 J
∆U = KE =
1
2
mv
2
v =
2∆
m
U
=
(2)
0
(
.
2
2
0
5
9
k
.3
g
J)
= 41 m/s
Heat, Practice B
3. m = 505 kg
h = 50.0 m
g = 9.81 m/s
2
∆U = PE
i
= mgh = (505 kg)(9.81 m/s
2
)(50.0 m) = 2.48 × 10
5
J
Heat, Section 2 Review
Section One—Student Edition Solutions I Ch. 9–3
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. m
g
= 3.0 kg
T
g
= 99°C
c
p,g
= 129 J/kg
•
°C
m
w
= 0.22 kg
T
w
= 25°C
c
p,w
= 4186 J/kg
•
°C
2. m
t
= 0.225 kg
T
t
= 97.5°C
m
w
= 0.115 kg
T
w
= 10.0°C
c
p,t
= 230 J/kg
•
°C
c
p,w
= 4186 J/kg
•
°C
c
p,w
m
w
∆T
w
=−c
p,g
m
g
∆T
g
c
p,w
m
w
(T
f
− T
w
) =−c
p,g
m
g
(T
f
− T
g
)
T
f
=
c
p,w
m
w
= (4186 J/kg
•
°C)(0.22 kg) = 920 J/°C
T
w
c
p,w
m
w
= (25°C)(4186 J/kg
•
°C)(0.22 kg) = 2.3 × 10
4
J
c
p,g
m
g
= (129 J/kg
•
°C)(3.0 kg) = 390 J/°C
T
g
c
p,g
m
g
= (99°C)(129 J/kg
•
°C)(3.0 kg) = 3.8 × 10
4
J
T
f
==
6
1
.
3
1
1
×
0
1
J/
0
°
4
C
J
T
f
= 47°C
2.3 × 10
4
J + 3.8 × 10
4
J
920 J/°C + 390 J/°C
T
w
c
p,w
m
w
+ T
g
c
p,g
m
g
c
p,w
m
w
+ c
p,g
m
g
c
p,w
m
w
∆T
w
=−c
p,t
m
t
∆T
t
c
p,w
m
w
(T
f
− T
w
) =−c
p,t
m
t
(T
f
− T
t
)
T
f
=
c
p,w
m
w
= (4186 J/kg
•
°C)(0.115 kg) = 481 J/°C
T
w
c
p,w
m
w
= (10.0°)(4186 J/kg
•
°C)(0.115 kg) = 4.81 × 10
3
J
c
p,t
m
t
= (230 J/kg
•
°C)(0.225 kg) = 52 J/°C
T
t
c
p,t
m
t
= (97.5°C)(230 J/kg
•
°C)(0.225 kg) = 5.0 × 10
3
J
T
f
= =
T
f
= 18°C
9.8 × 10
3
J
533 J/°C
4.81 × 10
3
J + 5.0 × 10
3
J
481 J/°C + 52 J/°C
T
w
c
p,w
m
w
+ T
t
c
p,t
m
t
c
p,w
m
w
+ c
p,t
m
t
Givens Solutions
Heat, Practice C
3. m
b
= 0.59 kg
T
b
= 98.0°C
m
w
= 2.80 kg
T
w
= 5.0°C
T
f
= 6.8°C
c
p,w
= 4186 J/kg
•
°C
−c
p,b
m
b
∆T
b
= c
p,w
m
w
∆T
w
∆T
w
= T
f
− T
w
= 6.8°C − 5.0°C = 1.8°C
∆T
b
= T
f
− T
b
= 6.8°C − 98.0°C =−91.2°C
c
p,b
=−
c
p,
m
w
m
b
∆
w
T
∆
b
T
w
=−
c
p,b
= 390 J/kg
•
°C
(4186 J/kg
•
°C)(2.80 kg)(1.8°C)
(0.59 kg)(−91.2°C)
4. ∆T
w
= 8.39°C
m
w
= 101 g
c
p,w
= 4186 J/kg
•
°C
∆T
c
=−68.0°C
c
p,c
= 387 J/kg
•
°C
−c
p,c
m
c
∆T
c
= c
p,w
m
w
∆T
w
m
c
= −
c
p
,w
c
p
m
,c
∆
w
T
∆
c
T
w
m
c
= −
m
c
= 0.135 kg = 135 g
(4186 J/kg
•
°C)(0.101 kg)(8.39°C)
(387 J/kg
•
°C)(−68.0°C)
Holt Physics Solution ManualI Ch. 9–4
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. T
f
= 175°C
T
p
= 21°C
c
p,p
= 1650 J/kg
•
°C
m
p
= (0.105 g/kernel)
(125 kernels)
3. m
w
= (0.14)(95.0 g)
L
v
= (0.90)(2.26 × 10
6
J/kg)
∆T = T
f
− T
p
= 175°C − 21°C = 154°C
Q = m
p
c
p,p
∆T = (0.105 × 10
−3
kg/kernel)(125 kernels)(1650 J/kg
•
°C)(154°C)
Q = 3340 J
Q = m
w
L
v
= (0.14)(95.0 × 10
−3
kg)(0.90)(2.26 × 10
6
J/kg)
Q = 2.7 × 10
4
J
Givens Solutions
9. T
F
= 136°F
10. T
F
= 1947°F
T
C
=
5
9
(T
F
− 32.0) =
5
9
(136 − 32.0)°C =
5
9
(104)°C =
T = (T
C
+ 273.15)K = (57.8 + 273.15)K
T = 331.0 K
57.8°C
T
C
=
5
9
(T
F
− 32.0) =
5
9
(1947 − 32.0) =
5
9
(1915)°C =
T = T
C
+ 273.15 = (1064 + 273.15) K = 1337 K
1064°C
Heat, Chapter Review
1. m
g
= 47 g
T
g
= 99°C
T
w
= 25°C
T
f
= 38°C
c
p,g
= 1.29 × 10
2
J/kg
•
°C
c
p,w
= 4186 J/kg
•
°C
6. m = 15 g = 0.015 kg
c
p,w
m
w
∆T
w
=−c
p,g
m
g
∆T
g
∆T
g
= T
f
− T
g
= 38°C − 99°C =−61°C
∆T
w
= T
f
− T
w
= 38°C − 25°C = 13°C
m
w
=−
c
c
p
p
,g
,
m
w
∆
g
∆
T
T
w
g
=−
m
w
= 6.8 × 10
−3
kg = 6.8 g
(1.29 × 10
2
J/kg
•
°C)(47 × 10
−3
kg)(−61°C)
(4186 J/kg
•
°C)(13°C)
a. c
p,l
=
m
Q
∆T
==
(0.01
7
5
.4
k
×
g)
1
(
0
2
3
0
J
0°C)
=
b. L
f
=
m
Q
=
8.37
0
k
.0
J
1
−
5
1
k
.
g
27 kJ
=
7.
0
1
.
0
01
×
5
1
k
0
g
3
J
=
c. c
p,s
=
m
Q
∆T
==
(0.0
1
1
.2
5
7
k
×
g)
1
(
0
8
3
0
J
°C)
=
d. c
p,v
=
m
Q
∆T
==
(0.01
1
5
×
kg
1
)
0
(
3
10
J
0°C)
=
e. L
v
=
m
Q
=
795
0
k
.
J
01
−
5
1
k
5
g
.8 kJ
=
77
0
9
.0
×
15
1
k
0
g
3
J
= 5.2 × 10
7
J/kg
7 × 10
2
J/kg
•
°C
796 kJ − 795 kJ
(0.015 kg)(400°C − 300°C)
1 × 10
3
J/kg
•
°C
1.27 kJ − 0 kJ
(0.015 kg)(80°C − 0°C)
4.7 × 10
5
J/kg
2 × 10
3
J/kg
•
°C
15.8 kJ − 8.37 kJ
(0.015 kg)(300°C − 80°C)
Heat, Section 3 Review
24. F = 315 N
d = 35.0 m
W = (0.14)(U
i
)
W = (0.14)(U
i
)
U
i
=
0
W
.14
=
0
F
.1
d
4
=
(315 N
0
)
.
(
1
3
4
5.0 m)
= 7.9 × 10
4
J
Section One—Student Edition Solutions I Ch. 9–5
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
25. m = 0.75 kg
v
i
= 3.0 m/s
31. m
r
= 25.5 g
T
r
= 84.0°C
m
w
= 5.00 × 10
−2
kg
T
w
= 24.0°C
Q
w
=−Q
r
− 0.14 kJ
c
p,r
= 234 J/kg
•
°C
c
p,w
= 4186 J/kg
•
°C
32. m
1
= 1500 kg
v
i
= 32 m/s
v
f
= 0 m/s
c
p,iron
= 448 J/kg
•
°C
m
2
= (4)(3.5 kg)
a. ∆U = (0.85)(KE) = (0.85)
1
2
mv
2
∆U =
1
2
(0.85)(0.75 kg)(3.0 m/s)
2
= 2.9 J
Q
w
=−Q
r
− 0.14 kJ
c
p,w
m
w
(T
f
− T
w
) =−c
p,r
m
r
(T
f
− T
r
) − 0.14 kJ
T
f
=
c
p,r
m
r
= (234 J/kg
•
°C)(2.55 × 10
−2
kg) = 5.97 J/°C
c
p,r
m
r
T
r
= (234 J/kg
•
°C)(2.55 × 10
−2
kg)(84.0°C) = 501 J
c
p,w
m
w
= 4186 J/kg
•
°C)(5.00 × 10
−2
kg) = 209 J/°C
c
p,w
m
w
T
w
= (4186 J/kg
•
°C)(5.00 × 10
−2
kg)(24.0°C) = 5.02 × 10
3
J
T
f
==
5.
2
3
1
8
5
×
J/
1
°
0
C
3
J
T
f
= 25.0°C
501 J + (5.02 × 10
3
J) − 140 J
209 J/°C + 5.97 J/°C
c
p,r
m
r
T
r
+ c
p,w
m
w
T
w
− 0.14 kJ
c
p,w
m
w
+ c
p,r
m
r
∆U =∆KE =
1
2
m
1
(v
f
− v
i
)
2
= (0.5)(1500 kg)(0 m/s − 32 m/s)
2
= 7.7 × 10
5
J
Q =∆U = 7.7 × 10
5
J
Q = m
2
c
p,iron
∆T
∆T =
m
2
c
Q
p,iron
==120°C
7.7 × 10
5
J
(4)(3.5 kg)(448 J/kg
•
°C)
33. T
R
= 0°R = absolute zero
one Rankine degree =
one Fahrenheit degree
a. T
R
= T
F
− (absolute zero in T
F
)
T
F
=
9
5
T
C
+ 32.0
absolute zero in T
c
=−273.15°C
absolute zero in T
F
=
9
5
(−273.15)°F + 32.0°F
absolute zero in T
F
= (−491.67 + 32.0)°F =−459.7°F
T
R
= T
F
− (−459.7)°F = T
F
+ 459.7°F
b. T = T
C
+ 273.15
T
C
=
5
9
(T
F
− 32.0)
T =
5
9
(T
F
− 32.0) + 273.15
T
F
= T
R
− 459.7
T =
5
9
(T
R
− 459.7 − 32.0) + 273.15
T =
5
9
(T
R
− 491.7) + 273.15
T =
5
9
T
R
−
5
9
(491.7) + 273.15
T =
5
9
T
R
− 273.2 + 273.15
T =
5
9
T
R
, or T
R
=
9
5
T
T
R
= T
F
+ 459.7, or T
F
= T
R
− 459.7
Holt Physics Solution ManualI Ch. 9–6
Givens Solutions
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
34. m
r
= 3.0 kg
m
w
= 1.0 kg
∆T = 0.10°C
c
p,w
= 4186 J/kg
•
°C
g = 9.81 m/s
2
PE
i
=∆U
m
r
gh = c
p,w
m
w
∆T
h =
c
p,w
m
m
r
w
g
∆T
=
h = 14 m
(4186 J/kg
•
°C)(1.0 kg)(0.10°C)
(3.0 kg)(9.81 m/s
2
)
35. freezing point = 50°TH
(0°C)
boiling point = 200°TH
(100°C)
T
C
= absolute zero =
−273.15°C
a. Set up a graph with Celsius on the x-axis and “Too Hot” on the y-axis. The equa-
tion relating the two scales can be found by graphing one scale versus the other
scale and then finding the equation of the resulting line. In this case, the two
known coordinates of the line are (0, 50) and (100, 200).
slope = a =
∆
∆
x
y
=
(
(
2
1
0
0
0
0
−
−
5
0
0
)
)
=
1
1
5
0
0
0
=
3
2
y = ax + b
b = y − ax = 50 −
3
2
0 = 50
The values y = T
TH
,a=
3
2
, x = T
C
, and b = 50 can be substituted into the equation
for a line to find the conversion equation.
y = ax + b
or x =
y −
a
b
T
C
=
b. T
TH
=
3
2
(T
C
) + 50 =
3
2
(−273.15)°TH + 50°TH = (−409.72 + 50)°TH =−360°TH
T
C
=
2
3
(T
TH
− 50)
T
TH
− 50
3
2
T
TH
=
3
2
T
C
+ 50
36. A = 6.0 m
2
P/A = 550 W/m
2
V
w
= 1.0 m
3
T
i
= 21°C
T
f
= 61°C
r
w
= 1.00 × 10
3
kg/m
3
c
p,w
= 4186 J/kg
•
°C
∆T = T
f
− T
i
= 61°C − 21°C = (4.0 × 10
1
)°C
m
w
= V
w
r
w
= (1.0 m
3
)(1.00 × 10
3
kg/m
3
) = 1.0 × 10
3
kg
∆t =
Q
P
=
m
(P
w
/
c
A
p,
)
w
(A
∆
)
T
=
∆t =
or (5.1 × 10
4
s)(1 h/3600 s) = 14 h
5.1 × 10
4
s
(1.0 × 10
3
kg)(4186 J/kg
•
°C)(4.0 × 10
1
°C)
(550 W/m
2
)(6.0 m
2
)
Section One—Student Edition Solutions I Ch. 9–7
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
37. m
c
= 253 g
T
c
= 85°C
T
a
= 5°C
T
f
= 25°C
c
p,a
= 8.99 × 10
2
J/kg
•
°C
c
p,c
= 3.87 × 10
2
J/kg
•
°C
c
p,a
m
a
∆T
a
=−c
p,c
m
c
∆T
c
∆T
c
= T
f
− T
c
= 25°C − 85°C = (−6.0 × 10
1
)°C
∆T
a
= T
f
− T
a
= 25°C − 5°C = (2.0 × 10
1
)°C
m
a
=−
m
∆
c
T
∆
a
T
c
c
p
c
,a
p,c
=−
m
a
= 0.33 kg = 330 g
(0.253 kg)(−6.0 × 10
1
°C)(3.87 × 10
2
J/kg
•
°C)
(2.0 × 10
1
°C)(8.99 × 10
2
J/kg
•
°C)
39. m
a
= 250 g
m
w
= 850 g
∆
∆
T
t
= 1.5°C/min
c
p,a
= 899 J/kg
•
°C
c
p,w
= 4186 J/kg
•
°C
∆
Q
t
=
Q
a
∆
+
t
Q
w
==(
m
a
c
p,a
+
m
w
c
p,w
)
∆
∆
T
t
∆
Q
t
= [(0.250 kg)(899 J/kg
•
°C) + (0.850 kg)(4186 J/kg
•
°)](1.5°C/min)
∆
Q
t
= (225 J/°C + 3.56 × 10
3
J/°C)(1.5°C/min) = (3.78 × 10
3
J/°C)(1.5°C/min)
∆
Q
t
=
or (5700 J/min)(1 min/60 s) = 95 J/s
5.7 × 10
3
J/min
m
a
c
p,a
∆T + m
w
c
p,w
∆T
∆t
38.
T
F
=
9
5
T
C
+ 32.0 T
C
= T − 273.15
T
F
− 32.0 =
9
5
T
C
5
9
T
F
−
5
9
(32.0) = T
C
5
9
T
F
−
5
9
(32.0) + 273.15 = T
T = T
F
5
9
T
F
−
5
9
(32.0) + 273.15 = T
F
5
9
T
F
− 17.8 + 273.15 = T
F
5
9
T
F
+ 255.4 = T
F
255.4 =
4
9
T
F
T
F
=
9
4
(255.4)°F = 574.6°F
T
F
= T
574.6°F = 574.6 K
Holt Physics Solution ManualI Ch. 9–8
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
40. T
tea
= 32°C
T
ice
= 0°C
T
f
= 15°C
m
tea
= 180 g
m
ice,tot
= 112 g
c
p,tea
= c
p,w
= 4186 J/kg
•
°C
L
f
= 3.33 × 10
5
J/kg
−∆Q
tea
=∆Q
melted ice
−m
tea
c
p,tea
∆T
tea
= m
ice
L
f
+ m
ice
c
p,w
∆T
ice
m
ice
=
∆T
tea
= T
f
− T
tea
= 15°C − 32°C =−17°C
∆T
ice
= T
f
− T
ice
= 15°C − 0°C = 15°C
m
ice
=
m
ice
=
m
ice
==3.2 × 10
−2
kg = 32 g
mass of unmelted ice = m
ice,tot
− m
ice
= 112 g − 32 g = 8.0 × 10
1
g
(180 × 10
−3
kg)(4186 J/kg
•
°C)(17°C)
3.96 × 10
5
kg
(180 × 10
−3
kg)(4186 J/kg
•
°C)(17°C)
3.33 × 10
5
J/kg + 6.3 × 10
4
J/kg
−(180 × 10
−3
kg)(4186 J/kg
•
°C)(−17°C)
3.33 × 10
5
J/kg + (4186 J/kg
•
°C)(15°C)
−m
tea
c
p,tea
∆T
tea
L
f
+ c
p,w
∆T
ice
Heat, Standardized Test Prep
8. m = 23 g
c
p,l
=
m
Q
∆T
==
c
p,l
= 1.1 × 10
3
J/kg
•
°C
4.6 × 10
3
J
(23 × 10
−3
kg)(180°C)
16.6 kJ − 12.0 kJ
(23 × 10
−3
kg)(340°C − 160°C)
9. m = 23 g
L
f
=
m
Q
=
12
2
.0
3
k
×
J
1
−
0
−
1
3
.8
k
5
g
kJ
=
2
1
3
0.
×
2
1
×
0
1
−
0
3
3
k
J
g
= 4.4 × 10
5
J/kg
3. T
C
= −252.87°C
T
F
=
9
5
T
C
+ 32.0 =
9
5
(−252.87)°F + 32.0°F
T
F
= (−455.17 + 32.0)°F =−423.2°F
4. T
C
= −252.87°C
T = T
C
+ 273.15 = (−252.87 + 273.15) K = 20.28 K
10. m = 23 g
c
p,s
=
m
Q
∆T
==
c
p,s
= 5.0 × 10
2
J/kg
•
°C
1.85 × 10
3
J
(23 × 10
−3
kg)(160°C)
1.85 kJ − 0 kJ
(23 × 10
−3
kg)(160°C − 0°C)
11. m
w
= 1.20 × 10
16
kg
c
p,w
= 4186 J/kg
•
°C
∆T = 1.0°C
Q = m
w
c
p,w
∆T = (1.20 × 10
16
kg)(4186 J/kg
•
°C)(1.0°C) = 5.0 × 10
19
J
Section One—Student Edition Solutions I Ch. 9–9
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
12. m
w
= 1.20 × 10
16
kg
L
f
= 3.33 × 10
5
J/kg
Q = m
w
L
f
= (1.20 × 10
16
kg)(3.33 × 10
5
J/kg) = 4.00 × 10
21
J
14. m
g
= 0.200 kg
m
w
= 0.300 kg
∆T = 2.0°C
c
p,g
= 837 J/kg
•
°C
c
p,w
= 4186 J/kg
•
°C
Q = Q
g
+ Q
w
= m
g
c
p,g
∆T + m
w
c
p,w
∆T = (m
g
c
p,g
+ m
w
c
p,w
)(∆T)
Q = [(0.200 kg)(837 J/kg
•
°C) + (0.300 kg)(4186 J/kg
•
°C)](2.0°C)
Q = (167 J/°C + 1260 J/°C)(2.0°C) = (1430 J/°C)(2.0°C) = 2900 J
16. T
C
=−40.0°C
T
F
=
9
5
T
C
+ 32.0 =
9
5
(−40.0)°F + 32.0°F = (−72.0 + 32.0)°F
T
F
=−40.0°F
Section One—Student Edition Solutions I Ch. 10–1
Thermodynamics
Student Edition Solutions
I
1. P = 1.6 × 10
5
Pa
V
i
= 4.0 m
3
2. P = 599.5 kPa
V
i
= 5.317 × 10
−4
m
3
V
f
= 2.523 × 10
−4
m
3
3. P = 4.3 × 10
5
Pa
V
i
= 1.8 × 10
−4
m
3
V
f
= 9.5 × 10
−4
m
3
4. r =
1.6
2
cm
= 0.80 cm
d = 2.1 cm
W = 0.84 J
a. V
f
= 2V
i
= (2)(4.0 m
3
) = 8.0 m
3
W = P∆V = P(V
f
− V
i
) = (1.6 × 10
5
Pa)(8.0 m
3
− 4.0 m
3
)
W = (1.6 × 10
5
Pa)(4.0 m
3
) =
b. V
f
=
1
4
V
i
=
1
4
(4.0 m
3
) = 1.0 m
3
W = P∆V = P(V
f
− V
i
) = (1.6 × 10
5
Pa)(1.0 m
3
− 4.0 m
3
)
W = (1.6 × 10
5
Pa)(−3.0 m
3
) =−4.8 × 10
5
J
6.4 × 10
5
J
W = P∆V = P(V
f
− V
i
) = (599.5 × 10
3
Pa)[(2.523 × 10
−4
m
3
) − (5.317 × 10
−4
m
3
)]
W = (599.5 × 10
3
Pa)(−2.794 × 10
−4
m
3
) =−167.5 J
W = P∆V = P(V
f
− V
i
) = (4.3 × 10
5
Pa)[(9.5 × 10
−4
m
3
) − (1.8 × 10
−4
m
3
)]
W = (4.3 × 10
5
Pa)(7.7 × 10
−4
m
3
) = 3.3 × 10
2
J
W = P∆V = PAd = Ppr
2
d
P =
p
W
r
2
d
==2.0 × 10
5
Pa
0.84 J
p(0.80 × 10
−2
m)
2
(2.1 × 10
−2
m)
Thermodynamics, Practice A
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. A = 7.4 × 10
−3
m
2
d =−7.2 × 10
−2
m
P = 9.5 × 10
5
Pa
3. P = 1.5 × 10
3
Pa
∆V = 5.4 × 10
−5
m
3
W = P∆V = PAd = (9.5 × 10
5
Pa)(7.4 × 10
−3
m
2
)(−7.2 × 10
−2
m) =−5.1 × 10
2
J
W = P∆V = (1.5 × 10
3
Pa)(5.4 × 10
−5
m
3
) = 8.1 × 10
−2
J
Thermodynamics, Section 1 Review
1. W = 26 J
∆U = 7 J
∆U = Q − W
Q = W +∆U = 26 J + 7 J = 33 J
Thermodynamics, Practice B
Holt Physics Solution ManualI Ch. 10–2
I
2. ∆U =−195 J
W = 52.0 J
3. U
lost
= 2.0 × 10
3
J
W = 0 J
∆U = 8.0 × 10
3
J
4. ∆U =−344 J
5. Q = 3.50 × 10
8
J
W = 1.76 × 10
8
J
Q =∆U + W =−195 J + 52.0 J =−143 J
Q =∆U + W + U
lost
= 8.0 × 10
3
J + 0 J + 2.0 × 10
3
J = 1.00 × 10
4
J
Q = for adiabatic processes.
W = Q −∆U = 0 J − (−344 J) = 344 J
0 J
∆U = Q − W = 3.50 × 10
8
J − 1.76 × 10
8
J = 1.74 × 10
8
J
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
4. P = 8.6 × 10
5
Pa
∆V = 4.05 × 10
−4
m
3
Q =−9.5 J
5. P = 7.07 × 10
5
Pa
∆V =−1.1 × 10
−4
m
3
∆U = 62 J
6. W =−1.51 × 10
4
J
Q
c
= 7.55 × 10
4
J
7. Q =−15 J
W = 13 J
a. W = P∆V = (8.6 × 10
5
Pa)(4.05 × 10
−4
m
3
) =
b. ∆U = Q − W =−9.5 J − 350 J =−3.6 × 10
2
J
3.5 × 10
2
J
Q = W +∆U = P∆V +∆U = (7.07 × 10
5
Pa)(−1.1 × 10
−4
m
3
) + 62 J
Q =−78 J + 62 J =−16 J
a. For removal of energy from inside refrigerator,
∆U
c
= Q
c
− W = (7.55 × 10
4
J) − (−1.51 × 10
4
J) = 9.06 × 10
4
J
No work is done on or by outside air, so all internal energy is given up as heat.
Q
h
=∆U
h
=∆U
c
=
b. For cyclic processes, ∆U
ref
=
c. Because there is no change in the air’s volume, W
air
=
d. For air inside refrigerator, Q
air
=−Q
c
and W
air
= 0 J.
Q
air
− W
air
=∆U
air
=−Q
c
=−7.55 × 10
4
J
0 J
0 J
9.06 × 10
4
J transferred to outside air
∆U = Q − W =−15 J − 13 J =−28 J
Thermodynamics, Section 2 Review
1. Q
h
= 2.254 × 10
4
kJ
Q
c
= 1.915 × 10
4
kJ
2. W = 45 J
Q
c
= 31 J
eff = 1 −
Q
Q
h
c
= 1 −
1
2
.
.
9
2
1
5
5
4
×
×
1
1
0
0
4
4
k
k
J
J
= 1 − 0.8496 = 0.1504
Q
h
= W + Q
c
= 45 J + 31 J = 76 J
eff =
Q
W
h
=
4
7
5
6
J
J
= 0.59
Thermodynamics, Practice C
Section One—Student Edition Solutions I Ch. 10–3
I
4. eff = 0.21
Q
c
= 780 J
5. W = 372 J
eff = 0.330
eff = 1 −
Q
Q
h
c
eff − 1 =−
Q
Q
h
c
1 − eff =
Q
Q
h
c
Q
h
=
1
Q
−
c
eff
=
1
7
−
8
0
0
.2
J
1
=
7
0
8
.7
0
9
J
= 990 J
W = Q
h
− Q
c
= 990 J − 780 J = 210 J
Q
h
= W + Q
c
eff = 1 −
Q
Q
h
c
= 1 −
W
Q
+
c
Q
c
=
W
W
+ Q
+
c
Q
−
c
Q
c
=
W
W
+ Q
c
W + Q
c
=
e
W
ff
Q
c
=
e
W
ff
− W =
e
1
ff
− 1
W =
0.3
1
30
− 1
(372 J)
Q
c
= (3.03 − 1)(372 J) = (2.03)(372 J) = 755 J
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. Q
h
= 75 000 J
Q
c
= 35 000 J
a. W = Q
h
− Q
c
= 75 000 J − 35 000 J =
b. eff =
Q
W
h
=
4
7
.0
5
×
00
1
0
0
4
J
J
= 0.53
4.0 × 10
4
J
Thermodynamics, Section 3 Review
9. V
i
= 35.25 × 10
−3
m
3
V
f
= 39.47 × 10
−3
m
3
P = 2.55 × 10
5
Pa
10. P = 2.52 × 10
5
Pa
V
i
= 1.1 × 10
−4
m
3
V
f
= 1.50 × 10
−3
m
3
W = P∆V = P(V
f
− V
i
) = (2.55 × 10
5
Pa)[(39.47 × 10
−3
m
3
) − (35.25 × 10
−3
m
3
)]
W = (2.55 × 10
5
Pa)(4.22 × 10
−3
m
3
) = 1.08 × 10
3
J
W = P∆V = P(V
f
− V
i
)
W = (2.52 × 10
5
Pa)(1.50 × 10
−3
m
3
− 1.1 × 10
−4
m
3
)
W = (2.52 × 10
5
Pa)(1.4 × 10
−3
m
3
)
W = 3.5 × 10
2
J
Thermodynamics, Chapter Review
3. Q
h
= 1.98 × 10
5
J
Q
c
= 1.49 × 10
5
J
a. eff = 1 −
Q
Q
h
c
= 1 −
1
1
.
.
4
9
9
8
×
×
1
1
0
0
5
5
J
J
= 1 − 0.753 =
b. W = Q
h
− Q
c
= (1.98 × 10
5
J) − (1.49 × 10
5
J) = 4.9 × 10
4
J
0.247
6. Q
c
= 6.0 × 10
2
J
eff = 0.31
Q
h
=
1
Q
−
c
eff
=
6
1
.0
−
×
0
1
.3
0
1
2
J
=
6.0
0
×
.6
1
9
0
2
J
= 8.7 × 10
2
J
Holt Physics Solution ManualI Ch. 10–4
I
16. ∆U = 604 × 10
3
J
W = 43.0 × 10
3
J
17. m
1
= 150 kg
m
2
= 6050 kg
T
i
= 22°C
T
f
= 47°C
d = 5.5 mm
c
p
= 448 J/kg
•
°C
g = 9.81 m/s
2
26. Q
h
= 525 J
Q
c
= 415 J
27. Q
h
= 9.5 × 10
12
J
Q
c
= 6.5 × 10
12
J
Q =∆U + W = (604 × 10
3
J) + (43.0 × 10
3
J) = 647 × 10
3
J
a. Q = m
1
c
p
∆T = m
1
c
p
(T
f
− T
i
) = (150 kg)(448 J/kg
•
°C)(47°C − 22°C)
Q = (150 kg)(448 J/kg
•
°C)(25°C) =
b. W = Fd = m
2
gd = (6050 kg)(9.81 m/s
2
)(5.5 × 10
−3
m)
W =
c. ∆U = Q − W = (1.7 × 10
6
J) − (3.3 × 10
2
J) = 1.7 × 10
6
J
3.3 × 10
2
J
1.7 × 10
6
J
eff = 1 −
Q
Q
h
c
= 1 −
4
5
1
2
5
5
J
J
= 1 − 0.790 = 0.210
eff = 1 −
Q
Q
h
c
= 1 −
6
9
.
.
5
5
×
×
1
1
0
0
1
1
2
2
J
J
= 1 − 0.68 = 0.32
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
28. Q
h
= 850 J
Q
c
= 5.0 × 10
2
J
W = 3.5 × 10
2
J
eff = 1 −
Q
Q
h
c
= 1 −
5.0
8
×
50
10
J
2
J
= 1 − 0.59 =
Alternatively,
eff =
Q
W
h
=
3.5
8
×
50
10
J
2
J
= 0.41
0.41
29. Q
1
= 606 J
W
1
= 418 J
W
2
= 1212 J
a. ∆U
1
= Q
1
− W
1
= 606 J − 418 J =
b. Because ∆U
2
=∆U
1
, Q
2
=∆U
1
+ W
2
Q
2
= 188 J + 1212 J = 1.400 × 10
3
J
188 J
30. Q = 5175 J
d. Because ∆V = 0, W = 0 J and ∆U = Q = .5175 J
9. P = 1055 MW
eff = 0.330
Q
h
=
e
W
ff
Q
∆t
h
=
ef
W
f ∆t
=
e
P
ff
=
10
0
5
.
5
33
M
0
W
= 3.20 × 10
3
MW
Q
c
= Q
h
− W
Q
∆t
c
=
Q
∆t
h
−
∆
W
t
=
Q
∆t
h
− P = 3.20 × 10
3
MW − 1055 MW
Q
∆t
c
= 2140 MW = 2140 MJ/s = 2.14 × 10
9
J/s
Thermodynamics, Standardized Test Prep
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 10–5
10. ∆V = 0.041 m
3
− 0.031 m
3
= 0.010 m
3
P = 300.0 kPa
W = P∆V = (300.0 × 10
3
Pa)(0.010 m
3
) = 3.0 × 10
3
J
13. Q
h
= 1600 J
Q
c
= 1200 J
eff = 1 −
Q
Q
h
c
= 1 −
1
1
2
6
0
0
0
0
J
J
= 1 − 0.75
eff = 0.25
15. m = 450.0 kg
h = 8.6 m
W = mgh = (450.0 kg)(9.81 m/s
2
)(8.6 m) = 3.8 × 10
4
J
16. Q
h
= 2.00 × 10
5
J
W = 3.8 × 10
4
J (see 15.)
eff =
Q
W
h
=
2
3
.
.
0
8
0
×
×
1
1
0
0
4
5
J
J
= 0.19
17. Q
h
= 2.00 × 10
5
J
eff = 0.19 (see 16.)
eff =
Q
h
Q
−
h
Q
c
eff(Q
h
) = Q
h
− Q
c
Q
c
= Q
h
− eff(Q
h
) = 2.00 × 10
5
J − (0.19)(2.00 × 10
5
J)
Q
c
= 2.00 × 10
5
J − 3.8 × 10
4
J = 1.62 × 10
5
J
18. Q
h
= 2.00 × 10
5
J
W = 3.8 × 10
4
J (see 15.)
∆U = 5.0 × 10
3
J
∆U = Q − W = Q
h
− Q
c
− W
Q
c
= Q
h
− W −∆U
Q
c
= 2.00 × 10
5
J − 3.8 × 10
4
J − 5.0 × 10
3
J = 1.57 × 10
5
J
Section One—Student Edition Solutions I Ch. 11–1
Vibrations and Waves
Student Edition Solutions
I
1. x =−36 cm
m = 0.55 kg
g = 9.81 m/s
2
2. F
g
=−45 N
x =−0.14 m
4. x
2
=−3.0 cm
a. F
g
+ F
elastic
= 0
F
g
=−mg
F
elastic
=−kx
−mg − kx = 0
k =
−m
x
g
==15 N/m
−(0.55 kg)(9.81 m/s
2
)
−0.36 m
F
g
+ F
elastic
= 0
F
g
+ (−kx) = 0
k =
F
x
g
=
−
−
0
4
.1
5
4
N
m
= 3.2 × 10
2
N/m
F
2
=−kx
2
F
2
=−(2.7 × 10
3
N/m)(−0.030 m) = 81 N
Vibrations and Waves, Practice A
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. x =−4.0 cm
k = 13 N/m
F =−kx =−(13 N/m)(−0.040 m)
F = 0.52 N
Vibrations and Waves, Section 1 Review
1. T = 24 s
a
g
= g = 9.81 m/s
2
2. T = 1.0 s
a
g
= g = 9.81 m/s
2
T = 2p
a
L
g
L = a
g
2
T
p
2
= (9.81 m/s
2
)
2
2
4
p
s
2
= 1.4 × 10
2
m
T = 2p
a
L
g
L = a
g
2
T
p
2
= (9.81 m/s
2
)
1
2
.0
p
s
2
= 0.25 m = 25 cm
Vibrations and Waves, Practice B
3. F
1
= 32 N
x
1
=−1.2 cm
k =
−
x
F
1
1
=
−0
−
.
3
0
2
12
N
m
= 2.7 × 10
3
N/m
Holt Physics Solution ManualI Ch. 11–2
I
3. T = 3.8 s
a
g
= g = 9.81 m/s
2
4. L = 3.500 m
a
g
= 9.832 m/s
2
a
g
= 9.803 m/s
2
a
g
= 9.782 m/s
2
T = 2p
a
L
g
L = a
g
2
T
p
2
= (9.81 m/s
2
)
3
2
.8
p
s
2
= 3.6 m
a. T
1
= 2p
a
L
g
= 2p
9.
3
8
.
3
5
2
00
m
m
/
s
2
=
f
1
=
T
1
1
=
3.7
1
49 s
=
b. T
2
= 2p
a
L
g
= 2p
9.
3
8
.
0
5
3
00
m
m
/
s
2
=
f
2
=
T
1
2
=
3.7
1
54 s
=
c. T
3
= 2p
a
L
g
= 2p
9.
3
7
.
8
5
2
00
m
m
/
s
2
=
f
3
=
T
1
3
=
3.7
1
58 s
= 0.2661 Hz
3.758 s
0.2664 Hz
3.754 s
0.2667 Hz
3.749 s
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. T = 0.24 s
m = 0.30 kg
4. m
p
= 255 kg
m
c
= 1275 kg
k = 2.00 × 10
4
N/m
T = 2p
m
k
k =
4p
T
2
2
m
=
4p
2
(0
(
.
0
2
.
4
30
s)
kg)
= 2.1 × 10
2
N/m
m =
m
p
4
+ m
c
=
255 kg +
4
1275 kg
=
1.530 ×
4
10
3
kg
= 382.5 kg
T = 2p
m
k
= 2p
= 0.869 s
382.5 kg
2.00 × 10
4
N/m
Vibrations and Waves, Practice C
2. m = 25 g = 0.025 kg
f =
20 vi
4
b
.
r
0
a
s
tions
= 5.0 Hz
T =
1
f
= 2p
m
k
k = 4p
2
mf
2
= 4p
2
(0.025 kg)(5.0 Hz)
2
= 25 N/m
3. F = 125 N
g = 9.81 m/s
2
T = 3.56 s
T = 2p
m
k
= 2p
g
F
k
k =
4
g
p
T
2
2
F
=
(9.8
(
1
4p
m
2
/
)
s
(
2
1
)
2
(
5
3.
N
56
)
s)
2
k = 39.7 N/m
Section One—Student Edition Solutions I Ch. 11–3
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
5. k = 30.0 N/m
m
1
= 2.3 kg
m
2
= 15 g
m
3
= 1.9 kg
a. T
1
= 2p
m
k
1
= 2p
30
2
.
.
0
3
N
kg
/m
T
1
=
f
1
=
T
1
1
=
1.
1
7s
=
b. T
2
= 2p
m
k
2
= 2p
3
0
0
.0
.0
1
N
5
k
/
m
g
T
2
=
f
2
=
T
1
2
=
0.1
1
4s
=
c. T
3
= 2p
m
k
3
= 2p
30
1
.
.
0
9
N
kg
/m
T
3
=
f
3
=
T
1
3
=
1.
1
6s
= 0.62 Hz
1.6 s
7.1 Hz
0.14 s
0.59 Hz
1.7 s
1. f = 180 oscillations/min
2. L = 2.5 m
a
g
= g = 9.81 m/s
2
3. m = 0.75 kg
x =−0.30 m
g = 9.81 m/s
2
f = (180 oscillations/min)(1 min/60 s)
f =
T =
1
f
=
3.0
1
Hz
= 0.33 s
3.0 Hz
a. T = 2p
a
L
g
= 2p
9.
8
2
1
.5
m
m
/s
2
T =
b. f =
T
1
=
3.
1
2s
= 0.31 Hz
3.2 s
a. −kx − mg = 0
k =
−m
x
g
=
k =
b. T = 2p
m
k
= 2p
2
0
5
.7
N
5
/
k
m
g
T = 1.1 s
25 N/m
−(0.75 kg)(9.81 m/s
2
)
−0.30 m
Vibrations and Waves, Section 2 Review
1. f
1
= 28 Hz
f
2
= 4200 Hz
v = 340 m/s
l
1
=
f
v
1
=
3
2
4
8
0
H
m
z
/s
=
l
2
=
f
v
2
=
4
3
2
4
0
0
0
m
H
/s
z
= 0.081 m
12 m
Vibrations and Waves, Practice D
Holt Physics Solution ManualI Ch. 11–4
I
2. v = 3.00 × 10
8
m/s
f
1
= 88.0 MHz
f
2
= 6.0 × 10
8
MHz
f
3
= 3.0 × 10
12
MHz
3. l = 633 nm
l = 6.33 × 10
−7
m
v = 3.00 × 10
8
m/s
4. f = 256 Hz
l
air
= 1.35 m
v
water
= 1500 m/s
a. l
1
=
f
v
1
=
3
8
.
.
0
8
0
0
×
×
1
1
0
0
8
7
m
H
/
z
s
l
1
=
b. l
2
=
f
v
2
=
3
6
.
.
0
0
0
×
×
1
1
0
0
1
8
4
m
H
/
z
s
l
2
=
c. l
3
=
f
v
3
=
3
3
.
.
0
0
0
×
×
1
1
0
0
1
8
8
m
H
/
z
s
l
3
= 1.0 × 10
−10
m
5.0 × 10
−7
m
3.41 m
f =
l
v
=
3
6
.
.
0
3
0
3
×
×
1
1
0
0
8
−7
m
m
/s
f = 4.74 × 10
14
Hz
a. v
air
= l
air
f = (1.35 m)(256 Hz)
v
air
=
b. l
water
=
v
w
f
ater
=
1
2
5
5
0
6
0
H
m
z
/s
l
water
= 5.86 m
346 m/s
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
5. l = 0.57 cm = 5.7 × 10
−3
m
v = 340 m/s
f =
l
v
=
5.7
34
×
0
1
m
0
−
/
3
s
m
f = 6.0 × 10
4
Hz
Vibrations and Waves, Section 3 Review
8. m = 0.40 kg
x =−3.0 cm
g = 9.81 m/s
2
−kx − mg = 0
k =
−m
x
g
=
k = 130 N/m
−(0.40 kg)(9.81 m/s
2
)
−0.030 m
Vibrations and Waves, Chapter Review
9. x =−0.40 m
F = 230 N
k =
−
x
F
=
−
−
0
2
.
3
4
0
0
N
m
= 580 N/m
19. f = 0.16 Hz
a
g
= g = 9.81 m/s
2
T =
1
f
= 2p
a
L
g
L ==
(4p
(9
2
.
)
8
(
1
0.
m
16
/s
H
2
)
z)
2
L = 9.7 m
a
g
(2pf)
2
Section One—Student Edition Solutions I Ch. 11–5
I
20.
L
1
= 0.9942 m
L
2
= 0.9927 m
21. k = 1.8 × 10
2
N/m
m = 1.5 kg
34. f = 25.0 Hz
1
2
l = 10.0 cm
2(amplitude) = 18 cm
35. v = 3.00 × 10
8
m/s
f = 9.00 × 10
9
Hz
a. Because a pendulum passes through its equilibrium position twice each cycle,
T = (2)(1.000 s) = .
b. a
g
=
4p
T
2
2
L
1
=
(4p
(
2
2
)
.
(
0
0
0
.9
0
9
s
4
)
2
2
m)
a
g
=
c. a
g
=
4p
T
2
2
L
2
=
(4p
(
2
2
)
.
(
0
0
0
.9
0
9
s
2
)
7
2
m)
a
g
= 9.798 m/s
2
9.812 m/s
2
2.000 s
a. T = 2p
m
k
= 2p
1.
8
×
1
.
1
5
0
k
2
g
N
/m
T =
b. f =
T
1
=
0.5
1
7s
= 1.8 Hz
0.57 s
a. amplitude =
18
2
cm
=
b. l = (2)(10.0 cm) =
c. T =
1
f
=
25.0
1
Hz
=
d. v = lf = (0.200 m)(25.0 Hz) = 5.00 m/s
0.0400 s
20.0 cm
9.0 cm
l =
v
f
=
3
9
.
.
0
0
0
0
×
×
1
1
0
0
8
9
m
H
/
z
s
= 0.0333 m
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
44. k = 230 N/m
x =−6.0 cm
F =−kx
F =−(230 N/m)(−0.060 m)
F = 14 N
45. x =−2.0 cm
k = 85 N/m
F =−kx =−(85 N/m)(−0.020 m)
F = 1.7 N
46. l = 0.15 m
Because a wave is generated twice each second, f = .
T =
1
f
=
2.0
1
Hz
=
v = lf = (0.15 m)(2.0 Hz) = 0.30 m/s
0.50 s
2.0 Hz
Holt Physics Solution ManualI Ch. 11–6
I
47. v = 343 m/s
∆t = 2.60 s
48. f
1
= 196 Hz
f
2
= 2637 Hz
v = 340 m/s
49. L = 0.850 m
T = 1.86 s
∆x =
v
2
∆t
=
(343 m/s
2
)(2.60 s)
= 446 m
l
1
=
f
v
1
=
3
1
4
9
0
6
m
H
/
z
s
=
l
2
=
f
v
2
=
2
3
6
4
3
0
7
m
H
/s
z
= 0.129 m
1.73 m
T = 2p
a
L
g
a
g
=
4
T
p
2
2
L
=
(4p
(
2
1
)
.
(
8
0
6
.8
s
5
)
0
2
m)
= 9.70 m/s
2
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
50. v = 1.97 × 10
8
m/s
l = 3.81 × 10
−7
m
f =
l
v
=
1
3
.
.
9
8
7
1
×
×
1
1
0
0
8
−7
m
m
/s
= 5.17 × 10
14
Hz
51. a
g
,
moon
= 1.63 m/s
2
∆t = 24 h
a
g
,
Earth
= 9.81 m/s
2
T
Earth
= 2p
a
g
,
E
L
arth
T
moon
= 2p
a
g
,
m
L
oon
T
T
m
Ea
o
r
o
t
n
h
=
a
a
g
g
,
,
m
Ea
o
r
o
t
n
h
=
9
1
.
.
8
6
1
3
m
m
/
/
s
s
2
2
= 2.45
The clock on the moon runs slower than the same clock on Earth by a factor of 2.45.
Thus, after 24.0 h Earth time, the clock on the moon will have advanced by
2
2
4
.
.
4
0
5
h
= 9.80 h = 9 h + (0.80 h)(60 min/h) = 9 h, 48 min
Thus, the clock will read 9:48
A
.
M
.
2. F = 7.0 N
x = −0.35 m
F = −kx
k = −
F
x
= −
(−
(
0
7
.
.
3
0
5
N
m
)
)
= 2.0 × 10
1
N/m
Vibrations and Waves, Standardized Test Prep
6. m = 48 kg
k = 12 N/m
T = 2p
m
k
= 2p
1
4
2
8
N
k
/
g
m
= 2p × 2 s = 4p s
9. t = 2.0 min
f = 12 cycles/120 s = 0.10 Hz
I
10. L = 2.00 m
a
g
= 9.80 m/s
2
∆t = 5.00 min
oscillations =
∆
T
t
=
oscillations =
oscillations = 106
(5.00 min)(60 s/min)
(2p)
9.
2
8
.
0
0
0
m
m
/
s
2
∆t
2p
a
L
g
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 11–7
17. l = 5.20 × 10
−7
m
v = 3.00 × 10
8
m/s
f =
l
v
=
3
5
.
.
0
2
0
0
×
×
1
1
0
0
8
−7
m
m
/s
=
T =
1
f
=
5.77 ×
1
10
14
Hz
= 1.73 × 10
−15
s
5.77 × 10
14
Hz
20. T = 9.49 s
a
g
= g = 9.81 m/s
2
T = 2p
a
L
g
L =
T
4p
2
a
2
g
=
(9.49 s)
2
4
(
p
9.
2
81 m/s
2
)
L = 22.4 m
21. f =
4
3
0
0
.
.
0
0
Hz
v =
4
1
2
0
5
.0
cm
s
=
4
1
.
0
2
.
5
0
m/s
l =
v
f
==0.319 m
4
1
.
0
2
.
5
0
m/s
4
3
0
0
.
.
0
0
Hz
16. l = 1.20 m
f =
12
8
.0 s
v = lf = (1.20 m)
12
8
.0 s
= 0.800 m/s
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 12–1
1. r = 5.0 m
P
1
= 0.25 W
P
2
= 0.50 W
P
3
= 2.0 W
3. intensity = 4.6 × 10
−7
W/m
2
r = 2.0 m
4. intensity = 1.6 × 10
−3
W/m
2
r = 15 m
2. P = 70.0 W
r = 25.0 m
5. P = 0.35 W
intensity = 1.2 × 10
−3
W/m
2
a. intensity =
4p
P
1
r
2
=
(4p
0
)
.
(
2
5
5
.0
W
m)
2
=
b. intensity =
4
P
p
2
r
2
=
(4p
0
)
.
(
5
5
0
.0
W
m)
2
=
c. intensity =
4
P
p
3
r
2
=
(4p
2
)(
.0
5.
W
0m)
2
= 6.4 × 10
−3
W/m
2
1.6 × 10
−3
W/m
2
8.0 × 10
−4
W/m
2
P = (intensity)(4pr
2
) = (4.6 × 10
−7
W/m
2
)(4p)(2.0 m)
2
= 2.3 × 10
−5
W
P = (intensity)(4pr
2
) = (1.6 × 10
−3
W/m
2
)(4p)(15 m)
2
= 4.5 W
intensity =
4p
P
r
2
=
(4p
7
)(
0
2
.0
5.
W
0m)
2
= 8.91 × 10
−3
W/m
2
r =
(i
n
te
n
s
P
i
ty
)(
4p
)
=
= 4.8 m
0.35 W
(1.2 × 10
−3
W/m
2
)(4p)
Sound, Practice A
Givens Solutions
4. decibel level = 10 dB
P = 0.050 W
intensity at 10 dB = 1.0 × 10
−11
W/m
2
(See Table 2 of this chapter in the textbook.)
r =
(i
n
te
n
s
P
i
ty
)(
4p
)
=
= 2.0 × 10
4
m
0.050 W
(1.0 × 10
−11
W/m
2
)(4p)
Sound, Section 2 Review
1. L = 0.20 m
v = 352 m/s
f
1
=
4
n
L
v
=
(
(
1
4
)
)
(
(
3
0
5
.2
2
0
m
m
/s
)
)
= 440 Hz
Sound, Practice B
2. L = 66.0 cm
v = 340 m/s
f
1
=
n
2L
v
=
(
(
2
1
)
)
(
(
0
3
.
4
6
0
60
m
m
/s)
)
=
f
2
= 2f
1
= (2)(260 Hz) =
f
3
= 3f
1
= (3)(260 Hz) = 780 Hz
520 Hz
260 Hz
Sound
Student Edition Solutions
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualI Ch. 12–2
3. v = 115 m/s
L
1
= 70.0 cm
L
2
= 50.0 cm
L
3
= 40.0 cm
a. f
1
=
⎯
2
n
L
v
1
⎯
=
⎯
(
(
2
1
)
)
(
(
0
1
.
1
7
5
00
m
m
/s)
)
⎯
=
b. f
1
=
⎯
2
n
L
v
2
⎯
=
⎯
(
(
2
1
)
)
(
(
0
1
.
1
5
5
00
m
m
/s)
)
⎯
=
c. f
1
=
⎯
2
n
L
v
3
⎯
=
⎯
(
(
2
1
)
)
(
(
0
1
.
1
4
5
00
m
m
/s)
)
⎯
= 144 Hz
115 Hz
82.1 Hz
Givens Solutions
35. L = 2.8 cm
v = 340 m/s
f
1
=
⎯
n
4L
v
⎯
=
⎯
(
(
4
1
)
)
(
(
0
3
.
4
0
0
28
m
m
/s)
)
⎯
= 3.0 × 10
3
Hz
4. L = 50.0 cm
f
1
= 440 Hz
v =
⎯
f
1
n
2L
⎯
==440 m/s
(440 Hz)(2)(0.500 m)
⎯⎯⎯
1
1. f
1
= 262 Hz
f
2
= 2f
1
= (2)(262 Hz) = 524 Hz
Sound, Section 3 Review
2. f
1
= 264 Hz
L = 66.0 cm
v =
⎯
f
1
n
2L
⎯
==348 m/s
(264 Hz)(2)(0.660 m)
⎯⎯⎯
1
intensity =
⎯
4p
P
r
2
⎯
=
⎯
3
4
.1
p
×
(5
1
.0
0
−
m
3
)
W
2
⎯
= 1.0 × 10
−5
W/m
2
= 70 dB
Sound, Chapter Review
23. P = 100.0 W
r = 10.0 m
intensity =
⎯
4p
P
r
2
⎯
=
⎯
(4p
1
)
0
(
0
1
.
0
0
.0
W
m)
2
⎯
= 7.96 × 10
−2
W/m
2
34. L = 31.0 cm
v = 274.4 m/s
f
1
=
⎯
n
2L
v
⎯
=
⎯
(
(
1
2
)
)
(
(
2
0
7
.
4
3
.
1
4
0
m
m
/s
)
)
⎯
=
f
2
= 2f
1
= (2)(443 Hz) =
f
3
= 3f
1
= (3)(443 Hz) = 1330 Hz
886 Hz
443 Hz
22. P = 3.1 × 10
−3
W
r = 5.0 m
36. f
1
= 320 Hz
v = 331 m/s
a. L =
⎯
2
n
f
v
1
⎯
=
⎯
(
(
1
2
)
)
(
(
3
3
3
2
1
0
m
H
/
z
s
)
)
⎯
= 0.52 m =
b. f
2
= 2f
1
= (2)(320 Hz) =
f
3
= 3f
1
= (3)(320 Hz) = 960 Hz
640 Hz
52.0 cm
Section One—Student Edition Solutions I Ch. 12–3
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
I
Givens Solutions
37. f
1
= 132 Hz
f
2
= 137 Hz
number of beats each second = f
2
− f
1
= 137 Hz − 132 Hz = 5 Hz
38. v = 343 m/s
f
1
= 20 Hz
f
2
= 20 000 Hz
l
1
=
v
f
1
=
3
2
4
0
3
H
m
z
/s
=
l
2
=
v
f
2
=
2
3
0
4
0
3
0
m
0H
/s
z
= 2 × 10
−2
m
20 m
40. L = 2.46 m
v = 345 m/s
a. f
1
=
2
n
L
v
=
(
(
1
2
)
)
(
(
3
2
4
.4
5
6
m
m
/s
)
)
=
b.
n
2L
v
≤ 20 000 Hz
n ≤
(20 000 H
v
z)(2)(L)
==285
(20 000 Hz)(2)(2.46 m)
345 m/s
70.1 Hz
39. ∆x = (150 m)(2)
v = 1530 m/s
∆t =
∆
v
x
=
(1
1
5
5
0
30
m
m
)(
/
2
s
)
= 0.20 s
41. f
1,open
= 261.6 Hz
f
3,closed
= 261.6 Hz
L
open
=
(f
1,op
v
en
)(2)
L
closed
=
(f
3,clo
3
se
v
d
)(4)
L
L
c
o
lo
p
s
e
e
n
d
==
(3
(
)
f
3
(
,
f
c
1
lo
,o
se
p
d
en
)(
)
4
(2
)
)
Because f
1,open
= f
3,closed
,
L
L
c
o
lo
p
s
e
e
n
d
=
6
4
=
1
1
.5
(L
closed
) = 1.5(L
open
)
(f
3,clo
3
s
v
ed
)(4)
(f
1,op
v
en
)(2)
42. f = 2.0 × 10
4
Hz
v = 378 m/s
l =
v
f
=
2.0
37
×
8
1
m
0
4
/s
Hz
= 1.9 × 10
−2
m
43. decibel level = 130 dB
r = 20.0 m
diameter = 1.9 × 10
−2
m
a. intensity at 30 dB = 1.0 × 10
1
W/m
2
(See Table 2 of this chapter in the textbook.)
P = (intensity)(4pr
2
) = (1.0 × 10
1
W/m
2
)(4p)(20.0 m)
2
=
b. area = p
diam
2
eter
2
= p
1.9 × 1
2
0
−2
m
2
P = (intensity)(area) = (1.0 × 10
1
W/m
2
)(p)
1.9 × 1
2
0
−2
m
2
P = 2.8 × 10
−3
W
5.0 × 10
4
W
Holt Physics Solution ManualI Ch. 12–4
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
16. A = 5.0 × 10
−5
m
2
intensity =
1.0 × 10
−12
W/m
2
P = (intensity)(A) = (1.0 × 10
−12
W/m
2
)(5.0 × 10
−5
m
2
) = 5.0 × 10
−17
W
15. A = 5.0 × 10
−5
m
2
intensity =
1.0 × 10
0
W/m
2
P = (intensity)(A) = (1.0 × 10
0
W/m
2
)(5.0 × 10
−5
m
2
) = 5.0 × 10
−5
W
8. v = 1.0 × 10
4
m/s
f = 2.0 × 10
10
Hz
l =
v
f
=
2
1
.
.
0
0
×
×
1
1
0
0
1
4
0
m
H
/
z
s
= 5.0 × 10
−7
m
12. f
1
= 250 Hz
f
3
= 3f
1
= (3)(250 Hz) = 750 Hz
10. f
2
= 165 Hz
v = 120 m/s
f
2
=
L
v
L =
f
v
2
=
1
1
2
6
0
5
m
H
/
z
s
= 0.73 m
13. L = 1.0 m
l
6
=
2
6
L =
1
3
L =
1
3
(1.0 m) = 0.33 m
14. P = 250.0 W
r = 6.5 m
I =
4p
P
r
2
=
4p
25
(6
0
.
.
5
0
m
W
)
2
= 0.47 W/m
2
17. f
1
= 456 Hz
v = 331 m/s
f
1
=
2
v
L
L =
2
v
f
1
=
(2
3
)(
3
4
1
5
m
6H
/s
z)
= 0.363 m
19. v = 367 m/s
L = 0.363 m (see 17.)
f
1
=
2
v
L
=
(2)
3
(
6
0
7
.3
m
63
/s
m)
= 506 Hz
18. f
1
= 456 Hz
f
2
= 2f
1
= 2(456 Hz)= 912 Hz
Sound, Standardized Test Prep
Givens Solutions
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 12–1
1. r = 5.0 m
P
1
= 0.25 W
P
2
= 0.50 W
P
3
= 2.0 W
3. intensity = 4.6 × 10
−7
W/m
2
r = 2.0 m
4. intensity = 1.6 × 10
−3
W/m
2
r = 15 m
2. P = 70.0 W
r = 25.0 m
5. P = 0.35 W
intensity = 1.2 × 10
−3
W/m
2
a. intensity =
4p
P
1
r
2
=
(4p
0
)
.
(
2
5
5
.0
W
m)
2
=
b. intensity =
4
P
p
2
r
2
=
(4p
0
)
.
(
5
5
0
.0
W
m)
2
=
c. intensity =
4
P
p
3
r
2
=
(4p
2
)(
.0
5.
W
0m)
2
= 6.4 × 10
−3
W/m
2
1.6 × 10
−3
W/m
2
8.0 × 10
−4
W/m
2
P = (intensity)(4pr
2
) = (4.6 × 10
−7
W/m
2
)(4p)(2.0 m)
2
= 2.3 × 10
−5
W
P = (intensity)(4pr
2
) = (1.6 × 10
−3
W/m
2
)(4p)(15 m)
2
= 4.5 W
intensity =
4p
P
r
2
=
(4p
7
)(
0
2
.0
5.
W
0m)
2
= 8.91 × 10
−3
W/m
2
r =
(i
n
te
n
s
P
i
ty
)(
4p
)
=
= 4.8 m
0.35 W
(1.2 × 10
−3
W/m
2
)(4p)
Sound, Practice A
Givens Solutions
4. decibel level = 10 dB
P = 0.050 W
intensity at 10 dB = 1.0 × 10
−11
W/m
2
(See Table 2 of this chapter in the textbook.)
r =
(i
n
te
n
s
P
i
ty
)(
4p
)
=
= 2.0 × 10
4
m
0.050 W
(1.0 × 10
−11
W/m
2
)(4p)
Sound, Section 2 Review
1. L = 0.20 m
v = 352 m/s
f
1
=
4
n
L
v
=
(
(
1
4
)
)
(
(
3
0
5
.2
2
0
m
m
/s
)
)
= 440 Hz
Sound, Practice B
2. L = 66.0 cm
v = 340 m/s
f
1
=
n
2L
v
=
(
(
2
1
)
)
(
(
0
3
.
4
6
0
60
m
m
/s)
)
=
f
2
= 2f
1
= (2)(260 Hz) =
f
3
= 3f
1
= (3)(260 Hz) = 780 Hz
520 Hz
260 Hz
Sound
Student Edition Solutions
Section One—Student Edition Solutions I Ch. 12–3
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
I
Givens Solutions
37. f
1
= 132 Hz
f
2
= 137 Hz
number of beats each second = f
2
− f
1
= 137 Hz − 132 Hz = 5 Hz
38. v = 343 m/s
f
1
= 20 Hz
f
2
= 20 000 Hz
l
1
=
v
f
1
=
3
2
4
0
3
H
m
z
/s
=
l
2
=
v
f
2
=
2
3
0
4
0
3
0
m
0H
/s
z
= 2 × 10
−2
m
20 m
40. L = 2.46 m
v = 345 m/s
a. f
1
=
2
n
L
v
=
(
(
1
2
)
)
(
(
3
2
4
.4
5
6
m
m
/s
)
)
=
b.
n
2L
v
≤ 20 000 Hz
n ≤
(20 000 H
v
z)(2)(L)
==285
(20 000 Hz)(2)(2.46 m)
345 m/s
70.1 Hz
39. ∆x = (150 m)(2)
v = 1530 m/s
∆t =
∆
v
x
=
(1
1
5
5
0
30
m
m
)(
/
2
s
)
= 0.20 s
41. f
1,open
= 261.6 Hz
f
3,closed
= 261.6 Hz
L
open
=
(f
1,op
v
en
)(2)
L
closed
=
(f
3,clo
3
se
v
d
)(4)
L
L
c
o
lo
p
s
e
e
n
d
==
(3
(
)
f
3
(
,
f
c
1
lo
,o
se
p
d
en
)(
)
4
(2
)
)
Because f
1,open
= f
3,closed
,
L
L
c
o
lo
p
s
e
e
n
d
=
6
4
=
1
1
.5
(L
closed
) = 1.5(L
open
)
(f
3,clo
3
s
v
ed
)(4)
(f
1,op
v
en
)(2)
42. f = 2.0 × 10
4
Hz
v = 378 m/s
l =
v
f
=
2.0
37
×
8
1
m
0
4
/s
Hz
= 1.9 × 10
−2
m
43. decibel level = 130 dB
r = 20.0 m
diameter = 1.9 × 10
−2
m
a. intensity at 30 dB = 1.0 × 10
1
W/m
2
(See Table 2 of this chapter in the textbook.)
P = (intensity)(4pr
2
) = (1.0 × 10
1
W/m
2
)(4p)(20.0 m)
2
=
b. area = p
diam
2
eter
2
= p
1.9 × 1
2
0
−2
m
2
P = (intensity)(area) = (1.0 × 10
1
W/m
2
)(p)
1.9 × 1
2
0
−2
m
2
P = 2.8 × 10
−3
W
5.0 × 10
4
W
Holt Physics Solution ManualI Ch. 12–4
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
16. A = 5.0 × 10
−5
m
2
intensity =
1.0 × 10
−12
W/m
2
P = (intensity)(A) = (1.0 × 10
−12
W/m
2
)(5.0 × 10
−5
m
2
) = 5.0 × 10
−17
W
15. A = 5.0 × 10
−5
m
2
intensity =
1.0 × 10
0
W/m
2
P = (intensity)(A) = (1.0 × 10
0
W/m
2
)(5.0 × 10
−5
m
2
) = 5.0 × 10
−5
W
8. v = 1.0 × 10
4
m/s
f = 2.0 × 10
10
Hz
l =
v
f
=
2
1
.
.
0
0
×
×
1
1
0
0
1
4
0
m
H
/
z
s
= 5.0 × 10
−7
m
12. f
1
= 250 Hz
f
3
= 3f
1
= (3)(250 Hz) = 750 Hz
10. f
2
= 165 Hz
v = 120 m/s
f
2
=
L
v
L =
f
v
2
=
1
1
2
6
0
5
m
H
/
z
s
= 0.73 m
13. L = 1.0 m
l
6
=
2
6
L =
1
3
L =
1
3
(1.0 m) = 0.33 m
14. P = 250.0 W
r = 6.5 m
I =
4p
P
r
2
=
4p
25
(6
0
.
.
5
0
m
W
)
2
= 0.47 W/m
2
17. f
1
= 456 Hz
v = 331 m/s
f
1
=
2
v
L
L =
2
v
f
1
=
(2
3
)(
3
4
1
5
m
6H
/s
z)
= 0.363 m
19. v = 367 m/s
L = 0.363 m (see 17.)
f
1
=
2
v
L
=
(2)
3
(
6
0
7
.3
m
63
/s
m)
= 506 Hz
18. f
1
= 456 Hz
f
2
= 2f
1
= 2(456 Hz)= 912 Hz
Sound, Standardized Test Prep
Givens Solutions
Light and Reflection
Student Edition Solutions
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 13–1
1. f = 3.0 × 10
21
Hz
c = 3.00 × 10
8
m/s
l =
c
f
=
3
3
.
.
0
0
0
×
×
1
1
0
0
2
8
1
m
H
/
z
s
= 1.0 × 10
−13
m
Light and Reflection, Practice A
Givens Solutions
2. f
1
= 88 MHz
f
2
= 108 MHz
c = 3.00 × 10
8
m/s
l
1
=
f
c
1
=
3
8
.0
.8
0
×
×
1
1
0
0
7
8
H
m
z
/s
=
l
2
=
f
c
2
=
3
1
.
.
0
0
0
8
×
×
1
1
0
0
8
8
m
H
/
z
s
= 2.78 m
3.4 m
3. f
1
= 3.50 MHz
f
2
= 29.7 MHz
c = 3.00 × 10
8
m/s
l
1
=
f
c
1
=
3
3
.
.
0
5
0
0
×
×
1
1
0
0
8
6
m
H
/
z
s
=
l
2
=
f
c
2
=
3
2
.
.
0
9
0
7
×
×
1
1
0
0
8
7
m
m
/
/
s
s
= 10.1 m
85.7 m
4. l = 1.0 km
c = 3.00 × 10
8
m/s
f =
l
c
=
3.
1
0
.
0
0
×
×
1
1
0
0
8
3
m
m
/s
= 3.0 × 10
5
Hz
5. l = 560 nm
c = 3.00 × 10
8
m/s
f =
l
c
=
3
5
.0
.6
0
×
×
1
1
0
0
−
8
7
m
m
/s
= 5.4 × 10
14
Hz
6. l = 125 nm
c = 3.00 × 10
8
m/s
f =
l
c
=
3
1
.
.
0
2
0
5
×
×
1
1
0
0
8
−7
m
m
/s
= 2.40 × 10
15
Hz
2. f = 7.57 × 10
14
Hz
c = 3.00 × 10
8
m/s
l =
c
f
=
7
3
.
.
5
0
7
0
×
×
1
1
0
0
1
8
4
m
H
/
z
s
= 3.96 × 10
−7
m
Light and Reflection, Section 1 Review
2.
The normal to the surface of the mirror is halfway between 12 o’clock and 5 o’clock.
q =
1
2
(5.0 h)
1
3
2
6
.0
0°
h
=
q = q = 75°
75°
Light and Reflection, Section 2 Review
1. p
1
= 10.0 cm
p
2
= 5.00 cm
f = 10.0 cm
q
1
1
=
1
f
−
p
1
1
=
10.0
1
cm
−
10.0
1
cm
= 0
q
1
2
=
1
f
−
p
1
2
=
10.0
1
cm
−
5.00
1
cm
q
1
2
=
0
1
.1
c
0
m
0
−
0
1
.2
c
0
m
0
=
−
1
0.
c
1
m
00
q
2
=
M =−
p
q
=−
−
5
1
.0
0
0
.0
c
c
m
m
= virtual, upright image
2.00
−10.0 cm
no image (infinite q)
Light and Reflection, Practice B
Givens Solutions
2. f = 33 cm
p = 93 cm
1
q
=
1
f
−
p
1
=
33
1
cm
−
93
1
cm
1
q
=
0
1
.0
c
3
m
0
−
0
1
.0
c
1
m
1
=
0
1
.0
c
1
m
9
q =
M =−
p
q
=−
5
9
3
3
c
c
m
m
= real, inverted image
−0.57
53 cm
3. p = 25.0 cm
q =−50.0 cm
R
2
=
p
1
+
1
q
R
1
=
2
1
p
+
2
1
q
=
(2)(25
1
.0 cm)
+
(2)(−5
1
0.0 cm)
=
50.0
1
cm
−
1.00 ×
1
10
2
cm
R
1
=
0
1
.0
c
2
m
00
−
0
1
.0
c
1
m
00
=
0
1
.0
c
1
m
00
R =
M =−
p
q
=−
−
2
5
5
0
.0
.0
c
c
m
m
= virtual image2.00
1.00 × 10
2
cm
4. concave spherical mirror
p
1
= 11.0 cm
p
2
= 27.0 cm
q
1
= 13.2 cm
1
f
=
p
1
+
1
q
=
11.0
1
cm
+
13.2
1
cm
1
f
=
0.
c
0
m
909
+
0.
c
0
m
758
=
0.
c
1
m
667
f =
M =−
p
q
=−
1
1
3
1
.
.
2
0
c
c
m
m
=−1.20
6.00 cm
Holt Physics Solution ManualI Ch. 13–2
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 13–3
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
p = 27.0 cm
1
q
=
1
f
−
p
1
=
5.99
1
9cm
−
27.0
1
cm
1
q
=
0
1
.1
c
6
m
67
−
0
1
.0
c
3
m
70
=
0
1
.1
c
2
m
97
q =
M =−
p
q
=−
7
2
.7
7
1
.0
0
c
c
m
m
= real image
−0.286
7.71 cm
Givens Solutions
1. q = 23.0 cm
h = 1.70 cm
f = 46.0 cm
p
1
=
1
f
−
1
q
=
46.0
1
cm
−
23.0
1
cm
p
1
=
46.0
1
cm
−
46.0
2
cm
=
46.
−
0
1
cm
p =
M =
h
h
=
−
p
q
=−
−
2
4
3
6
.0
.0
c
c
m
m
=
h =
M
h
=
1.
0
7
.
0
50
c
0
m
= 3.40 cm
virtual, upright image0.500
−46.0 cm
Light and Reflection, Practice C
2. f =−0.25 m
q =−0.24 m
h = 0.080 m
3. f =−33 cm
q =−19 cm
h = 7.0 cm
p
1
=
1
f
−
1
q
=
−33
1
cm
−
−19
1
cm
p
1
=
63
−
0
1
c
9
m
+
630
33
cm
=
630
14
cm
p =
h =−
p
q
h
=−
(45
(
c
−
m
1
)
9
(
c
7
m
.0
)
cm)
=
M =
h
h
=
7
1
.
7
0
c
c
m
m
= virtual, upright image0.41
17 cm
45 cm
p
1
=
1
f
−
1
q
=
−0.2
1
5m
−
−0.2
1
4m
p
1
=
0.
−
0
0
6
.
0
24
m
+
0.0
0
6
.2
0
5
m
=
0.0
0
6
.0
0
1
m
p =
M =−
p
q
=−
−0
6
.2
m
4m
M =
h =
p
q
h
=−
(6 m
(−
)
0
(
.
0
2
.
4
08
m
0
)
m)
= 2 m
virtual, upright image0.04
6 m
Holt Physics Solution ManualI Ch. 13–4
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
4. R =−0.550 m
p = 3.1 m
p
1
+
1
q
=
R
2
1
q
=
R
2
−
p
1
=
−0.5
2
50 m
−
3.1
1
m
1
q
=
−
1
3.
m
64
−
0
1
.3
m
2
=
1
4.
m
0
q =
M =−
p
q
=−
−
3
0
.
.
1
25
m
m
= virtual, upright image
0.081
−0.25 m
Givens Solutions
5. R =
−6.0
2
0cm
=−3.00 cm
p = 10.5 cm
1
q
=
R
2
−
p
1
=
−3.0
2
0cm
−
10.5
1
cm
1
q
=
−
1
0.
c
6
m
67
−
0
1
.0
c
9
m
52
=
−
1
0.
c
7
m
62
q =
M =−
p
q
=
−
−
1
1
.
0
3
.
1
5
c
c
m
m
= virtual, upright image
0.125
−1.31 cm
6. p = 49 cm
f =−35 cm
1
q
=
1
f
−
p
1
=
−35
1
cm
−
49
1
cm
1
q
=
−
1
0.
c
0
m
29
−
0
1
.0
c
2
m
0
=
−
1
0.
c
0
m
49
q =
M = −
p
q
=−
−2.0
4
×
9c
1
m
0
1
cm
= virtual, upright image
0.41
−2.0 × 10
1
cm
Light and Reflection, Section 3 Review
1. R =−1.5 cm
p = 1.1 cm
1
q
=
R
2
−
p
1
=
−1.5
2
cm
−
1.1
1
cm
1
q
=
1
−1
cm
.3
−
1
0.
c
9
m
1
=
1
−2
cm
.2
q =
M =−
p
q
=−
−
1
0
.
.
1
45
cm
cm
= virtual, upright image0.41
−0.45 cm
2. M =−95
q = 13 m
p =−
M
q
=−
1
−
3
9
m
5
= 0.14 m
Section One—Student Edition Solutions I Ch. 13–5
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
12. f = 99.5 MHz
c = 3.00 × 10
8
m/s
l =
c
f
=
3
9
.
.
0
9
0
5
×
×
1
1
0
0
8
7
m
H
/
z
s
= 3.02 m
Givens Solutions
13. f = 33 GHz
c = 3.00 × 10
8
m/s
l =
c
f
=
3
3
.
.
0
3
0
×
×
1
1
0
0
1
8
0
m
H
/
z
s
= 9.1 × 10
−3
m
34. R = 25.0 cm
p = 45.0 cm
p = 25.0 cm
a.
p
1
+
1
q
=
R
2
1
q
=
R
2
−
p
1
=
25.0
2
cm
−
45.0
1
cm
1
q
=
0
1
.0
c
8
m
00
−
0
1
.0
c
2
m
22
=
0
1
.0
c
5
m
78
q = 17.3 cm
M =−
p
q
=−
1
4
7
5
.
.
3
0
c
c
m
m
=
b.
1
q
=
R
2
−
p
1
=
25.0
2
cm
−
25.0
1
cm
1
q
=
0
1
.0
c
8
m
00
−
0
1
.0
c
4
m
00
=
0
1
.0
c
4
m
00
q = 25.0 cm
M =−
p
q
=−
2
2
5
5
.
.
0
0
c
c
m
m
= real, inverted image−1.00
real, inverted image−0.384
11. c = 3.00 × 10
8
m/s
f = 3 × 10
14
Hz
l =
f
c
=
3.
3
00
×
×
10
1
1
0
4
8
H
m
z
/s
= 1 × 10
−6
m
Light and Reflection, Chapter Review
5. R = 265.0 m
p
1
+
1
q
=
R
2
Because objects in space are so far away,
p
1
= 0; therefore,
1
q
=
R
2
=
265
2
.0 m
=
7.547
1
×
m
10
−3
q = 132.5 m
10. f
1
= 7.5 × 10
14
Hz
f
2
= 1.0 × 10
15
Hz
c = 3.00 × 10
8
m/s
l
1
=
f
c
1
=
3
7
.0
.5
0
×
×
1
1
0
0
1
8
4
m
m
/s
=
l
2
=
f
c
2
=
3
1
.0
.0
0
×
×
1
1
0
0
1
8
5
m
m
/s
= 3.0 × 10
−7
m
4.0 × 10
−7
m
Holt Physics Solution ManualI Ch. 13–6
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
35. f = 8.5 cm
q = 2p
1
f
=
p
1
+
1
q
=
p
1
+
2
1
p
1
f
=
2
3
p
p =
3
2
f
q = 2p = 3f = 3(8.5 cm) =
M =
−
p
q
=
−
p
2p
= real, inverted image
−2
26 cm
46. M =−0.085
q = 35 cm
p =−
M
q
=−
−
3
0
5
.0
cm
85
=
1
f
=
p
1
+
1
q
=
410
1
cm
+
35
1
cm
1
f
=
0
1
.0
c
0
m
24
+
0
1
.0
c
2
m
9
=
0
1
.0
c
3
m
1
f =
R = 2f = (2)(32 cm) = real, inverted image
64 cm
32 cm
4.1 × 10
2
cm
Givens Solutions
p = 5.00 cm
c.
1
q
=
R
2
−
p
1
=
25.0
2
cm
−
5.00
1
cm
1
q
=
0
1
.0
c
8
m
00
−
0
1
.2
c
0
m
0
=
−
1
0.
c
1
m
20
q =−8.33 cm
M =−
p
q
=−
−
5
8
.0
.3
0
3
c
c
m
m
= virtual, upright image
1.67
36. R =−45.0 cm
h = 1.70 cm
q =−15.8 cm
p
1
+
1
q
=
R
2
p
1
=
R
2
−
1
q
=
−45.
2
0cm
−
−15.
1
8cm
p
1
=
−0
c
.0
m
444
+
0.
c
0
m
633
=
0
1
.0
c
1
m
89
p =
M =
−
p
q
=−
(
(
−
5
1
2
5
.9
.8
c
c
m
m
)
)
=
h =
−p
q
h
= −
(52.9
(−
c
1
m
5
)
.8
(1
c
.
m
70
)
cm)
= virtual, upright image
5.69 cm
0.299
52.9 cm
Section One—Student Edition Solutions I Ch. 13–7
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
50. p = 195 cm
q =−12.8 cm
1
f
=
p
1
+
1
q
=
195
1
cm
+
−12.
1
8cm
1
f
=
5.13
1
×
cm
10
−3
+
−7.8
1
1
c
×
m
10
−2
=
−7.3
1
0
c
×
m
10
−2
f =
M =−
p
q
=−
−
1
1
9
2
5
.8
c
c
m
m
= virtual, upright image
0.0656
−13.7 cm
Givens Solutions
51. R =−11.3 cm
M =
1
3
M =−
p
q
=
1
3
q =−
p
3
R
2
=
p
1
+
1
q
=
p
1
−
p
3
=−
p
2
p =−R = 11.3 cm
47. M =−0.75
q = 4.6 cm
p =−
M
q
=−
4
−
.6
0.
c
7
m
5
=
1
f
=
p
1
+
1
q
=
6.1
1
cm
+
4.6
1
cm
1
f
=
1
0.
c
1
m
6
+
1
0.
c
2
m
2
=
1
0.
c
3
m
8
f = real, inverted image
2.6 cm
6.1 cm
48. p = 15.5 cm
M =
1
2
M =−
p
q
=
1
2
q =−
p
2
R
2
=
p
1
+
1
q
=
p
1
−
p
2
=−
p
1
R =−2p = (−2)(15.5 cm) =−31.0 cm
49. p
1
= 15 cm
q
1
= 8.5 cm
p
2
= 25 cm
1
f
=
p
1
1
+
q
1
1
=
15
1
cm
+
8.5
1
cm
1
f
=
0
1
.0
c
6
m
7
+
1
0.
c
1
m
2
=
1
0.
c
1
m
9
q
1
2
=
1
f
−
p
1
2
=
1
0.
c
1
m
9
−
25
1
cm
q
1
2
=
1
0.
c
1
m
9
−
0
1
.0
c
4
m
0
=
1
0.
c
1
m
5
q
2
=
M
1
=−
p
q
1
1
=−
8
1
.
5
5
c
c
m
m
=
M
2
=−
p
q
2
2
=−
6
2
.
5
7
c
c
m
m
= both images are inverted−0.27
−0.57
real image6.7 cm
Holt Physics Solution ManualI Ch. 13–8
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
52. p = 10.0 cm
q = 2.00 m
M =−
p
q
=−
2.0
1
0
0
×
.0
1
c
0
m
2
cm
= real, inverted image
−20.0
53.
Let q
1
and q
2
be the angles of incidence at the first and second surfaces, respectively.
Triangle 1:
2q
1
+ 2q
2
+ f = 180°
f = 180°−2(q
1
+ q
2
)
Triangle 2:
(90°−q
1
) + (90°−q
2
) + q = 180°
q = q
1
+ q
2
Substitute this q value into the equation for f.
f = 180°−2q
Triangle 2
Triangle 1
2
θ
θ
1
θ
f
f
54. R =∞
p
1
+
1
q
=
R
2
p
1
+
1
q
=
∞
2
p
1
+
1
q
= 0
1
q
=−
p
1
q =−p
Givens Solutions
55. p = 70.0 cm − 20.0 cm
q = 50.0 cm
q = 10.0 cm − 20.0 cm
q =−10.0 cm
R
2
=
p
1
+
1
q
R
1
=
2
1
p
+
2
1
q
=
(2)(50
1
.0 cm)
+
(2)(10
1
.0 cm)
R
1
=
0
1
.0
c
1
m
00
−
0
1
.0
c
5
m
00
=
−0
1
.0
cm
400
R =−25.0 cm
56. q
1
=−30.0 cm
q
2
=−10.0 cm
R
1
=−R
2
a. R
1
=−R
2
R
2
1
= −
R
2
2
p
1
1
+
q
1
1
=−
p
1
2
+
q
1
2
where p
1
= p
2
= p
p
2
= −
q
1
1
−
q
1
2
=−
−30.
1
0cm
+
10.0
1
cm
p
2
=
0
1
.0
c
3
m
33
+
0
1
.1
c
0
m
0
=
0
1
.1
c
3
m
3
p =
0.1
2
33
cm = 15.0 cm
Section One—Student Edition Solutions I Ch. 13–9
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
57. h = 2.70 cm
p = 12.0 cm
h = 5.40 cm
M =−
p
q
=
h
h
=
5
2
.
.
4
7
0
0
c
c
m
m
=
q =−Mp =−(2.00)(12.0 cm) =−24.0 cm
R
2
=
p
1
+
1
q
=
12.0
1
cm
+
−24.
1
0cm
R
2
=
0
1
.0
c
8
m
33
−
0
1
.0
c
4
m
17
=
0
1
.0
c
4
m
16
R =
0.0
2
416
cm = 48.1 cm
virtual image2.00
Givens Solutions
58. f = 7.5 cm
p
1
= 7.5 cm
Locate the image of the coins formed by the upper mirror:
q
1
1
=
1
f
−
p
1
1
=
7.5
1
cm
−
7.5
1
cm
= 0
Thus, q
1
=∞.
Now, locate the final image, realizing that parallel rays are reflected toward the lower
mirror by the upper mirror; thus, p
2
=∞.
q
1
2
=
1
f
−
p
1
2
=
7.5
1
cm
−
∞
1
=
7.5
1
cm
q
2
= 7.5 cm
M = M
1
M
2
=
−
p
q
1
1
−
q
p
2
2
where q
1
= p
2
M =
p
q
2
1
=
7
7
.
.
5
5
c
c
m
m
= 1.0
b.
R
2
=
p
1
+
q
1
1
=
15.0
1
cm
+
−30.
1
0cm
R
2
=
0
1
.0
c
6
m
67
−
0
1
.0
c
3
m
33
=
0
1
.0
c
3
m
34
R =
0.03
2
34
cm =
c. M
concave
= −
p
q
1
1
=−
−
1
3
5
0
.0
.0
c
c
m
m
=
M
convex
=−
p
q
2
2
=−
−
1
1
5
0
.0
.0
c
c
m
m
= 0.667
2.00
59.9 cm
Holt Physics Solution ManualI Ch. 13–10
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
59.
For a convex mirror:
f < 0, or f =−
f
1
q
=
−
1
f
−
p
1
=−
p
p
+
f
f
q =−
p
p
+
f
f
M =−
p
q
=−
p
1
−
p
p
+
f
f
=
p
p
+
f
f
For a real object (p > 0), 1 > M > 0; this means that the image is an upright, virtual
image.
For a spherical mirror, the image is virtual and upright if p
f
and f 0. For f 0:
f > 0, or f =+
f
1
q
=
1
f
−
p
1
=
p
p
−
f
f
q =
p
p
−
f
f
M =−
p
q
=−
p
1
p
p
−
f
f
=
f
f
−
p
When p < |f |, M > 1; thus the image is enlarged, upright, and virtual.
60.
tan q =
h
p
tan q =
−
q
h
q = q; thus, tan q = tan q.
h
p
=−
h
q
Cross multiply to find the magnification equation.
M =
h
h
=−
p
q
From two other triangles in the figure, we note that:
tan a =
p −
h
R
and tan a =−
R
h
−
q
so that
h
h
=−
p
R
−
−
R
q
=−
p
q
Cross multiply to find the following:
p(R − q) = q(p − R)
pR − pq = qp − qR
R(p + q) = 2pq
R
2
=
p
p
+
q
q
=
1
q
+
p
1
Givens Solutions
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 13–11
Light and Reflection, Standardized Test Prep
Givens Solutions
7. p = 15.0 cm
q = −6.00 cm
1
f
=
p
1
+
1
q
=
15.0
1
cm
+
−6.0
1
0cm
1
f
=
0.
c
0
m
667
−
0
c
.1
m
67
=
−0
c
.
m
100
f= −10.0 cm
9. l = 5.5 mm = 5.5 × 10
−6
m
c = 3.00 × 10
8
m/s
f =
l
c
=
3
5
.0
.5
0
×
×
1
1
0
0
−
8
6
m
m
/s
= 5.5 × 10
13
Hz
13. f = 5.0 × 10
19
Hz
c = 3.00 × 10
8
m/s
l =
c
f
=
3
5
.0
.0
0
×
×
1
1
0
0
1
8
9
m
/s
/s
= 6.0 × 10
−12
m = 6.0 pm
15. p = 30.0 cm
R = 20.0 cm
R
2
=
p
1
+
1
q
1
q
=
R
2
−
p
1
=
20.0
2
cm
−
30.0
1
cm
1
q
=
60
6
0
0.
c
0
m
−
60
2
0
0.
c
0
m
=
60
4
0
0.
c
0
m
q = 15.0 cm
16. p = 30.0 cm
q = 15.0 cm
1
f
=
p
1
+
1
q
=
30.0
1
cm
+
15.0
1
cm
1
f
=
45
1
0
5.
c
0
m
+
45
3
0
0.
c
0
m
=
45
4
0
5.
c
0
m
f = 10.0 cm
17. p = 30.0 cm
q = 15.0 cm
M =
−
p
q
=
−
3
1
0
5
.0
.0
c
c
m
m
=−0.500
18. h = 12 cm
M = −0.500
M =
h
h
h = Mh = (−0.500)(12 cm) = −6.0 cm
Refraction
Student Edition Solutions
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 14–1
1. n
i
= 1.00
n
r
= 1.333
q
i
= 25.0°
n
i
(sin q
i
) = n
r
(sin q
r
)
q
r
= sin
−1
n
n
r
i
(sin q
i
)
= sin
−1
1
1
.
.
3
0
3
0
3
(sin 25.0°)
= 18.5°
Refraction, Practice A
Givens Solutions
3. q
i
= 40.0°
q
r
= 26.0°
n
i
= 1.00
n
i
(sin q
i
) = n
r
(sin q
r
)
n
r
=
n
i
(
s
s
in
in
q
r
q
i
)
=
(1.00
si
)
n
(s
2
in
6.0
4
°
0.0°)
= 1.47
2. n
i
= 1.66
n
r
= 1.52
q
i
= 25.0°
n
i
= 1.00
q
i
= 14.5°
q
r
= 9.80°
n
i
= 1.00
n
r
= 2.419
q
i
= 31.6°
n
i
(sin q
i
) = n
r
(sin q
r
)
a. q
r
= sin
−1
n
n
r
i
(sin q
i
)
= sin
−1
1
1
.
.
6
5
6
2
(sin 25.0°)
=
b. n
r
=
n
i
s
(
i
s
n
in
q
q
r
i
)
=
1.00
si
(
n
si
9
n
.8
1
0
4
°
.5°)
= 1.47
c. q
r
= sin
−1
n
n
r
i
(sin q
i
)
= sin
−1
2
1
.
.
4
0
1
0
9
(sin 31.6°)
= 12.5°
glycerine
27.5°
1. n
i
= 1.00
n
r
= 1.333
q
i
= 22.5°
n
i
(sin q
i
) = n
r
(sin q
r
)
q
r
= sin
−1
n
n
r
i
(sin q
i
)
= sin
−1
1
1
.
.
3
0
3
0
3
(sin 22.5°)
= 16.7°
Refraction, Section 1 Review
3. n
i
= 1.00
n
r
= 2.419
q
i
= 15.0°
n
i
(sin q
i
) = n
r
(sin q
r
)
q
r
= sin
−1
n
n
r
i
(sin q
i
)
= sin
−1
2
1
.
.
4
0
1
0
9
(sin 15.0°)
= 6.14°
1. p = 20.0 cm
f = 10.0 cm
p
1
+
1
q
=
1
f
1
q
=
1
f
−
p
1
=
10.0
1
cm
−
20.0
1
cm
1
q
=
0
1
.1
c
0
m
0
−
0
1
.0
c
5
m
00
=
0
1
.0
c
5
m
00
q =
M = −
p
q
=−
2
2
0
0
.
.
0
0
c
c
m
m
= real, inverted image−1.00
20.0 cm
Refraction, Practice B
Givens Solutions
2. f = 15.0 cm
p = 10.0 cm
1
q
=
1
f
−
p
1
=
15.0
1
cm
−
10.0
1
cm
=
30.0
2
cm
−
30.0
3
cm
1
q
=
30.
−
0
1
cm
q =−30.0 cm
3. p = 20.0 cm
f =−10.0 cm
1
q
=
1
f
−
p
1
=
−10.
1
0cm
−
20.0
1
cm
1
q
=
−
1
0.
c
1
m
00
−
0
1
.0
c
5
m
00
=
−
1
0.
c
1
m
50
q =
M =−
p
q
=−
−
2
6
0
.
.
6
0
7
c
c
m
m
= virtual, upright image
0.333
−6.67 cm
4. f = 6.0 cm
q =−3.0 cm
f = 2.9 cm
q = 7.0 cm
a.
p
1
=
1
f
−
1
q
=
6.0
1
cm
−
−3.0
1
cm
p
1
=
1
0.
c
1
m
7
−
−
1
0
c
.
m
33
=
1
0.
c
5
m
0
p =
M = −
p
q
=−
−
2
3
.0
.0
c
c
m
m
=
b.
p
1
=
1
f
−
1
q
=
2.9
1
cm
−
7.0
1
cm
p
1
=
1
0.
c
3
m
4
−
1
0.
c
1
m
4
=
1
0.
c
2
m
0
p =
M = −
p
q
= −
7
5
.
.
0
0
c
c
m
m
=−1.4
5.0 cm
1.5
2.0 cm
Holt Physics Solution ManualI Ch. 14–2
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 14–3
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
f =−6.0 cm
p = 4.0 cm
p = 5.0 cm
M = 0.50
c.
1
q
=
1
f
−
p
1
=
−6.0
1
cm
−
4.0
1
cm
1
q
=
−
1
0
c
.
m
17
−
1
0.
c
2
m
5
=
−
1
0
c
.
m
42
q =
M = −
p
q
=−
−
4
2
.0
.4
c
c
m
m
=
d. q =−Mp =−(0.50)(5.0 cm) =
1
f
=
p
1
+
1
q
=
5.0
1
cm
+
−2.5
1
cm
1
f
=
1
0.
c
2
m
0
+
−
1
0
c
.
m
40
=
−
1
0
c
.
m
20
f =−5.0 cm
−2.5 cm
0.60
−2.4 cm
Givens Solutions
3. f = 4.0 cm
p = 3.0 cm + 4.0 cm = 7.0 cm
p
1
+
1
q
=
1
f
1
q
=
1
f
−
p
1
1
q
=
(4.0
1
cm)
−
(7.0
1
cm)
=
28
7
cm
−
28
4
cm
=
28
3
cm
q =
28
3
cm
= 9.3 cm
Refraction, Section 2 Review
4. p = 7.0 cm
q = 9.1 cm
M = −
p
q
= −
9
7
.
.
1
0
c
c
m
m
=−1.3
1. n
i
= 1.473
n
r
= 1.00
sin q
c
=
n
n
r
i
q
c
= sin
−1
n
n
r
i
= sin
−1
1
1
.
.
4
0
7
0
3
= 42.8°
Refraction, Practice C
2. n
i
= 1.473
n
r
= 1.333
q
c
= sin
−1
n
n
r
i
= sin
−1
1
1
.
.
3
4
3
7
3
3
= 64.82°
3. n
i
= 1.309
n
r
= 1.00
q
c
= sin
−1
n
n
r
i
= sin
−1
1
1
.
.
3
0
0
0
9
= 49.8°
Holt Physics Solution ManualI Ch. 14–4
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. n
i
= 1.333
n
r
= 1.309
sin q
c
=
n
n
r
i
q
c
= sin
−1
n
n
r
i
= sin
−1
1
1
.
.
3
3
0
3
9
3
= 79.11°
10. n
i
= 1.00
n
r
= 1.333
q
i
= 42.3°
n
i
(sin q
i
) = n
r
(sin q
r
)
q
r
= sin
−1
n
n
r
i
(sin q
i
)
= sin
−1
1
1
.
.
3
0
3
0
3
(sin 42.3°)
= 30.3°
11. n
i
= 1.00
n
r
= 1.333
q
i
= 36°
n
i
(sin q
i
) = n
r
(sin q
r
)
q
r
= sin
−1
n
n
r
i
(sin q
i
)
= sin
−1
1
1
.
.
3
0
3
0
3
(sin 36°)
= 26°
12. n
i
= 1.00
n
r
= 1.333
q
i
= 35.0°
n
i
(sin q
i
) = n
r
(sin q
r
)
q
r
= sin
−1
n
n
r
i
(sin q
i
)
= sin
−1
1
1
.
.
3
0
3
0
3
(sin 35.0°)
= 25.5°
13. q
i,1
= 30.0°
n
i,1
= 1.00
n
r,1
= 1.50
n
i
(sin q
i
) = n
r
(sin q
r
)
air to glass:
q
r,1
= sin
−1
n
n
r
i,
,
1
1
(sin q
i,1
)
= sin
−1
1
1
.
.
0
5
0
0
(sin 30.0°)
= 19.5°
glass to air:
q
i,2
= q
r,1
because they are alternate interior angles. q
r,2
= q
i,1
because of the
reversibility of refraction; thus, q
i,2
= 19.5° and q
r,2
= 30.0°
q
i,1
= 30.0° and q
r,1
= 19.5°
14. q
r
= 20.0°
n
i
= 1.00
n
r
= 1.48
q
i
= 20.0°
n
i
= 1.48
n
r
= 1.333
n
i
(sin q
i
) = n
r
(sin q
r
)
air to oil: q
1
= q
i
= sin
−1
n
n
r
i
(sin q
r
)
= sin
−1
1
1
.
.
4
0
8
0
(sin 20.0°)
=
oil to water: q
2
= q
r
= sin
−1
n
n
r
i
(sin q
i
)
= sin
−1
1
1
.
.
3
4
3
8
3
(sin 20.0°)
= 22.3°
30.4°
Refraction, Chapter Review
Refraction, Section 3 Review
Givens Solutions
4. n
i
= 2.419
n
r
= 1.00
n
i
= 2.20
n
r
= 1.00
diamond: q
c
= sin
−1
n
n
r
i
= sin
−1
2
1
.
.
4
0
1
0
9
=
cubic zirconia: q
c
= sin
−1
n
n
r
i
= sin
−1
1
2
.
.
0
2
0
0
= 27.0°
24.4°
Section One—Student Edition Solutions I Ch. 14–5
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
24. f =−20.0 cm
p = 40.0 cm
p = 20.0 cm
p = 10.0 cm
a.
p
1
+
1
q
=
1
f
1
q
=
1
f
−
p
1
=
−20.
1
0cm
−
40.0
1
cm
1
q
=
−0
1
.0
cm
500
−
0
1
.0
c
2
m
50
=
−0
1
.0
cm
750
q =
M = −
p
q
=−
−
4
1
0
3
.0
.3
c
c
m
m
=
b.
1
q
=
1
f
−
p
1
=
−20.
1
0cm
−
20.0
1
cm
1
q
=
−0
1
.0
cm
500
−
0
1
.0
c
5
m
00
=
−
1
0.
c
1
m
00
q =
M = −
p
q
= −
−
2
1
0
0
.0
.0
c
c
m
m
=
c.
1
q
=
1
f
−
p
1
=
−20.
1
0cm
−
10.0
1
cm
1
q
=
−0
1
.0
cm
500
−
0
1
.1
c
0
m
0
=
−
1
0.
c
1
m
50
q =
M = −
p
q
= −
−
1
6
0
.
.
6
0
7
c
c
m
m
= virtual, upright image0.667
−6.67 cm
virtual, upright image0.500
−10.0 cm
virtual, upright image0.332
−13.3 cm
25. f = 12.5 cm
q =−30.0 cm
p
1
=
1
f
−
1
q
=
12.5
1
cm
−
−30.
1
0cm
p
1
=
0
1
.0
c
8
m
00
−
−0
1
.0
cm
333
=
0
1
.1
c
1
m
33
p = 8.826 cm
M = −
p
q
=−
−
8.
3
8
0
2
.
6
0
c
c
m
m
= upright image3.40
26. f = 20.0 cm
p = 40.0 cm
p = 10.0 cm
a.
1
q
=
1
f
−
p
1
=
20.0
1
cm
−
40.0
1
cm
1
q
=
0
1
.0
c
5
m
00
−
0
1
.0
c
2
m
50
=
0
1
.0
c
2
m
50
q =
M =−
p
q
=−
4
4
0
0
.
.
0
0
c
c
m
m
=
b.
1
q
=
1
f
−
p
1
=
20.0
1
cm
−
10.0
1
cm
1
q
=
0
1
.0
c
5
m
00
−
0
1
.1
c
0
m
0
=
−0
1
.0
cm
500
q =
M = −
p
q
=−
−
1
2
0
0
.0
.0
c
c
m
m
= virtual, upright image
2.00
−20.0 cm
real, inverted image−1.00
40.0 cm
Holt Physics Solution ManualI Ch. 14–6
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
40. n
i
= 1.00
n
r
= 1.333
q
r
= 36.2°
n
i
(sin q
i
) = n
r
(sin q
r
)
q
i
= sin
−1
n
n
r
i
(sin q
r
)
= sin
−1
1
1
.3
.0
3
0
3
(sin 36.2°)
= 51.9°
Givens Solutions
41. v = 1.85 × 10
8
m/s
c = 3.00 × 10
8
m/s
n =
v
c
=
3
1
.
.
0
8
0
5
×
×
1
1
0
0
8
8
m
m
/
/
s
s
= carbon disulfide1.62
42. n
i
= 1.66
n
r
= 1.333
q
i
= 28.7°
q
r
= 90.0°
n
i
(sin q
i
) = n
r
(sin q
r
)
a. q
r
= sin
−1
n
n
r
i
(sin q
i
)
= sin
−1
1
1
.
.
3
6
3
6
3
(sin 28.7°)
=
b. q
i
= sin
−1
n
n
r
i
(sin q
r
)
= sin
−1
1
1
.3
.6
3
6
3
(sin 90.0°)
= 53.4°
36.7°
43. f = 15.0 cm
M =+2.00
M =−
q
p
q =−Mp =−2.00p
1
f
=
p
1
+
1
q
=
p
1
−
2.0
1
0p
=
2.0
1
0p
15.0
1
cm
=
2.0
1
0 p
p =
15
2
.0
.0
c
0
m
= 7.50 cm
36. n
i
= 1.473
n
r
= 1.00
sin q
c
=
n
n
r
i
q
c
= sin
−1
n
n
r
i
= sin
−1
1
1
.
.
4
0
7
0
3
= 42.8°
37. n
r
= 1.00
n
i
= 1.923
n
i
= 1.434
n
i
= 1.309
a. q
c
= sin
−1
n
n
r
i
= sin
−1
1
1
.
.
9
0
2
0
3
=
b. q
c
= sin
−1
n
n
r
i
= sin
−1
1
1
.
.
4
0
3
0
4
=
c. q
c
= sin
−1
n
n
r
i
= sin
−1
1
1
.
.
3
0
0
0
9
= 49.8°
44.2°
31.3°
38. n
i
= 1.52
n
r
= 1.00
q
r
= 45∞
q
c
= sin
−1
n
n
r
i
= sin
−1
1
1
.
.
0
5
0
2
= 41.1°
q
r
> q
c
, therefore the ray will be totally internally reflected.
39. n
i
= 1.00
q
i
= 63.5°
q
r
= 42.9°
n
i
(sin q
i
) = n
r
(sin q
r
)
n
r
=
n
i
s
(
i
s
n
in
q
q
r
i
)
=
(1.00
si
)
n
(s
4
in
2.9
6
°
3.5°)
= 1.31
Section One—Student Edition Solutions I Ch. 14–7
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
46. p = 80.0 cm
q =−40.0 cm
1
f
=
p
1
+
1
q
=
80.0
1
cm
+
−40.
1
0cm
1
f
=
0
1
.0
c
1
m
25
+
−0
1
.0
cm
250
=
−0
1
.0
cm
125
f =−80.0 cm
Givens Solutions
47. f = 2.44 cm
q = 12.9 cm
q =−12.9 cm
48. q =−30.0 cm
f =−40.0 cm
p
1
=
1
f
−
1
q
=
−40.
1
0cm
−
−30.
1
0cm
p
1
=
−0
1
.0
cm
250
−
−0
1
.0
cm
333
=
0
1
.0
c
0
m
83
p =
M =−
p
q
=−
−
1
3
2
0
0
.0
c
c
m
m
= 0.250
1.20 × 10
2
cm
a.
p
1
=
1
f
−
1
q
=
2.44
1
cm
+
12.9
1
cm
p
1
=
0
1
.4
c
1
m
0
+
0
1
.0
c
7
m
75
=
0
1
.3
c
3
m
2
p =
b.
p
1
=
1
f
−
1
q
=
2.44
1
cm
−
−12.
1
9cm
p
1
=
0
1
.4
c
1
m
0
−
−0
1
.0
cm
775
=
0
1
.4
c
8
m
8
p = 2.05 cm
3.01 cm
44. M = 1.50
p = 2.84 cm
M =−
p
q
= 1.50
q =−1.50p =−(1.50)(2.84 cm) =−4.26 cm
1
f
=
p
1
+
1
q
=
2.84
1
cm
+
−4.2
1
6cm
1
f
=
0
1
.3
c
5
m
2
+
−
1
0.
c
2
m
35
=
0
1
.1
c
1
m
7
f = 8.55 cm
45. M = 2.00
f = 12.0 cm
a. M =−
p
q
= 2.00
q =−2.00p
1
f
=
p
1
+
1
q
=
p
1
−
2.0
1
0p
=
2.0
1
0p
p =
M
f
=
12
2
.0
.0
c
0
m
= 6.00 cm
Holt Physics Solution ManualI Ch. 14–8
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
49. n
r
= 1.331
n
b
= 1.340
q
i
= 83.0°
n
i
= 1.00
n
i
(sin q
i
) = n
r
(sin q
r
)
blue: q
r
= sin
−1
n
n
r
i
(sin q
i
)
= sin
−1
1
1
.
.
3
0
4
0
0
(sin 83.0°)
=
red: q
r
= sin
−1
n
n
r
i
(sin q
r
)
= sin
−1
1
1
.
.
3
0
3
0
1
(sin 83.0°)
= 48.2°
47.8°
50. q
i
= 23.1°
v = 2.17 × 10
8
m/s
n
i
= 1.00
c = 3.00 × 10
8
m/s
n
r
=
v
c
=
3
2
.
.
0
1
0
7
×
×
1
1
0
0
8
8
m
m
/
/
s
s
= 1.38
n
i
(sin q
i
) = n
r
(sin q
r
)
q
r
= sin
−1
n
n
r
i
(sin q
i
)
= sin
−1
1
1
.
.
0
3
0
8
(sin 23.1°)
= 16.5°
52. v
a
= 340 m/s
v
w
= 1510 m/s
q
i
= 12.0°
n
i
(sin q
i
) = n
r
(sin q
r
)
q
r
= sin
−1
n
n
r
i
(sin q
i
)
= sin
−1
(
(
c
c
/
/
v
v
w
a
)
)
(sin q
i
)
q
r
= sin
−1
v
v
w
a
(sin q
i
)
= sin
−1
1
3
5
4
1
0
0
m
m
/
/
s
s
(sin 12.0°)
= 67°
Givens Solutions
53. n
i
= 1.333
n
r
= 1.00
∆y = 2.00 m
sin q
c
=
n
n
r
i
q
c
= sin
−1
n
n
r
i
= sin
−1
1
1
.
.
3
0
3
0
3
= 48.6°
tan q
c
=
(d
∆
/
y
2)
=
2∆
d
y
where d is the diameter of the piece of wood
d = 2∆y(tan q
c
) = (2)(2.00 m)(tan 48.6°) = 4.54 m
54. n
i
= 1.00
n
r
= 1.309
q
i
= 40.0°
n
i
(sin q
i
) = n
r
(sin q
r
)
q
r
= sin
−1
n
n
r
i
(sin q
i
)
= sin
−1
1
1
.
.
3
0
0
0
9
(sin 40.0°)
= 29.4°
q = 180.0°−29.4°= 110.6°
51. q
i
= 30.0°
q
r
= 22.0°
n
i
= 1.00
n
i
(sin q
i
) = n
r
(sin q
r
)
n
r
= n
i
s
s
i
i
n
n
q
q
r
i
= (1.00)
s
s
i
i
n
n
3
2
0
2
.
.
0
0
°
°
= 1.33
sin q
c
=
n
n
r
i
n
i
is now n
r
, and n
r
is now n
i
,so
q
c
= sin
−1
n
n
r
i
= sin
−1
1
1
.
.
0
3
0
3
= 48.8°
Section One—Student Edition Solutions I Ch. 14–9
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
58. n
i
= 1.8
q
c
= 45°
n
r
= n
i
(sin q
c
) = (1.8)(sin 45°) = 1.3
Givens Solutions
59. n
i
= 1.60
q
c
= 59.5°
n
r
= n
i
(sin q
c
) = (1.60)(sin 59.5°) = 1.38
60. n
i
= 1.333
n
r
= 1.00
∆y = 4.00 m
∆x = 2.00 m
q
i
= tan
−1
∆
∆
x
y
= tan
−1
2
4
.
.
0
0
0
0
m
m
= 26.6°
n
i
(sin q
i
) = n
r
(sin q
r
)
q
r
= sin
−1
n
n
r
i
(sin q
i
)
= sin
−1
1
1
.3
.0
3
0
3
(sin 26.6°)
= 36.6°
The angle, q, with respect to the water surface is 90°−q
r
.
q = 90°−36.6°= 53.4°
57. n
r
= 1.50
n
i
= 1.00
q
i
= 90°−30°=60°
n
i
= 1.50
n
r
= 1.00
q
i
= 24.7°
a. n
i
(sin q
i
) = n
r
(sin q
r
)
q
r
= sin
−1
n
n
r
i
(sin q
i
)
= sin
−1
1
1
.
.
0
5
0
0
(sin 60°)
= 35.3°
Using the figure at left, the angle of incidence of the ray at the bottom of the
prism can be found as follows.
q
i
= 180°−35.3°−30°−90°=
b. sin q
c
=
n
n
r
i
q
c
= sin
−1
n
n
r
i
= sin
−1
1
1
.
.
0
5
0
0
= 41.8°
The ray will pass through the bottom surface because q
i
< q
c
.
24.7°
30°
35.3°
i
θ
55. p = 10f
p
1
+
1
q
=
1
f
1
q
=
1
f
−
p
1
=
1
f
−
1
1
0f
=
1
9
0f
q =
1
9
0
f
56. n
i
= 1.53
n
r
= 1.00
n
r
= 1.333
sin q
c
=
n
n
r
i
a. q
c
= sin
−1
n
n
r
i
= sin
−1
1
1
.
.
0
5
0
3
=
b. q
c
= sin
−1
n
n
r
i
= sin
−1
1
1
.3
.5
3
3
3
= 60.6∞
40.8°
Holt Physics Solution ManualI Ch. 14–10
Givens Solutions
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
61. n
i
= 1.333
n
r
= 1.00
∆x = 325 m − 205 m = 120 m
∆y = 115 m
q
i
= tan
−1
∆
∆
x
y
= tan
−1
1
1
2
1
0
5
m
m
= 46.2°
n
i
(sin q
i
) = n
r
(sin q
r
)
q
r
= sin
−1
n
n
r
i
(sin q
i
)
= sin
−1
1
1
.3
.0
3
0
3
(sin 46.2°)
= 74.2°
h =
(ta
2
n
05
74
m
.2°)
= 58.0 m
62. n
i
= 1.00
q
i
= 50.0°
n
r
= 1.48
h = 3.1 mm = 0.31 cm
l
= 42.0 cm
n
i
sin q
i
= n
r
sin q
r
q
r
= sin
−1
n
i
s
n
in
r
q
i
= sin
−1
(1.00)
(
(
1
s
.
i
4
n
8)
50.0°)
q
r
= sin
−1
(0.518) = 31.2°
The distance, d, that the beam travels before being reflected is given by:
tanq
r
=
h
d
d =
tan
h
q
r
=
t
(
a
0
n
.3
(3
1
1
c
.
m
2°
)
)
= 0.51 cm
The incident beam hits at the midpoint, so the initially refracted beam travels a
distance of d/2 = 0.26 cm. The remaining reflections travel d = 0.51 cm.
The length (after the first beam) is
l
= d/2 = 42.5 cm − 0.26 cm = 41.7 cm.
Thereafter, the number of reflections is:
# of reflections ==1 +
4
0
1
.5
.7
1
c
c
m
m
(Note: the last, fractional reflection is not internal, but goes out the end of the
fiber optic)
# of reflections = 1 + 81.7 = 82
l
d
63. f = 4.80 cm
f = 4.80 × 10
−2
m
p = 10.0 m
p = 1.75 m
a.
1
q
=
1
f
−
p
1
=
4.80 ×
1
10
−2
m
−
10.
1
0m
1
q
=
2
1
0
m
.8
−
0
1
.1
m
00
=
2
1
0
m
.7
q = 4.83 × 10
−2
m =
b.
1
q
=
1
f
−
p
1
=
4.80 ×
1
10
−2
m
−
1.7
1
5m
1
q
=
2
1
0
m
.8
−
0
1
.5
m
71
=
2
1
0
m
.2
q = 4.95 × 10
−2
m = 4.95 cm
∆q = 4.95 cm − 4.83 cm = 0.12 cm
4.83 cm
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 14–11
64. q = 1.90 cm
p = 35.0 cm
1
f
=
p
1
+
1
q
=
35.0
1
cm
+
1.90
1
cm
1
f
=
0
1
.0
c
2
m
86
+
0
1
.5
c
2
m
6
=
0
1
.5
c
5
m
5
f = 1.80 cm
65. q = 1.90 cm
q = 1.90 × 10
−2
m
p = 15.0 m
1
f
=
p
1
+
1
q
=
15.
1
0m
+
1.90 ×
1
10
−2
m
1
f
=
0.
1
06
m
67
+
5
1
2
m
.6
=
5
1
2
m
.7
f = 1.90 × 10
−2
m = 1.90 cm
3. p = 50.0 cm
q = −10.0 cm
1
f
=
p
1
+
1
q
=
50.0
1
cm
+
−10.
1
0cm
=
50.0
1
cm
−
50.0
5
cm
= −
50.0
4
cm
f = −12.5 cm
Refraction, Standardized Test Prep
5. n
flint glass
= 1.66
n
air
= 1.00
n
oil
= 1.33
sin q
c
=
n
n
r
i
q
c
= sin
−1
n
n
r
i
= sin
−1
1
1
.
.
0
6
0
6
= (glass to air)
q
c
= sin
−1
n
n
r
i
= sin
−1
1
1
.
.
3
6
3
6
= (glass to oil)53.2°
37.0°
9. l = 500.0 nm
n = 1.5
n =
v
c
v
b
a
e
c
n
u
z
u
en
m
e
=
f
f
b
v
e
a
n
c
l
l
v
b
a
en
c
=
l
l
b
v
e
a
n
c
l
ben
=
l
n
vac
=
500
1
.0
.5
nm
= 330 nm
12. n
i
= 1.46
n
r
= 1.36
q
i
= 25.0°
n
i
sinq
i
= n
r
sinq
r
q
r
= sin
−1
n
i
s
n
i
r
nq
i
= sin
−1
(1.46)
(
(
1
s
.
i
3
n
6)
25.0°)
= 27.0°
13. n
i
= 1.92
n
r
= 1.47
sin q
c
=
n
n
r
i
q
c
= sin
−1
n
n
r
i
= sin
−1
1
1
.
.
4
9
7
2
= 50.0°
15. Converging Lens
p = −5.00 cm
(object behind lens)
q = +7.50 cm
(image in back of lens)
1
f
−
p
1
+
1
q
=
−5.0
1
0cm
+
7.50
1
cm
1
f
=
3
−
7.
7
5
.5
c
0
m
+
37
5
.5
.0
c
0
m
=
3
−
7.
2
5
.5
c
0
m
f = −15.0 cm or 15.0 cm (since focal point on both sides of lens)
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualI Ch. 14–12
16. p = −5.00 cm
q = +7.50 cm
M =
−
p
q
=
−
(
(
−
+
5
7
.0
.5
0
0
c
c
m
m
)
)
= 1.5
17. d
coin
= 2.8 cm
M =
h
h
=
d
d
im
co
a
in
ge
d
image
= M d
coin
= (1.5)(2.8 cm) = 4.2 cm
Section One—Student Edition Solutions I Ch. 15–1
Inference and Diffraction
Student Edition Solutions
I
1. d = 0.50 mm
q = 0.059°
m = 1
l =
d(s
m
in q)
==5.1 × 10
−7
m = 5.1 × 10
2
nm
(5.0 × 10
−4
m)(sin 0.059°)
1
Inference and Diffraction, Practice A
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. d = 2.02 × 10
−6
m
q = 16.5°
m = 1
l =
d(s
m
in q)
=
l = 574 nm
(2.02 × 10
−6
m)(sin 16.5°)
1
3. d = 0.250 mm
l = 546.1 nm
m = 1
q = sin
−1
l
d
m
= sin
−1
(5.4
2
6
.5
1
0
×
×
1
1
0
0
−
−
7
4
m
m
)(1)
= 0.125°
4. m = 1
d = 2.02 × 10
−6
m
l = 574 nm = 5.74 × 10
−7
m
q = sin
−1
= sin
−1
q = 25.2°
1 +
1
2
(5.74 × 10
−7
m)
(2.02 × 10
−6
m)
m +
1
2
l
d
3. d = 0.0550 mm
m = 1 and m = 2
l = 605 nm
m = 1: q
1
= sin
−1
l
d
m
= sin
−1
(6.
5
0
.
5
50
×
×
10
1
−
0
7
−
m
5
m
)(1)
= 0.630°
m = 2: q
2
= sin
−1
l
d
m
= sin
−1
(6.
5
0
.
5
50
×
×
10
1
−
0
7
−
m
5
m
)(2)
= 1.26°
∆q = q
2
− q
1
= 1.26°−0.630°= 0.63°
Inference and Diffraction, Section 1 Review
4. m = 2
q = 1.28°
l = 3.35 m
d =
s
l
in
m
q
=
(3
s
.
i
3
n
5
1
m
.2
)
8
(
°
2)
= 3.00 × 10
2
m
Holt Physics Solution ManualI Ch. 15–2
I
3. 1555 lines/cm
l = 565 nm
q < 90°
m = 11: q = sin
−1
m
d
l
= sin
−1
= 75.1°
m = 12: q = sin
−1
m
d
l
= sin
−1
=∞
Therefore, 11 is the highest-order number that can be observed.
(12)(5.65 × 10
−7
m)
155
1
500
m
(11)(5.65 × 10
−7
m)
155
1
500
m
Givens Solutions
2. 4525 lines/cm
m = 1
l
b
= 422 nm
l
r
= 655 nm
blue: q = sin
−1
m
d
l
b
= sin
−1
=
red: q = sin
−1
m
d
l
r
= sin
−1
= 17.2°
(1)(6.55 × 10
−7
m)
452
1
500
m
11.0°
(1)(4.22 × 10
−7
m)
452
1
500
m
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. 5000 × 10
3
lines/cm =
d
1
d = 2.000 × 10
−6
m
l
1
= 588.995 nm =
5.88995 × 10
−7
m
l
2
= 589.592 nm =
5.89592 × 10
−7
m
m = 1,2,3
For m = 1:
q
1
= sin
−1
m
d
l
1
= sin
−1
= 17.13°
q
2
= sin
−1
m
d
l
2
= sin
−1
= 17.15°
∆q = q
2
− q
1
= 17.15°−17.13°=
For m = 2:
q
1
= sin
−1
m
d
l
1
= sin
−1
= 36.09°
q
2
= sin
−1
m
d
l
2
= sin
−1
= 36.13°
∆q = q
2
− q
1
= 36.13°−36.09°=
For m = 3:
q
1
= sin
−1
m
d
l
1
= sin
−1
= 62.07°
q
2
= sin
−1
m
d
l
2
= sin
−1
= 62.18°
∆q = q
2
− q
1
= 62.18°−62.07°= 0.11°
(3)(5.89592 × 10
−7
m)
(2.000 × 10
−6
m)
(3)(5.88995 × 10
−7
m)
(2.000 × 10
−6
m)
0.04°
(2)(5.89592 × 10
−7
m)
(2.000 × 10
−6
m)
(2)(5.88995 × 10
−7
m)
(2.000 × 10
−6
m)
0.02°
(1)(5.89592 × 10
−7
m)
(2.000 × 10
−6
m)
(1)(5.88995 × 10
−7
m)
(2.000 × 10
−6
m)
Inference and Diffraction, Practice B
Section One—Student Edition Solutions I Ch. 15–3
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
4. 15 550 lines/cm
l = 565 nm
q < 90°
m = 1: q = sin
−1
m
d
l
= sin
−1
= 61.5°
m = 2: q = sin
−1
m
d
l
= sin
−1
=∞
Therefore, 1 is the highest-order number that can be observed.
(2)(5.65 × 10
−7
m)
155
1
5 000
m
(1)(5.65 × 10
−7
m)
155
1
5 000
m
1. 3550 lines/cm =
d
1
m = 1
q = 12.07°
a. l =
d s
m
in q
=
l = 5.89 × 10
−7
m =
b. m = 2, q
2
= ?
q
2
= sin
−1
m
d
l
= sin
−1
q
2
= 24.7°
(2)(5.89 × 10
−7
m)
355 0
1
00 m
589 nm
355
m
000
(sin 12.07°)
(1)
Inference and Diffraction, Section 2 Review
9. d = 0.33 mm = 3.3 × 10
−4
m
q = 0.055°
m = 0
l ==
l = 6.3 × 10
−7
m = 630 nm
(3.3 × 10
−4
m)(sin 0.055°)
0 +
1
2
d sin q
m +
1
2
Inference and Diffraction, Chapter Review
10. d = 0.3096 mm
q = 0.218°
m = 2
m = 3
m = 4
a. l =
d(s
m
in q)
==5.89 × 10
−7
m =
b. q = sin
−1
m
d
l
= sin
−1
(3
3
)(
.0
5
9
.8
6
9
×
×
1
1
0
0
−
−
4
7
m
m)
=
c. q = sin
−1
m
d
l
= sin
−1
(4
3
)(
.0
5
9
.8
6
9
×
×
1
1
0
0
−
−
4
7
m
m)
= 0.436°
0.327°
589 nm
(3.096 × 10
−4
m)(sin 0.218°)
2
5. q = 21.2°
l = 546.1 nm
m = 1
d =
s
m
in
l
q
=
(1)(5.
s
4
i
6
n
1
2
×
1.
1
2
0
°
−7
m)
= 1.51 × 10
−6
m = 1.51 × 10
−4
cm
Lines/cm =
1.51 × 1
1
0
−4
cm
= 6.62 × 10
3
lines/cm
Holt Physics Solution ManualI Ch. 15–4
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
20. 795 slits/cm
l = 353 nm = 3.53 × 10
−5
cm
m = 2:q
2
= sin
−1
m
d
l
= sin
−1
q
2
= 3.22°
(2)(3.53 × 10
−5
cm)
7
1
95
cm
21. 3661 slits/cm
l
1
= 478.5 nm
l
2
= 647.4 nm
l
3
= 696.4 nm
a. m = 1:
q
1
= sin
−1
m
d
l
= sin
−1
=
q
2
= sin
−1
m
d
l
= sin
−1
=
q
3
= sin
−1
m
d
l
= sin
−1
=
b. m = 2:
q
1
= sin
−1
m
d
l
= sin
−1
=
q
2
= sin
−1
m
d
l
= sin
−1
=
q
3
= sin
−1
m
d
l
= sin
−1
= 30.66°
(2)(6.964 × 10
−5
cm)
3661
1
cm
28.30°
(2)(6.474 × 10
−5
cm)
3661
1
cm
20.51°
(2)(4.785 × 10
−5
cm)
3661
1
cm
14.77°
6.964 × 10
−5
cm
3661
1
cm
13.71°
6.474 × 10
−5
cm
3661
1
cm
10.09°
4.785 × 10
−5
cm
3661
1
cm
26. l = 546.1 nm
q = 81.0°
m = 3
lines/mm =
s
m
in
l
q
==6030 lines/cm
sin 81.0°
(3)(5.461 × 10
−3
cm)
11. d = 3.2 cm = 3.2 × 10
−2
m
m = 2
q = 0.56°
l =
d(s
m
in q)
=
l = 1.6 × 10
−4
m = 1.6 × 10
2
µm
(3.2 × 10
−2
m)(sin 0.56°)
2
19. 795 slits/cm
l = 707 nm = 7.07 × 10
−5
cm
m = 1:q
1
= sin
−1
m
d
l
= sin
−1
q
1
= 3.22°
7.07 × 10
−5
cm
7
1
95
cm
Section One—Student Edition Solutions I Ch. 15–5
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
30. m = 2
l = 4.000 10
–7
m
q = 90.00°
d is at a maximum when l = 400.0 nm (red light).
d =
s
m
in
l
q
=
(2)(4
(s
.0
in
00
90
×
.0
1
0
0
°
−
)
7
m)
= 8.000 × 10
−7
m
28. l = 486 nm
m = 5
q = 0.578°
d =
s
m
in
l
q
=
(5)(
(
4
s
.
i
8
n
6
0
×
.5
1
7
0
8
−
°
7
)
m)
= 2.41 × 10
−4
m
31. l = 643 nm
q = 0.737°
d = 0.150 mm
path difference = d(sin q) = (0.150 mm)(sin 0.737°) =
a maximum
1.93 × 10
−3
mm = 3l
29. l
1
= 540.0 nm
4l
1
= 5l
2
l
2
=
4
5
l
1
=
4(540
5
.0 nm)
= 432.0 nm
5. l = 720 nm = 7.5 × 10
−7
m
d = 25 mm = 2.5 × 10
−5
m
m = 4
q = sin
−1
l
d
m
= sin
−1
q = 6.9°
(4)(7.5 × 10
−7
m)
(2.5 × 10
−5
m)
Inference and Diffraction, Standardized Test Prep
6. l = 640 nm = 6.4 × 10
−7
m
5.0 × 10
4
lines/m =
d
1
q = 11.1°
d sin q =±ml
±m =
d s
l
in q
=
m =±6
5.0 × 1
1
0
4
/m
(sin 11.1°)
(6.4 × 10
−7
m)
7. A
1
= 80 m
2
A
2
= 20 m
2
A =πr
2
=π
d
2
2
d = 2
A
π
d
1
= 2
A
π
1
= 2
80
π
m
2
= 10 m
d
2
= 2
A
π
2
= 2
20
π
m
2
= 5 m
Since resolving power is proportional to the diameter, d:
d
d
1
2
=
1
5
0
m
m
= 2
Holt Physics Solution ManualI Ch. 15–6
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
12. m = 3
l = 490 nm = 4.90 × 10
−7
m
q = 6.33°
d =
s
m
in
l
q
=
(3)(4
(s
.9
in
0
6
×
.3
1
3
0
°
−
)
7
m)
d = 1.33 × 10
−5
m
d
1
= 7.5 × 10
4
lines/m = 750 lines/cm
15. d = 15.0 m = 1.50 × 10
−5
m
m = 1
l = 2.25°
l =
d s
m
in q
=
l = 5.89 × 10
−7
m = 589 nm
(1.50 × 10
−5
m)(sin 2.25°)
(1)
16. d = 1.50 × 10
−5
m
m = 3 (bright)
l = 5.89 × 10
−7
m
q = sin
−1
m
d
l
= sin
−1
q = 6.77°
(3)(5.89 × 10
−7
m)
(1.50 × 10
−5
m)
17. d = 1.50 × 10
−5
m
m = 3 (dark)
l = 5.89 × 10
−7
m
q = sin
−1
= sin
−1
q = 7.90°
3 +
1
2
(5.89 × 10
−7
m)
(1.50 × 10
−5
m)
m +
1
2
l
d
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 16–1
3. q = 10.0 C
N ===6.25 × 10
19
electrons
10.0 C
1.60 × 10
−19
C/electron
q
1.60 × 10
−19
C/electron
Electric Forces and Fields, Section 1 Review
Givens Solutions
1. q
1
=−8.0 mC
q
2
= 8.0 mC
r = 5.0 cm
F =
k
C
r
q
2
1
q
2
=
F = 230 N
(8.99 × 10
9
N
•
m
2
/C
2
)(8.0 × 10
−6
C)
2
(0.050 m)
2
Electric Forces and Fields, Practice A
2. r = 0.30 m
q
1
= 12 × 10
−9
C
q
2
=−18 × 10
−9
C
q
1
=−3.0 × 10
−9
C
q
2
=−3.0 × 10
−9
C
a. F =
k
C
r
q
2
1
q
2
=
F =
b. F =
k
C
r
q
2
1
q
2
==9.0 × 10
−7
N
(8.99 × 10
9
N
•
m
2
/C
2
)(3.0 × 10
−9
C)
2
(0.30 m)
2
2.2 × 10
−5
N
(8.99 × 10
9
N
•
m
2
/C
2
)(12 × 10
−9
C)(18 × 10
−9
C)
(0.30 m)
2
3. q
1
= 60.0 mC
q
2
= 50.0 mC
F = 175 N
r =
k
C
q
F
1
q
2
=
r = 0.393 m = 39.3 cm
(8.99 × 10
9
N
•
m
2
/C
2
)(60.0 × 10
−6
C)(50.0 × 10
−6
C)
175 N
Electric Forces
and Fields
Student Edition Solutions
1. q
1
= 6.0 mC at x = 0 cm
q
2
= 1.5 mC at x = 3.0 cm
q
3
=−2.0 mC at x = 5.0 cm
F
1,2
=
k
(
C
r
1
q
,2
1
)
q
2
2
==9.0 × 10
1
N
F
2,3
=
k
(
C
r
2
q
,3
2
)
q
2
3
==67 N
F
1,3
=
k
(
C
r
1
q
,3
1
)
q
2
3
==43 N
(8.99 × 10
9
N
•
m
2
/C
2
)(6.0 × 10
−6
C)(2.0 × 10
−6
C)
(0.050 m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(1.5 × 10
−6
C)(2.0 × 10
−6
C)
(0.020 m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(6.0 × 10
−6
C)(1.5 × 10
−6
C)
(0.030 m)
2
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualI Ch. 16–2
F
1,tot
= F
1,2
+ F
1,3
=−(9.0 × 10
1
N) + (43 N) =−47 N
F
1,tot
=
F
2,tot
= F
1,2
+ F
2,3
= (9.0 × 10
1
N) + (67 N) = 157 N
F
2,tot
=
F
3,tot
= F
2,3
+ F
1,3
=−(67 N) − (43 N) =−11.0 × 10
1
N
F
3,tot
= 11.0 × 10
1
N, along the negative x-axis
157 N, along the positive x-axis
47 N, along the negative x-axis
Electric Forces and Fields, Practice B
Givens Solutions
2. q
1
= 3.0 mC
q
2
=−6.0 mC
q
3
=−2.4 mC
q
4
=−9.0 mC
r
1,2
= r
2,4
= r
3,4
= r
1,3
=
15 cm
a. r
1,4
= r
2,3
=
(1
5
cm
)
2
+
(
15
c
m
)
2
=
22
0
cm
2
+
2
20
c
m
2
=
44
0
cm
2
r
1,4
= r
2,3
= 21 cm
F
1,2
=
k
(
C
r
1
q
,2
1
)
q
2
2
==7.2 N
F
1,3
=
k
(
C
r
1
q
,3
1
)
q
2
3
==2.9 N
F
1,4
=
k
(
C
r
1
q
,4
1
)
q
2
4
==5.5 N
F
1,x
= (7.2 N) + (5.5 N)(cos 45°) = 7.2 N + 3.9 N = 11.1 N
F
1,y
=−(2.9 N) − (5.5 N)(sin 45°) =−2.9 N − 3.9 N =−6.8 N
F
1,tot
=
(F
1,
x
)
2
+
(
F
1,
y
)
2
=
(1
1.
1
N
)
2
+
(
6.
8
N
)
2
=
12
3
N
2
+
4
6
N
2
F
1,tot
=
16
9
N
2
= 13.0 N
q = tan
−1
1
6
1
.8
.1
= 31°
F
1,tot
=
b. F
2,1
= 7.2 N (See a.)
F
2,3
=
k
(
C
r
2
q
,3
2
)
q
2
3
==2.9 N
F
2,4
=
k
(
C
r
2
q
,4
2
)
q
2
4
==22 N
F
2,x
=−(7.2 N) + (2.9 N)(cos 45°) =−7.2 N + 2.1 N =−5.1 N
F
2,y
= (22 N) + (2.9 N)(sin 45°) = 22 N + 2.1 N = 24 N
F
2,tot
=
(F
2,
x
)
2
+
(
F
2,
y
)
2
=
(5
.1
N
)
2
+
(
24
N
)
2
=
26
N
2
+
5
80
N
2
F
2,tot
=
61
0
N
2
= 25 N
q = tan
−1
5
2
.
4
1
= 78°
F
2,tot
= 25 N, 78° above the negative x-axis
(8.99 × 10
9
N
•
m
2
/C
2
)(6.0 × 10
−6
C)(9.0 × 10
−6
C)
(0.15 m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(6.0 × 10
−6
C)(2.4 × 10
−6
C)
(0.21 m)
2
13.0 N, 31° below the positive x-axis
(8.99 × 10
9
N
•
m
2
/C
2
)(3.0 × 10
−6
C)(9.0 × 10
−6
C)
(0.21 m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(3.0 × 10
−6
C)(2.4 × 10
−6
C)
(0.15 m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(3.0 × 10
−6
C)(6.0 × 10
−6
C)
(0.15 m)
2
Section One—Student Edition Solutions I Ch. 16–3
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
c. F
4,1
= 5.5 N (See a.)
F
4,2
= 22 N (See b.)
F
4,3
=
k
(
C
r
4
q
,3
4
)
q
2
3
==8.6 N
F
4,x
=−(5.5 N)(cos 45°) + (8.6 N) =−3.9 N + 8.6 N = 4.7 N
F
4,y
= (5.5 N)(sin 45°) − (22 N) = 3.9 N − 22 N =−18 N
F
4,tot
=
(F
4,
x
)
2
+
(
F
4,
y
)
2
=
(4
.7
N
)
2
+
(
18
N
)
2
=
22
N
2
+
3
20
N
2
F
4,tot
=
34
0
N
2
= 18 N
q = tan
−1
4
1
.
8
7
= 75°
F
4,tot
= 18 N, 75° below the positive x-axis
(8.99 × 10
9
N
•
m
2
/C
2
)(9.0 × 10
−6
C)(2.4 × 10
−6
C)
(0.15 m)
2
Givens Solutions
1. q
1
=+2.00 × 10
−9
C at
x
1
= 0, y
1
= 0
q
2
=+4.00 × 10
−9
C at
x
2
= 1.5 m, y
2
= 0
q
3
=+3.00 × 10
−9
C
F
3,1
= F
3,2
k
(
C
r
3
q
,1
3
)
q
2
1
=
k
(
C
r
3
q
,2
3
)
q
2
2
(r
3
q
,
1
1
)
2
=
(r
3
q
,
2
2
)
2
Lets define r
3,1
= P so that r
3,2
= 1.5 m − P.
P
q
1
2
=
(1.5 m
q
2
− P)
2
P
2
q
2
= (1.5 m − P)
2
q
1
P
q
2
= (1.5 m − P)
q
1
P
q
2
+ P
q
1
= (1.5 m)
q
1
P(
q
1
+
q
2
) = (1.5 m)
q
1
P =
P =
P =
P = 0.62 m
(1.5 m)(4.47 × 10
−5
C
(4.47 × 10
−5
C
) + (6.32 × 10
−5
C
)
(1.5 m)
2.00 ×
10
−9
C
2.00 ×
10
−9
C
+
4.00 ×
10
−9
C
(1.5 m)
q
1
q
1
+
q
2
Electric Forces and Fields, Practice C
Holt Physics Solution ManualI Ch. 16–4
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. q
1
=−5.00 × 10
−9
C
q
2
=−2.00 × 10
−9
C
r
1,2
= 40.0 cm
q
3
= 15.0 × 10
−9
C
Givens Solutions
3. q
1
= q
2
= 1.60 × 10
−19
C
m
e
= 9.109 × 10
−31
kg
F
electric
= F
g
k
C
r
q
2
1
q
2
= m
e
g
r =
k
C
m
q
e
1
g
q
2
=
= 5.07 m
(8.99 × 10
9
N
•
m
2
/C
2
)(1.60 × 10
−19
C)
2
(9.109 × 10
−31
kg)(9.81 m/s
2
)
1. q
1
= 2.0 mC
r = 12 cm
q
2
=−3.5 mC
a. F =
k
C
r
q
2
1
q
2
=
F =
c. N == =1.2 × 10
13
electrons
2.0 × 10
−6
C
1.60 × 10
−19
C/electron
q
1
1.60 × 10
−19
C/electron
4.4 N
(8.99 × 10
9
N
•
m
2
/C
2
)(2.0 × 10
−6
C)(3.5 × 10
−6
C)
(0.12 m)
2
Electric Forces and Fields, Section 2 Review
3. q
1
= 2.2 × 10
−9
C at x = 1.5 m
q
2
= 5.4 × 10
−9
C at x = 2.0 m
q
3
= 3.5 × 10
−9
C at the
origin
F
1,3
=
k
(
C
r
1
q
,3
1
)
q
2
3
=
F
1,3
= 3.1 × 10
−8
N
F
2,3
=
k
(
C
r
2
q
,3
2
)
q
2
3
=
F
2,3
= 4.2 × 10
−8
N
F
3,tot
=−(3.1 × 10
−8
N) − (4.2 × 10
−8
N) =−7.3 × 10
−8
N
F
3,tot
= 7.3 × 10
−8
N, along the negative x-axis
(8.99 × 10
9
N
•
m
2
/C
2
)(5.4 × 10
−9
C)(3.5 × 10
−9
C)
(2.0 m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(2.2 × 10
−9
C)(3.5 × 10
−9
C)
(1.5 m)
2
k
(
C
r
1
q
,3
1
)
q
2
3
=
k
(
C
r
2
q
,3
2
)
q
2
3
(r
1
q
,
1
3
)
2
=
(r
2
q
,
2
3
)
2
5.00 ×
P
1
2
0
−9
C
=
(
2
0
.
.
0
4
0
00
×
m
10
−
−9
P
C
)
2
(2.00 × 10
−9
C)(P
2
) = (5.00 × 10
−9
C)(0.400 m − P)
2
P =
5
2
.
.
0
0
0
0
×
×
1
1
0
0
−
−
9
9
C
C
(0.400 m − P)
P = 0.632 m − (1.58)(P)
(2.58)(P) = 0.632 m
P = 0.245 m =
or (40.0 cm − 24.5 cm) = 15.5 cm from q
2
24.5 cm from q
1
Section One—Student Edition Solutions I Ch. 16–5
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
4. q
1
=−6.00 × 10
−9
C
q
2
=−3.00 × 10
−9
C
r
1,2
= 60.0 cm
k
(
C
r
1
q
,3
1
)
q
2
3
=
k
(
C
r
2
q
,3
2
)
q
2
3
(r
1
q
,
1
3
)
2
=
(r
2
q
,
2
3
)
2
6.00 ×
P
1
2
0
−9
C
=
(
3
0
.
.
0
6
0
00
×
m
10
−
−9
P
C
)
2
(3.00 × 10
−9
C)(P
2
) = (6.00 × 10
−9
C)(0.600 m − P)
2
P =
6
3
.
.
0
0
0
0
×
×
1
1
0
0
−
−
9
9
C
C
(0.600 m − P)
P = 0.849 m − (1.41)(P)
(2.41)(P) = 0.849 m
P = 0.352 m from q
1
=
or (60.0 cm − 35.2 cm) = 24.8 cm from q
2
35.2 cm from q
1
Givens Solutions
1. q
1
= 5.00 mC at the origin
q
2
=−3.00 mC at
x = 0.800 m
For the point y = 0.500 m on the y-axis,
E
1
=
k
r
C
1
q
2
1
==1.80 × 10
5
N/C
E
2
=
k
r
C
2
q
2
2
=
E
2
=
E
2
==3.03 × 10
4
N/C
q = tan
−1
0
0
.
.
8
5
0
0
0
0
= 58.0°
E
y
= (1.80 × 10
5
N/C) − (3.03 × 10
4
N/C)(cos 58.0°)
E
y
= (1.80 × 10
5
N/C) − (1.61 × 10
4
N/C) = 1.64 × 10
5
N/C
E
x
= (3.03 × 10
4
N/C)(sin 58.0°) = 2.57 × 10
4
N/C
E
tot
=
(E
y
)
2
+
(
E
x
)
2
=
(1
.6
4
×
1
0
5
N
/C
)
2
+
(
2.
57
×
1
0
4
N
/C
)
2
E
tot
=
(2
.6
9
×
1
0
1
0
N
2
/
C
2
)
+
(
6.
60
×
1
0
8
N
2
/
C
2
)
E
tot
=
2.
76
×
1
0
1
0
N
2
/
C
2
= 1.66 × 10
5
N/C
j = tan
−1
1
2
.
.
6
5
4
7
×
×
1
1
0
0
5
4
= 81.1°
E
tot
= 1.66 × 10
5
N/C, 81.1° above the positive x-axis
(8.99 × 10
9
N
•
m
2
/C
2
)(3.00 × 10
−6
C)
0.
89
0
m
2
2
(8.99 × 10
9
N
•
m
2
/C
2
)(3.00 × 10
−6
C)
0.
64
0
m
2
+
0
.2
50
m
2
2
(8.99 × 10
9
N
•
m
2
/C
2
)(3.00 × 10
−6
C)
(0
.8
00
m
)
2
+
(
0.
50
0
m
)
2
2
(8.99 × 10
9
N
•
m
2
/C
2
)(5.00 × 10
−6
C)
(0.500 m)
2
Electric Forces and Fields, Practice D
Holt Physics Solution ManualI Ch. 16–6
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. r = 5.3 × 10
−11
m
q = 1.60 × 10
−19
C
E =
k
r
C
2
q
==5.1 × 10
11
N/C
E = 5.1 × 10
11
N/C, away from the proton
(8.99 × 10
9
N
•
m
2
/C
2
)(1.60 × 10
−19
C)
(5.3 × 10
−11
m)
2
3. E = 2.0 × 10
4
N/C, along the
positive x-axis
q
e
= q
p
= 1.60 × 10
−19
C
a. F = Eq
e
= (2.0 × 10
4
N/C)(1.60 × 10
−19
C)
F =
b. F = Eq
p
= (2.0 × 10
4
N/C)(1.60 × 10
−19
C)
F = 3.2 × 10
−15
N, along the positive x-axis
3.2 × 10
−15
N, along the negative x-axis
Givens Solutions
1. q
1
= 40.0 × 10
−9
C
q
2
= 60.0 × 10
−9
C
r =
30.0
2
cm
= 15.0 cm
E
1
=
k
C
r
2
q
1
==1.60 × 10
4
N/C
E
2
=
k
C
r
2
q
2
==2.40 × 10
4
N/C
E
tot
= E
1
+ E
2
= (1.60 × 10
4
N/C) − (2.40 × 10
4
N/C) =−0.80 × 10
4
N/C
E
tot
= 8.0 × 10
3
N/C toward the 40.0 × 10
−9
C charge
(8.99 × 10
9
N
•
m
2
/C
2
)(60.0 × 10
−9
C)
(0.150 m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(40.0 × 10
−9
C)
(0.150 m)
2
Electric Forces and Fields, Section 3 Review
3. q = 3.5 mC
N == =2.2 × 10
13
electrons
3.5 × 10
−6
C
1.60 × 10
−19
C/electron
q
1.60 × 10
−19
C/electron
Electric Forces and Fields, Chapter Review
15. q
1
= q
2
= (46)(1.60 × 10
−19
C)
r = (2)(5.90 × 10
−15
m)
F =
k
C
r
q
2
1
q
2
=
F = 3.50 × 10
3
N
(8.99 × 10
9
N
•
m
2
/C
2
)[(46)(1.60 × 10
−19
C)]
2
[(2)(5.90 × 10
−15
m)]
2
16. q
1
= 2.5 mC
q
2
=−5.0 mC
r = 5.0 cm
F =
k
C
r
q
2
1
q
2
=
F = 45 N
(8.99 × 10
9
N
•
m
2
/C
2
)(2.5 × 10
−6
C)(5.0 × 10
−6
C)
(0.050 m)
2
17. q
1
= 2.0e
q
2
= 79e
r = 2.0 × 10
−14
m
e = 1.60 × 10
−19
C
F =
k
C
r
q
2
1
q
2
=
F = 91 N
(8.99 × 10
9
N
•
m
2
/C
2
)(2.0)(79)(1.60 × 10
−19
C)
2
(2.0 × 10
−14
m)
2
Section One—Student Edition Solutions I Ch. 16–7
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
18. q
1
= 3.0 nC
q
2
= 6.0 nC
q
3
= 2.0 nC
r
1,2
= r
2,3
=
(1
.0
m
)
2
+
(
1.
0
m
)
2
r
1,2
= r
2,3
=
(1
.0
m
)
2
+
(
1.
0
m
)
2
=
2.
0
m
2
= 1.4 m
F
1,2
=
k
(
C
r
1
q
,2
1
)
q
2
2
=
F
1,2
= 8.3 × 10
−8
N
F
2,3
=
k
(
C
r
2
q
,3
2
)
q
2
3
=
F
2,3
= 5.5 × 10
−8
N
F
x
= (8.3 × 10
−8
N)(cos 45°) + (5.5 × 10
−8
N)(cos 45°)
F
x
= (5.9 × 10
−8
N) + (3.9 × 10
−8
N) = 9.8 × 10
−8
N
F
y
=−(8.3 × 10
−8
N)(sin 45°) + (5.5 × 10
−8
N)(sin 45°)
F
y
=−(5.9 × 10
−8
N) + (3.9 × 10
−8
N) =−2.0 × 10
−8
N
F
tot
=
(F
x
)
2
+
(
F
y
)
2
=
(9
.8
×
1
0
−
8
N
)
2
+
(
2.
0
×
1
0
−
8
N
)
2
F
tot
=
(9
.6
×
1
0
−
15
N
2
)
+
(
4.
0
×
1
0
−
16
N
2
)
=
1.
00
×
1
0
−
14
N
2
F
tot
= 1.00 × 10
−7
N
q = tan
−1
2
9
.
.
0
8
= 12°
F
tot
= 1.00 × 10
−7
N, 12° below the positive x-axis
(8.99 × 10
9
N
•
m
2
/C
2
)(6.0 × 10
−9
C)(2.0 × 10
−9
C)
(1.4 m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(3.0 × 10
−9
C)(6.0 × 10
−9
C)
(1.4 m)
2
Givens Solutions
19. q
1
= q
2
= 2.5 × 10
−9
C
q
3
= 3.0 × 10
−9
C
r
2,1
= 1.0 m
r
3,1
= r
3,2
r
3,1
= r
3,2
=
(0
.5
0
m
)
2
+
(
0.
70
m
)
2
= 0.86 m
F
3,1
= F
3,2
=
k
(
C
r
3
q
,1
3
)
q
2
1
=
F
3,1
= F
3,2
= 9.1 × 10
−8
N
F
x
= F
3,1
cos q + F
3,2
cos q
F
x
=(9.1 × 10
−8
N)
0
0
.
.
7
8
0
6
m
m
+ (9.1 × 10
−8
N)
0
0
.
.
7
8
0
6
m
m
F
x
= 7.4 × 10
−8
N + 7.4 × 10
−8
N = 14.8 × 10
−8
N
F
y
= F
3,1
sin q + F
3,2
sin q
F
x
=(9.1 × 10
−8
N)
0
0
.
.
5
8
0
6
m
m
+ (9.1 × 10
−8
N)
−
0
0
.8
.5
6
0
m
m
= 0 N
F
tot
=
(F
1
)
2
+
(
F
4
)
2
=
(1
4.
8
×
1
0
−
8
N
)
2
= 14.8 × 10
−8
N
q = tan
−1
14.8 ×
0
1
N
0
−8
N
=0
F
tot
= 1.48 × 10
−7
N along the +x-axis
(8.99 × 10
9
N
•
m
2
/C
2
)(3.0 × 10
−9
C)(2.5 × 10
−9
C)
(0.86 m)
2
Holt Physics Solution ManualI Ch. 16–8
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
20. q
1
=−9.0 mC at y = 6.0 m
q
2
=−8.0 mC at y =−4.0 m
k
(
C
r
1
q
,3
1
)
q
2
3
=
k
(
C
r
2
q
,3
2
)
q
2
3
9.0 ×
P
1
2
0
−6
C
=
(
8
1
.
0
0
.0
×
m
10
−
−6
P
C
)
2
(8.0 × 10
−6
C)(P
2
) = (9.0 × 10
−6
C)(10.0 m − P)
2
P =
9
8
.
.
0
0
×
×
1
1
0
0
−
−
6
6
C
C
(10.0 m −P)
P = 11 m − (1.1)(P)
(2.1)(P) = 11 m
P = 5.2 m below q
1
, or y = 6.0 m − 5.2 m = 0.8 m
q
3
is located at y = 0.8 m
Givens Solutions
21. q
1
= 3.5 nC
q
2
= 5.0 nC
r = 40.0 cm
q
3
=−6.0 nC
k
(
C
r
1
q
,3
1
)
q
2
3
=
k
(
C
r
2
q
,3
2
)
q
2
3
3.5 ×
P
1
2
0
−9
C
=
(0
5
.
.
4
0
0
×
0m
10
−
−
9
P
C
)
2
(5.0 × 10
−9
C)(P
2
) = (3.5 × 10
−9
C)(0.400 m − P)
2
P =
3
5
.
.
5
0
×
×
1
1
0
0
−
−
9
9
C
C
(0.400 m − P)
P = 0.33 m − (0.84)(P)
(1.84)(P) = 0.33 m
P = 0.18 m = 18 cm from q
1
32. q
1
= 30.0 × 10
−9
C
q
2
= 60.0 × 10
−9
C
r =
30.0
2
cm
= 15.0 cm
E
1
=
k
C
r
2
q
1
==1.20 × 10
4
N/C
E
2
=
k
C
r
2
q
2
==2.40 × 10
4
N/C
E
tot
= (1.20 × 10
4
N/C) − (2.40 × 10
4
N/C) =−12.0 × 10
3
N/C
E
tot
= 12.0 × 10
3
N/C toward the 30.0 × 10
−9
C charge
(8.99 × 10
9
N
•
m
2
/C
2
)(60.0 × 10
−9
C)
(0.150 m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(30.0 × 10
−9
C)
(0.150 m)
2
Section One—Student Edition Solutions I Ch. 16–9
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
33. q
1
= 5.7 mC at x =−3.0 m
q
2
= 2.0 mC at x = 1.0 m
For E at y = 2.0 m on the y-axis,
r
1
=
(2
.0
m
)
2
+
(
3.
0
m
)
2
=
4.
0
m
2
+
9
.0
m
2
=
13
.0
m
2
= 3.61 m
r
2
=
(2
.0
m
)
2
+
(
1.
0
m
)
2
=
4.
0
m
2
+
1
.0
m
2
=
5.
0
m
2
= 2.2 m
E
1
=
k
r
C
1
q
2
1
==3.9 × 10
3
N/C
E
2
=
k
r
C
2
q
2
2
==3.7 × 10
3
N/C
q
1
= tan
−1
2
3
.
.
0
0
= 34°
q
2
= tan
−1
1
2
.
.
0
0
= 63°
E
x
= (3.9 × 10
3
N/C)(cos 34°) − (3.7 × 10
3
N/C)(cos 63°)
E
x
= (3.2 × 10
3
N/C) − (1.7 × 10
3
N/C) = 1.5 × 10
3
N/C
E
y
= (3.9 × 10
3
N/C)(sin 34°) + (3.7 × 10
3
N/C)(sin 63°)
E
y
= (2.2 × 10
3
N/C) + (3.3 × 10
3
N/C) = 5.5 × 10
3
N/C
E
tot
=
(E
x
)
2
+
(
E
y
)
2
=
(1
.5
×
1
0
3
N
/C
)
2
+
(
5.
5
×
1
0
3
N
/C
)
2
E
tot
=
(2
.2
×
1
0
6
N
2
/
C
2
)
+
(
3.
0
×
1
0
7
N
2
/
C
2
)
=
(3
.2
×
1
0
7
N
2
/
C
2
)
= 5.7 × 10
3
N/C
q = tan
−1
1
5
.
.
5
5
= 75°
E
tot
= 5.7 × 10
3
N/C, 75° above the positive x-axis
(8.99 × 10
9
N
•
m
2
/C
2
)(2.0 × 10
−6
C)
(2.2 m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(5.7 × 10
−6
C)
(3.61 m)
2
Givens Solutions
34. q
1
= (7.0 × 10
13
protons)(e)
q
2
= (4.0 × 10
13
electrons)(e)
e = 1.60 × 10
−19
C
Q
net
= q
1
+ q
2
= [(7.0 × 10
13
) − (4.0 × 10
13
)](e) = (3.0 × 10
13
)(e)
Q
net
= (3.0 × 10
13
)(1.60 × 10
−19
C)
Q
net
= 4.8 × 10
−6
C
35. a = 6.3 × 10
3
m/s
2
m
e
= 9.109 × 10
−31
kg
q = 1.60 × 10
−19
C
a. F = m
e
a = (9.109 × 10
−31
kg)(6.3 × 10
3
m/s
2
) = 5.7 × 10
−27
N
F =
b. E =
F
q
=
1
5
.
.
6
7
0
×
×
1
1
0
0
−
−
2
1
7
9
N
C
= 3.6 × 10
−8
N/C
5.7 × 10
−27
N, in a direction opposite E
36. 1.00 g of Cu has 9.48 × 10
21
atoms.
1 Cu atom has 29 electrons.
a. 1.00 g of Cu has (9.48 × 10
21
atoms)(29 electrons/atom) =
b. q
tot
= (2.75 × 10
23
electrons)(1.60 × 10
−19
C/electron) = 4.40 × 10
4
C
2.75 × 10
23
electrons
Holt Physics Solution ManualI Ch. 16–10
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
37. q
1
= 6.0 mC
q
2
= 1.5 mC
q
3
=−2.0 mC
r
1,2
= 3.0 cm
r
2,3
= 2.0 cm
q
4
=−2.0 mC
a. E at 1.0 cm left of q
2
= E
1
+ E
2
+ E
3
r
1
= r
1,2
− 1.0 cm = 3.0 cm − 1.0 cm = 2.0 cm
r
2
= 1.0 cm
r
3
= r
2,3
+ 1.0 cm = 2.0 cm + 1.0 cm = 3.0 cm
E
1
=
k
r
C
1
q
2
1
==1.3 × 10
8
N/C
E
2
=
k
r
C
2
q
2
2
==1.3 × 10
8
N/C
E
3
=
k
r
C
3
q
2
3
==2.0 × 10
7
N/C
E
tot
= (1.3 × 10
8
N/C) − (1.3 × 10
8
N/C) + (2.0 × 10
7
N/C)
E
tot
=
b. F = q
4
E = (2.0 × 10
−6
C)(2.0 × 10
7
N/C) = 4.0 × 10
1
N
2.0 × 10
7
N/C along the positive x-axis
(8.99 × 10
9
N
•
m
2
/C
2
)(2.0 × 10
−6
C)
(0.030 m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(1.5 × 10
−6
C)
(0.010 m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(6.0 × 10
−6
C)
(0.020 m)
2
Givens Solutions
38. q
1
= 5.0 nC
q
2
= 6.0 nC
q
3
=−3.0 nC
r
1,2
= 0.30 m
r
1,3
= 0.10 m
a. F
1,2
=
k
(
C
r
1
q
,2
1
)
q
2
2
=
F
1,2
= 3.0 × 10
−6
N
F
1,3
=
k
(
C
r
1
q
,3
1
)
q
2
3
=
F
1,3
= 1.3 × 10
−5
N
F
1,tot
=
(F
1,
2
)
2
+
(
F
1,
3
)
2
=
(3
.0
×
1
0
−
6
N
)
2
+
(
1.
3
×
1
0
−
5
N
)
2
F
1,tot
=
(9
.0
×
1
0
−
12
N
2
)
+
(
1.
7
×
1
0
−
10
N
2
)
=
1.
8
×
1
0
−
10
N
2
= 1.3 × 10
−5
N
q = tan
−1
3
1
.
3
0
= 77°
F
1,tot
=
b. E =
q
F
1
=
1
5
.
.
3
0
×
×
1
1
0
0
−
−
5
9
N
C
= 2.6 × 10
3
N/C, 77° below the negative x-axis
1.3 × 10
−5
N, 77° below the negative x-axis
(8.99 × 10
9
N
•
m
2
/C
2
)(5.0 × 10
−9
C)(3.0 × 10
−9
C)
(0.10 m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(5.0 × 10
−9
C)(6.0 × 10
−9
C)
(0.30 m)
2
40. m
1
= 7.36 × 10
22
kg
m
2
= 5.98 × 10
24
kg
F
g
= F
electric
Gm
r
1
2
m
2
=
k
C
r
2
q
2
q =
G
m
k
1
C
m
2
=
q = 5.72 × 10
13
C
(6.673 × 10
−11
N
•
m
2
/kg
2
)(7.36 × 10
22
kg)(5.98 × 10
24
kg)
8.99 × 10
9
N
•
m
2
/C
2
Section One—Student Edition Solutions I Ch. 16–11
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
41. m
1
= m
2
= 0.20 g
q = 5.0°
L = 30.0 cm
ΣF
y
= 0 N, so F
g
= F
T, y
= F
T
(cos 5.0°)
ΣF
x
= 0 N, so F
electric
= F
T, x
= F
T
(sin 5.0°)
F
el
F
ec
g
tric
=
F
F
T
T
(
(
c
si
o
n
s
5
5
.
.
0
0
°
°
)
)
= tan 5.0°
r
k
2
C
m
q
g
2
= tan 5.0°
r = (2)(0.300 m)(sin 5.0°)
q =
r
2
m
g(
t
k
a
C
n
5
.0
°)
q =
q = 7.2 × 10
−9
C
[(2)(0.300 m)(sin 5.0°)]
2
(0.20 × 10
−3
kg)(9.81 m/s
2
)(tan 5.0°)
8.99 × 10
9
N
•
m
2
/C
2
Givens Solutions
42. m
e
= 9.109 × 10
−31
kg
m
p
= 1.673 × 10
−27
kg
q = 1.60 × 10
−19
C
a. F = Eq = mg
E
e
=
m
q
e
g
==5.58 × 10
−11
N/C
E
e
=
b. E
p
=
m
q
p
g
==1.03 × 10
−7
N/C
E
p
= 1.03 × 10
−7
N/C upward
(1.673 × 10
−27
kg)(9.81 m/s
2
)
1.60 × 10
−19
C
5.58 × 10
−11
N/C, downward
(9.109 × 10
−31
kg)(9.81 m/s
2
)
1.60 × 10
−19
C
43. E = 520 N/C
∆t = 48 ns
v
i
= 0 m/s
m
e
= 9.109 × 10
−31
kg
m
p
= 1.673 × 10
−27
kg
q = 1.60 × 10
−19
C
a =
m
F
=
q
m
E
v
f
= a∆t =
q
m
E
∆t
For the electron,
v
f,e
=
q
m
E∆
e
t
==
For the proton,
v
f,p
=
q
m
E∆
p
t
==2.4 × 10
3
m/s
(1.60 ×10
−19
C)(520 N/C)(48 × 10
−9
s)
1.673 × 10
−27
kg
4.4 × 10
6
m/s
(1.60 ×10
−19
C)(520 N/C)(48 × 10
−9
s)
9.109 × 10
−31
kg
44. E = 3.0 × 10
4
N/C
q = 1.60 × 10
−19
C
m
p
= 1.673 × 10
−27
kg
a. F = qE = (1.60 × 10
−19
C)(3.0 × 10
4
N/C) =
b. a =
m
F
p
==2.9 × 10
12
m/s
2
4.8 × 10
−15
N
1.673 × 10
−27
kg
4.8 × 10
−15
N
Holt Physics Solution ManualI Ch. 16–12
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
45. E = 3.4 × 10
5
N/C
q = 1.60 × 10
−19
C
F = qE = (1.60 × 10
−19
C)(3.4 × 10
5
N/C) = 5.4 × 10
−14
N
Givens Solutions
46. q = 24 mC
E = 610 N/C
F
electric
= F
g
qE = mg
m =
q
g
E
==1.5 × 10
−3
kg
(24 × 10
−6
C)(610 N/C)
9.81 m/s
2
47. m = 0.10 kg
L = 30.0 cm
q = 45°
ΣF
x
= 0 N = F
electric
− F
T, x
F
T, x
= F
electric
= F
T
(sin 45°)
ΣF
y
= 0 N = F
T, y
− F
g
F
T, y
= F
g
= F
T
(cos 45°)
F
el
F
ec
g
tric
=
F
F
T
T
(
(
c
si
o
n
s
4
4
5
5
°
°
)
)
= tan 45°
F
electric
=
(L
k
s
C
in
q
q
2
)
2
+
(2L
k
s
C
in
q
2
q)
2
=
4k
4
C
L
q
2
(
2
si
+
n
k
2
q
C
)
q
2
=
4L
5
2
(
k
s
C
in
q
2
2
q)
F
g
= mg
F
el
F
ec
g
tric
=
4L
2
(
5
s
k
in
C
2
q
q
2
)mg
= tan 45°
5k
C
q
2
= 4L
2
(sin
2
q)mg(tan 45°)
q =
= 2L(sin q)
m
g
(t
5
a
k
n
C
45
°)
q = (2)(0.300 m)(sin 45°)
q = 2.0 × 10
−6
C
(0.10 kg)(9.81 m/s
2
)(tan 45°)
(5)(8.99 × 10
9
N
•
m
2
/C
2
)
4L
2
(sin
2
q)mg(tan 45°)
5k
C
48.
Because each charge is the same size and all are the same distance from the center,
E
1
= E
2
= E
3
= E
4
= E
5
=
k
r
C
2
q
E
1,y
= 0 N/C
E
5,y
=−E
2,y
=−E(sin 72°)
E
4,y
=−E
3,y
=−E(sin 36°)
E
y
= E
1,y
+ E
2,y
+ E
3,y
+ E
4,y
+ E
5,y
E
y
= 0 N/C + E(sin 72°) + E(sin 36°) − E(sin 36°) − E(sin 72°) = 0 N/C
E
1,x
= E
E
2,x
= E
5,x
= E(cos 72°)
E
3,x
= E
4,x
=−E(cos 36°)
E
x
= E
1,x
+ E
2,x
+ E
3,x
+ E
4,x
+ E
5,x
E
x
= E + E(cos 72°) − E(cos 36°) − E(cos 36°) + E(cos 72°)
E
x
= E + 2E(cos 72°) − 2E(cos 36°) = E(1 + 0.62 − 1.62)
E
x
= 0 N/C
E =
(E
x
)
2
+
(
E
y
)
2
=
(0
N
/C
)
2
+
(
0
N
/C
)
2
= 0 N/C
E
1
E
2
E
3
E
4
E
5
36°
36°
72°
72°
72°
72°
+y
+x
−q
−q
−q
−q
−q
Section One—Student Edition Solutions I Ch. 16–13
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
49. E = 370.0 N/C
∆t = 1.00 ms
m
e
= 9.109 × 10
−31
kg
m
p
= 1.673 × 10
−27
kg
q = 1.60 × 10
−19
C
a
e
=
m
F
e
=
m
qE
e
==6.50 × 10
13
m/s
2
∆x
e
=
1
2
a
e
∆t
2
= (0.5)(6.50 × 10
13
m/s
2
)(1.00 × 10
−6
s)
2
= 32.5 m
a
p
=
m
F
p
=
m
qE
p
==3.54 × 10
10
m/s
2
∆x
p
=
2
1
a
p
∆t
2
= (0.5)(3.54 × 10
10
m/s
2
)(1.00 × 10
−6
s)
2
∆x
p
= 1.77 × 10
−2
m
∆x
tot
=∆x
e
+∆x
p
= 32.5 m + (1.77 × 10
−2
m) = 32.5 m
(1.60 × 10
−19
C)(370.0 N/C)
1.673 × 10
−27
kg
(1.60 × 10
−19
C)(370.0 N/C)
9.109 × 10
−31
kg
50. E = 300.0 N/C
m
e
= 9.109 × 10
−31
kg
q = 1.60 × 10
−19
C
∆t = 1.00 × 10
−8
s
a. a =
m
F
e
=
m
qE
e
==
b. v
f
= a∆t = (5.27 × 10
13
m/s
2
)(1.00 × 10
−8
s) = 5.27 × 10
5
m/s
5.27 × 10
13
m/s
2
(1.60 × 10
−19
C)(300.0 N/C)
9.109 × 10
−31
kg
51. E = 3.0 × 10
6
N/C
q = 1.60 × 10
−19
C
m
e
= 9.109 × 10
−31
kg
v
i
= 0 m/s
v
f
= (0.100)(3.00 × 10
8
m/s)
m
p
= 1.673 × 10
−27
kg
a. a =
m
F
e
=
m
qE
e
==
b. v
f
2
= 2a∆x
∆x =
v
2
f
a
2
==
c. a =
m
F
p
=
m
qE
p
==2.9 × 10
14
m/s
2
(1.60 × 10
−19
C)(3.0 × 10
6
N/C)
1.673 × 10
−27
kg
8.5 × 10
−4
m
[(0.100)(3.00 × 10
8
m/s)]
2
(2)(5.3 × 10
17
m/s
2
)
5.3 × 10
17
m/s
2
(1.60 × 10
−19
C)(3.0 × 10
6
N/C)
9.109 × 10
−31
kg
52. KE = 3.25 × 10
−15
J
∆x = 1.25 m
v
f
= 0 m/s
q = 1.60 × 10
−19
C
m
p
= 1.673 × 10
−27
kg
KE =
2
1
m
p
v
i
2
v
i
=
2
m
K
p
E
a =
v
f
2
2∆
−
x
v
i
2
F = qE = m
p
a
E =
m
q
p
a
=
(m
p
(
)
q
(
)
v
(
f
2
2
∆
−
x)
v
i
2
)
==
m
p
(q
v
)
f
(
2
2
−
∆
2
x
K
)
E
E ==−1.62 × 10
4
N/C
E = 1.62 × 10
4
N/C opposite the proton’s velocity
(1.673 × 10
−27
kg)(0 m/s)
2
− (2)(3.25 × 10
−15
J)
(1.60 × 10
−19
C)(2)(1.25 m)
m
p
v
f
2
− m
p
2
m
K
p
E
2
(q)(2∆x)
Holt Physics Solution ManualI Ch. 16–14
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
53. m = 2.0 g
L = 20.0 cm
E = 1.0 × 10
4
N/C
q = 15°
b. F
T, y
= F
g
= mg
F
T
=
co
F
s
T
1
,y
5°
=
co
m
s1
g
5°
qE = F
T, x
= F
T
(sin 15°) =
mg
c
(
o
s
s
in
15
1
°
5°)
= mg(tan 15°)
q =
mg(ta
E
n15°)
==5.3 × 10
−7
C
(2.0 × 10
−3
kg)(9.81 m/s
2
)(tan 15°)
1.0 × 10
4
N/C
54. E = 2.0 × 10
3
N/C along the
positive x-axis
q = 1.60 × 10
−19
C
m
p
= 1.673 × 10
−27
kg
v
f
= 1.00 × 10
6
m/s
a. F = qE = (1.60 × 10
−19
C)(2.0 × 10
3
N/C) = 3.2 × 10
−16
N
F =
b. a =
m
F
p
=
1.
3
6
.
7
2
3
×
×
1
1
0
0
−
−
1
2
6
7
N
kg
=
c. ∆t =
v
a
f
==5.3 × 10
−6
s
1.00 × 10
6
m/s
1.9 × 10
11
m/s
2
1.9 × 10
11
m/s
2
3.2 × 10
−16
N, along the positive x-axis
55. v
f,1
= (0.010)(3.00 × 10
8
m/s)
∆x
1
= 2.0 mm
q = 1.60 × 10
−19
C
m
e
= 9.109 × 10
−31
kg
∆x
2
= 4.0 mm
a. a =
2
v
∆
f,1
x
2
1
E =
m
q
e
a
=
m
2∆
e
v
x
f
1
,1
q
2
E =
E =
b. a =
2
v
∆
f,1
x
2
1
==2.2 × 10
15
m/s
2
v
f,2
2
= 2a∆x
2
v
f,2
=
2a
∆
x
2
=
(2
)(
2.
2
×
1
0
1
5
m
/s
2
)
(4
.0
×
1
0
−
3
m
)
= 4.2 × 10
6
m/s
[(0.010)(3.00 × 10
8
m/s)]
2
(2)(2.0 × 10
−3
m)
1.3 × 10
4
N/C
(9.109 × 10
−31
kg)[(0.010)(3.00 × 10
8
m/s)]
2
(2)(2.0 × 10
−3
m)(1.60 × 10
−19
C)
56. r
1
= 2.17 mm
q
1
= 1.60 × 10
−19
C
q
2
=−1.60 × 10
−19
C
r
2
= (0.0100)(2.17 mm)
F
electric
= F
elastic
k
C
r
q
1
1
2
q
2
= kr
2
k =
k
C
r
1
q
2
1
r
q
2
2
=
k = 2.25 × 10
−9
N/m
(8.99 × 10
9
N
•
m
2
/C
2
)(1.60 × 10
−19
C)
2
(2.17 × 10
−6
m)
3
(0.0100)
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 16–15
Electric Forces and Fields, Standardized Test Prep
Givens Solutions
11. q = 5.0 mC
r = 2.0 m
E
1
= E
2
= E
3
=
k
r
C
2
q
==1.1 × 10
4
N/C
E
x
= (1.1 × 10
4
N/C)(sin 60°) − (1.1 × 10
4
N)(sin 60°) = 0.0 N/C
E
y
= (1.1 × 10
4
N/C) − (1.1 × 10
4
N/C)(cos 60°) − (1.1 × 10
4
N/C)(cos 60°)
E
y
= (1.1 × 10
4
N/C) − (5.5 × 10
3
N/C) − (5.5 × 10
3
N/C) = 0.0 N/C
E
tot
=
(0
.0
N
/C
)
2
+
(
0.
0
N
/C
)
2
= 0.0 N/C
(8.99 × 10
9
N
•
m
2
/C
2
)(5.0 × 10
−6
C)
(2.0 m)
2
13. q
1
= (6.02 × 10
23
)(e)
q
2
= (6.02 × 10
23
)(e)
r = (2)(6.38 × 10
6
m)
e = 1.60 × 10
−19
C
F =
k
C
r
q
2
1
q
2
=
F = 5.12 × 10
5
N
(8.99 × 10
9
N
•
m
2
/C
2
)[(6.02 × 10
23
)(1.60 × 10
−19
C)]
2
[(2)(6.38 × 10
6
m)]
2
14. E = 3.0 × 10
6
N/C
r = 2.0 m
q =
E
k
r
C
2
==1.3 × 10
−3
C
(3.0 × 10
6
N/C)(2.0 m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)
15. E = 640 N/C
m
p
= 1.673 × 10
−27
kg
q = 1.60 × 10
−19
C
a =
m
F
p
=
m
qE
p
==6.1 × 10
10
m/s
2
(1.60 × 10
−19
C)(640 N/C)
1.673 × 10
−27
kg
16. v
f
= 1.20 × 10
6
m/s
a = 6.1 × 10
10
m/s
2
∆t =
v
a
f
==2.0 × 10
−5
s
1.20 × 10
6
m/s
6.1 × 10
10
m/s
2
17. a = 6.1 × 10
10
m/s
2
∆t = 2.0 × 10
−5
s
∆x =
1
2
a∆t
2
= (0.5)(6.1 × 10
10
m/s
2
)(2.0 × 10
−5
s)
2
∆x = 12 m
18. m
p
= 1.673 × 10
−27
kg
v
f
= 1.20 × 10
6
m/s
KE
f
=
1
2
m
p
v
f
2
= (0.5)(1.673 × 10
−27
kg)(1.20 × 10
6
m/s)
2
KE
f
= 1.20 × 10
−15
J
Section One—Student Edition Solutions I Ch. 17–1
Electrical Energy
and Current
Student Edition Solutions
I
1. ∆PE
electric
=−4.8 × 10
−16
J
d = 10.0 m
E = 75 N/C
∆PE
electric
= −qEd
q = −
∆PE
E
e
d
lectric
=−
(7
(−
5
4
N
.8
/C
×
)
1
(1
0
0
−1
.0
6
m
J)
)
q = 6.4 × 10
−19
C
Electrical Energy and Current, Practice A
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
5. E = 250 N/C, in the positive
x direction
q
1
= 12 mC
q
1
moves from the origin to
(20.0 cm, 50.0 cm).
The displacement in the direction of the field (d) is 20.0 cm.
∆PE =−qEd =−(12 × 10
−6
C)(250 N/C)(20.0 × 10
−2
m)
∆PE =−6.0 × 10
−4
J
2. E = 75 N/C
d = 10.0 m
∆V = −Ed = −(75 N/C)(10.0 m)
∆V = −750 V
3. q = −1.6 × 10
−19
C
d = 4.5 m
E = 325 N/C
∆PE
electric
= −qEd
∆PE
electric
= −(−1.6 × 10
−19
C)(325 N/C)(4.5 m)
∆PE
electric
= 2.3 × 10
−16
J
6. q = 35 C
d = 2.0 km
E = 1.0 × 10
6
N/C
∆PE =−qEd =−(35 C)(1.0 × 10
6
N/C)(2.0 × 10
3
m) =−7.0 × 10
10
J
Electrical Energy and Current, Section 1 Review
7. ∆d = 0.060 cm
E = 3.0 × 10
6
V/m
∆V =−E∆d =−(3.0 × 10
6
V/m)(0.060 × 10
−2
m) =−1.8 × 10
3
V
∆V = 1.8 × 10
3
V
8. E = 8.0 × 10
4
V/m
∆d = 0.50 m
q = 1.60 × 10
−19
C
a. ∆V =−E∆d =−(8.0 × 10
4
V/m)(0.50 m) =
b. ∆PE =−qEd =−(1.60 × 10
−19
C)(8.0 × 10
4
V/m)(0.50 m)
∆PE =−6.4 × 10
−15
J
−4.0 × 10
4
V
Holt Physics Solution ManualI Ch. 17–2
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. Q = 6.0 mC
∆V
1
= 1.25 V
∆V
2
= 1.50 V
a. C =
∆
Q
V
1
=
6.0
1
×
.2
1
5
0
V
−6
C
=
b. PE =
1
2
C(∆V
2
)
2
= (0.5)(4.8 × 10
−6
F)(1.50 V)
2
= 5.4 × 10
−6
J
4.8 × 10
−6
F
4. C = 1.00 F
d = 1.00 mm
A =
C
e
0
d
==1.13 × 10
8
m
2
(1.00 F)(1.00 × 10
−3
m)
8.85 × 10
−12
C
2
/N
•
m
2
3. C = 2.00 pF
Q = 18.0 pC
∆V
2
= 2.5 V
a. ∆V
1
=
Q
C
=
1
2
8
.0
.0
0
×
×
1
1
0
0
−
−
1
1
2
2
C
F
=
b. Q = C∆V
2
= (2.00 × 10
−12
F)(2.5 V) = 5.0 × 10
−12
C
9.00 V
1. d = 800.0 m
A = 1.00 × 10
6
m
2
E = 2.0 × 10
6
N/C
a. C =
e
0
d
A
==
b. ∆V =−E∆d
Q = C∆V = C(−E∆d) = (1.11 × 10
−8
F)(−2.0 × 10
6
N/C)(800.0 m) =−18 C
Q =±18 C
1.11 × 10
−8
F
(8.85 × 10
−12
C
2
/N
•
m
2
)(1.00 × 10
6
m
2
)
800.0 m
Electrical Energy and Current, Section 2 Review
2. A = 2.0 cm
2
d = 2.0 mm
∆V = 6.0 V
a. C =
e
0
d
A
==
b. Q = C∆V = (8.8 × 10
−13
F)(6.0 V) = 5.3 × 10
−12
C
8.8 × 10
−13
F
(8.85 × 10
−12
C
2
/N
•
m
2
)(2.0 × 10
−4
m
2
)
2.0 × 10
−3
m
3. C = 1.35 pF
∆V = 12.0 V
PE =
1
2
C(∆V)
2
= (0.5)(1.35 × 10
−12
F)(12.0 V)
2
PE = 9.72 × 10
−11
J
9. E = 1.0 × 10
6
V/m
∆d = 1.60 km
∆V =−E∆d =−(1.0 × 10
6
V/m)(1.60 × 10
3
m) =−1.6 × 10
9
V
∆V = 1.6 × 10
9
V
Givens Solutions
1. C = 4.00 mF
∆V
1
= 12.0 V
∆V
2
= 1.50 V
a. Q = C∆V
1
= (4.00 × 10
−6
F)(12.0 V) =
b. PE =
1
2
C(∆V
2
)
2
= (0.5)(4.00 × 10
−6
F)(1.50 V)
2
= 4.50 × 10
−6
J
4.80 × 10
−5
C
Electrical Energy and Current, Practice B
Section One—Student Edition Solutions I Ch. 17–3
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. I = 5.00 × 10
−3
A
∆Q = 2.00 C
I =
∆
∆
Q
t
∆t =
∆
I
Q
==4.00 × 10
2
s
2.00 C
5.00 × 10
−3
A
Electrical Energy and Current, Practice C
Givens Solutions
2. I = 60.0 × 10
−6
A
N = 3.75 × 10
14
electrons
q
e
= 1.60 × 10
−19
C
∆t =
∆t =
∆t = 1.00 s
(3.75 × 10
14
electrons)(1.60 × 10
−19
C/electron)
6.00 × 10
−5
A
N(1.60 × 10
−19
C/electron)
I
3. I = 8.00 × 10
−2
A
N = 3.00 × 10
20
electrons
q
e
= 1.60 × 10
−19
C
∆t =
∆t =
∆t = 6.00 × 10
2
s
(3.00 × 10
20
electrons)(1.60 × 10
−19
C/electron)
8.00 × 10
−2
A
N(1.60 × 10
−19
C/electron)
I
4. I = 40.0 A
∆t = 0.50 s
∆Q = I∆t = (40.0 A)(0.50 s) = 2.0 × 10
1
C
5. ∆Q
1
= 9.0 mC
∆t
1
= 3.5 s
∆t
2
= 10.0 s
∆Q
2
= 2∆Q
1
q
e
= 1.60 × 10
−19
C
a. I =
∆
∆
Q
t
1
1
=
9.0 ×
3.
1
5
0
s
−3
C
=
b. N ===
c. I =
∆
∆
Q
t
1
2
=
2
∆
∆
t
Q
1
1
=
2(9.0
3
×
.5
10
s
−3
C)
= 5.1 × 10
−3
A
1.6 × 10
17
electrons
(2.6 × 10
−3
A)(10.0 s)
1.60 × 10
−19
C/electron
I∆t
2
1.60 × 10
−19
C/electron
2.6 × 10
−3
A
2. ∆V = 120 V
R = 65 Ω
I =
∆
R
V
=
1
6
2
5
0
Ω
V
= 1.8 A
3. ∆V = 120 V
R
1
= 48 Ω
R
2
= 20.0 Ω
a. I
1
=
∆
R
V
1
=
1
4
2
8
0
Ω
V
=
b. I
2
=
∆
R
V
2
=
2
1
0
2
.
0
0
V
Ω
= 6.0 A
2.5 A
Givens Solutions
1. ∆V = 1.5 V
R = 3.5 Ω
I =
∆
R
V
=
3
1
.
.
5
5
Ω
V
= 0.43 A
Electrical Energy and Current, Practice D
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualI Ch. 17–4
Givens Solutions
2. ∆t
1
= 5.00 s
∆Q = 3.0 C
∆t
2
= 1.0 min
a. I =
∆
∆
Q
t
1
=
5
3
.
.
0
0
0
C
s
=
b. N ==
N = 2.2 × 10
20
electrons
(0.60 A)(1.0 min)(60 s/min)
1.60 × 10
−19
C/electrons
I∆t
2
1.60 × 10
−19
C/electron
0.60 A
Electrical Energy and Current, Section 3 Review
4. I = 6.25 A
R = 17.6 Ω
∆V = IR = (6.25 A)(17.6 Ω) = 1.10 × 10
2
V
5. I = 2.5 A
∆V = 115 V
R =
∆
I
V
=
1
2
1
.5
5
A
V
= 46 Ω
6. I
1
= 0.50 A
∆V
1
= 110 V
∆V
2
= 90.0 V
∆V
3
= 130 V
a. R =
∆
I
V
1
1
=
0
1
.
1
5
0
0
V
A
= 220 Ω
I
2
=
∆
R
V
2
=
9
2
0
2
.
0
0
Ω
V
=
b. I
3
=
∆
R
V
3
=
2
1
2
3
0
0
Ω
V
= 0.59 A
0.41 A
3. R = 10.2 Ω
∆V = 120 V
I =
∆
R
V
=
1
1
0
2
.
0
2
V
Ω
= 12 A
4. I = 2.5 A
∆V = 9.0 V
R =
∆
I
V
=
9
2
.
.
0
5
V
A
= 3.6 Ω
7. R
1
= 75 Ω
∆V = 115 V
R
2
= 47 Ω
I
1
=
∆
R
V
1
=
1
7
1
5
5
Ω
V
=
I
2
=
∆
R
V
2
=
1
4
1
7
5
Ω
V
= 2.4 A
1.5 A
1. P = 1050 W
∆V = 120 V
P =
(∆V
R
)
2
R =
(∆
P
V)
2
=
(
1
1
0
2
5
0
0
V
W
)
2
= 14 Ω
Electrical Energy and Current, Practice E
2. P = 0.25 W
∆V = 120 V
R =
(∆
P
V)
2
=
(
0
1
.
2
2
0
5
V
W
)
2
= 5.8 × 10
4
Ω
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 17–5
3. P = 0.10 W
R = 22 Ω
P =
(∆
R
V)
2
∆V =
PR
=
(0.10 W
)(22 Ω
)
= 1.5 V
4. ∆V = 50.0 V
R = 8.00 Ω
I =
∆
R
V
=
8
5
.
0
0
.
0
0
Ω
V
=
P =
(∆V
R
)
2
=
(5
8
0
.0
.0
0
V
Ω
)
2
= 312 W
6.25 A
5. ∆V = 50.0 V
R = 0.100 Ω
I =
∆
R
V
=
0
5
.1
0
0
.0
0
V
Ω
I = 5.00 × 10
2
A
3. ∆V = 70 mV
I = 200 mA
P = I∆V = (200 × 10
−6
A)(70 × 10
−3
V) = 1 × 10
−5
W
Electrical Energy and Current, Section 4 Review
4. ∆t = 21 h
P = 90.0 W
cost of energy =
$0.070/kW
•
h
cost = (P∆t)(cost/kW
•
h)
cost = (90.0 × 10
−3
kW)(21 h)($0.070/kW
•
h) = $0.13
Electrical Energy and Current, Chapter Review
8. E = 1.7 × 10
6
N/C
∆d = 1.5 cm
∆V =−E∆d =−(1.7 × 10
6
N/C)(1.5 × 10
−2
m) =−2.6 × 10
4
V
∆V = 2.6 × 10
4
V
Holt Physics Solution ManualI Ch. 17–6
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
18. ∆V = 12.0 V
C = 6.0 pF
Q = C∆V = (6.0 × 10
−12
F)(12.0 V) = 7.2 × 10
−11
C
Q =±7.2 × 10
−11
C
9. q
1
=+8.0 mC
q
2
=−8.0 mC
q
3
=−12 mC
r
1,P
= 0.35 m
r
2,P
= 0.20 m
V
1
=
k
r
C
1,
q
P
1
==2.1 × 10
5
V
V
2
=
k
r
C
2,
q
P
2
==−3.6 × 10
5
V
(r
1,P
)
2
+ (r
2,P
)
2
= (r
3,P
)
2
r
3,P
=
(r
1,
P
)
2
+
(
r
2
,P
)
2
=
(0
.3
5
m
)
2
+
(
0.
20
m
)
2
V
3
=
k
r
C
3,
q
P
3
=
V
3
=
V
3
==−2.7 × 10
5
V
V
tot
= V
1
+ V
2
+ V
3
= (2.1 × 10
5
V) + (−3.6 × 10
5
V) + (−2.7 × 10
5
V)
V
tot
=−4.2 × 10
5
V
(8.99 × 10
9
N
•
m
2
/C
2
)(−12 × 10
−6
C)
0.
16
m
2
(8.99 × 10
9
N
•
m
2
/C
2
)(−12 × 10
−6
C)
0.
12
m
2
+
0
.0
40
m
2
(8.99 × 10
9
N
•
m
2
/C
2
)(−12 × 10
−6
C)
(0
.3
5
m
)
2
+
(
0.
20
m
)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(−8.0 × 10
−6
C)
0.20 m
(8.99 × 10
9
N
•
m
2
/C
2
)(8.0 × 10
−6
C)
0.35 m
19. C
1
= 25 mF
C
2
= 5.0 mF
∆V = 120 V
PE
1
=
1
2
C
1
(∆V )
2
= (0.5)(25 × 10
−6
F)(120 V)
2
= 0.18 J
PE
2
=
1
2
C
2
(∆V )
2
= (0.5)(5.0 × 10
−6
F)(120 V)
2
= 3.6 × 10
−2
J
PE
tot
= PE
1
+ PE
2
= 0.18 J + (3.6 × 10
−2
J) = 0.22 J
32. ∆Q = 10.0 C
I = 5.0 A
∆t =
∆
I
Q
=
1
5
0
.
.
0
0
A
C
= 2.0 s
33. I = 9.1 A
∆Q = 1.9 × 10
3
C
q
e
= 1.60 × 10
−19
C
a. ∆t =
∆
I
Q
=
1.9
9
×
.1
1
A
0
3
C
= 2.1 × 10
2
s =
b. N ===1.2 × 10
22
electrons
1.9 × 10
3
C
1.60 × 10
−19
C/electron
∆Q
1.60 × 10
−19
C/electron
3.5 min
40. R = 15 Ω
∆V = 3.0 V
I =
∆
R
V
=
3
1
.
5
0
Ω
V
= 0.20 A
41. R = 35 Ω
∆V = 120 V
I =
∆
R
V
=
1
3
2
5
0
Ω
V
= 3.4 A
Section One—Student Edition Solutions I Ch. 17–7
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
57. ∆V = 600.0 V
E = 200.0 N/C
58. d = 3.0 mm
E = 3.0 × 10
6
N/C
Q =−1.0 mC
C =
e
0
d
A
=
∆
Q
V
=
−E
Q
∆d
−e
0
AE∆d = Qd
A =
e
−
0
Q
E
A = pr
2
r =
A
p
=
e
−
0
E
Q
p
=
r = 0.11 m
−(−1.0 × 10
−6
C)
(8.85 × 10
−12
C
2
/N
•
m
2
)(3.0 × 10
6
N/C)(p)
∆
E
V
==r
r =
∆
E
V
=
20
6
0
0
.
0
0
.0
N
V
/C
=
q =
∆
k
V
C
r
==2.00 × 10
−7
C
(600.0 V)(3.000 m)
8.99 × 10
9
N
•
m
2
/C
2
3.000 m
k
C
r
q
k
r
C
2
q
59. ∆V = 12 V
∆d = 0.30 cm
E =
∆
∆
V
d
=
0.30
1
×
2
1
V
0
−2
m
= 4.0 × 10
3
V/m
42. ∆V = 9.0 V
R
1
= 5.0 Ω
R
2
= 2.0 Ω
R
3
= 20.0 Ω
a. I
1
=
∆
R
V
1
=
5
9
.
.
0
0
Ω
V
=
b. I
2
=
∆
R
V
2
=
2
9
.
.
0
0
Ω
V
=
c. I
3
=
∆
R
V
3
=
2
9
0
.
.
0
0
V
Ω
= 0.45 A
4.5 A
1.8 A
53. P/clock = 2.5 W
N = 2.5 × 10
8
clocks
∆t = 1.0 year
E = P∆t = (P/clock)N∆t
E = (2.5 W)(2.5 × 10
8
)(1.0 year)(365.25 d/year)(24 h/d)(3600 s/h)
E = 2.0 × 10
16
J
55. ∆V = 110 V
P = 130 W
R =
(∆
P
V)
2
=
(1
1
1
3
0
0
V
W
)
2
= 93 Ω
56. ∆V = 120 V
P = 75 W
I =
∆
P
V
=
1
7
2
5
0
W
V
=
R =
I
P
2
=
(0
7
.6
5
2
W
A)
2
= 190 Ω
0.62 A
Holt Physics Solution ManualI Ch. 17–8
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
61. ∆V = 25 700 V
v
i
= 0 m/s
q = 1.60 × 10
−19
C
m
p
= 1.673 × 10
−27
kg
a. KE
f
=∆PE = q∆V = (1.60 × 10
−19
C)(25 700 V) =
b. v
f
=
2
m
K
E
p
f
=
(2
1
)
.6
(
4
7
.
3
1
1
×
×
1
0
1
−
0
2
−
7
1
k
5
g
J
)
= 2.22 × 10
6
m/s
4.11 × 10
−15
J
62. ∆V = 120 V
v
i
= 0 m/s
m
p
= 1.673 × 10
−27
kg
q = 1.60 × 10
−19
C
KE
f
=∆PE = q∆V
1
2
m
p
v
f
2
= q∆V
v
f
=
2q
m
∆
p
V
=
= 1.5 × 10
5
m/s
(2)(1.60 × 10
−19
C)(120 V)
1.673 × 10
−27
kg
63. ∆d = 5.33 mm
∆V = 600.0 V
q =−1.60 × 10
−19
C
∆d = (5.33 mm − 2.90 mm)
= 2.43 mm
a. E =
∆
∆
V
d
=
5.33
60
×
0.
1
0
0
V
−3
m
=
b. F = qE = (−1.60 × 10
−19
C)(1.13 × 10
5
V/m) =−1.81 × 10
−14
N
F =
c. ∆PE =−qEd =−(−1.60 × 10
−19
C)(1.13 × 10
5
V/m)(2.43 × 10
−3
m)
∆PE = 4.39 × 10
−17
J
1.81 × 10
−14
N
1.13 × 10
5
V/m
60. A = 5.00 cm
2
d = 1.00 mm
Q = 400.0 pC
a. ∆V =
Q
C
C =
e
0
d
A
∆V ==
e
Q
0
d
A
==
b. E =
∆
∆
V
d
=
1.00
9
×
0.4
10
V
−3
m
= 9.04 × 10
4
V/m
90.4 V
(400.0 × 10
−12
C)(1.00 × 10
−3
m)
(8.85 × 10
−12
C
2
/N
•
m
2
)(5.00 × 10
−4
m
2
)
Q
ε
0
d
A
Section One—Student Edition Solutions I Ch. 17–9
I
64. q
1
= 5.0 × 10
−9
C
q
2
=−5.0 × 10
−9
C
q
3
=−5.0 × 10
−9
C
r
1,2
= r
1,3
= 4.0 cm
r
2,3
= 2.0 cm
r
1
2
+ (0.010 m)
2
= (0.040 m)
2
r
1
=
(0
.0
40
m
)
2
−
(
0.
01
0
m
)
2
V
1
=
k
C
r
1
q
1
=
V
1
=
V
1
==1200 V
r
2
= r
3
=
0.02
2
0m
= 0.010 m
V
2
=
k
C
r
2
q
2
==−4500 V
V
3
=
k
C
r
3
q
3
==−4500 V
V
tot
= V
1
+ V
2
+ V
3
= (1200 V) + (−4500 V) + (−4500 V) =−7800 V
(8.99 × 10
9
N
•
m
2
/C
2
)(−5.0 × 10
−9
C)
0.010 m
(8.99 × 10
9
N
•
m
2
/C
2
)(−5.0 × 10
−9
C)
0.010 m
(8.99 × 10
9
N
•
m
2
/C
2
)(5.0 × 10
−9
C)
1.
5
×
1
0
−
3
m
2
(8.99 × 10
9
N
•
m
2
/C
2
)(5.0 × 10
−9
C)
(1
.6
×
1
0
−
3
m
2
)
−
(
1.
0
×
1
0
−
4
m
2
)
(8.99 × 10
9
N
•
m
2
/C
2
)(5.0 × 10
−9
C)
(0
.0
40
m
)
2
−
(
0.
01
0
m
)
2
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
65. q
1
=−3.00 × 10
−9
C at the
origin
q
2
= 8.00 × 10
−9
C at
x = 2.00 m, y = 0.00 m
For the location between the two charges,
V
tot
= V
1
+ V
2
= 0V
V
1
=−V
2
V
1
=
k
C
P
q
1
V
2
=
(2.00
k
C
m
q
2
− P)
k
C
P
q
1
=
(2.0
−
0
k
m
C
q
−
2
P)
−Pq
2
= (2.00 m − P)(q
1
)
−Pq
2
= (2.00 m)(q
1
) − Pq
1
P(q
1
− q
2
) = (2.00 m)(q
1
)
P =
(2.0
q
0
1
−
m
q
)(
2
q
1
)
==0.545 m
P is 0.545 m to the right of the origin, at x = .
For the location to the left of the y-axis,
V
1
=
k
C
P
q
1
V
2
=
(2.00
k
C
m
q
2
+ P)
k
C
P
q
1
=
(2.0
−
0
k
m
C
q
+
2
P)
−Pq
2
= (2.00 m + P)(q
1
)
−Pq
2
= (2.00 m)(q
1
) + Pq
1
P(q
1
+ q
2
) =−(2.00 m)(q
1
)
P =
−(2.
q
0
1
0
+
m
q
)
2
(q
1
)
==1.20 m
P is 1.20 m to the left of the origin, at x = .−1.20 m
−(2.00 m)(−3.00 × 10
−9
C)
(−3.00 × 10
−9
C) + (8.00 × 10
−9
C)
0.545 m
(2.00 m)(−3.00 × 10
−9
C)
(−3.00 × 10
−9
C) − (8.00 × 10
−9
C)
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualI Ch. 17–10
67. ∆V = 4.5 × 10
6
V
v
i
= 0 m/s
q = 1.60 × 10
−19
C
m
p
= 1.673 × 10
−27
kg
a. KE
f
=∆PE =∆Vq = (4.5 × 10
6
V)(1.60 × 10
−19
C) =
b. v
f
=
2
m
K
E
p
f
=
(
1
2
.
)
6
(
7
7
3
.2
×
×
1
1
0
0
−2
−
7
13
k
J
g
)
= 2.9 × 10
7
m/s
7.2 × 10
−13
J
66. ∆V = 60.0 V
∆PE = 1.92 × 10
−17
J
q =
∆
∆
P
V
E
=
1.92
60
×
.0
10
V
−17
J
= 3.20 × 10
−19
C
68. C = 3750 pF
Q = 1.75 × 10
−8
C
d = 6.50 × 10
−4
m
a. ∆V =
Q
C
=
3
1
7
.7
5
5
0
×
×
1
1
0
0
−
−
8
12
C
F
=
b. E =
∆
d
V
=
6.50
4
×
.6
1
7
0
V
−4
m
= 7180 V/m
4.67 V
70. I = 2.0 × 10
5
A
∆t = 0.50 s
∆Q = I∆t = (2.0 × 10
5
A)(0.50 s) = 1.0 × 10
5
C
71. I = 80.0 mA
R
1
= 4.0 × 10
5
Ω
R
2
= 2.0 × 10
3
Ω
a. ∆V
1
= IR
1
= (80.0 × 10
−6
A)(4.0 × 10
5
Ω) =
b. ∆V
2
= IR
2
= (80.0 × 10
−6
A)(2.0 × 10
3
Ω) = 0.16 V
32 V
72. P = 325 W
∆V = 120 V
I =
∆
P
V
=
3
1
2
2
5
0
W
V
= 2.7 A
73. ∆V = 4.0 MV
I = 25 mA
P = I∆V = (25 × 10
−3
A)(4.0 × 10
6
V) = 1.0 × 10
5
W
69. ∆Q = 45 mC
∆t
1
= 15 s
∆t
2
= 1.0 min
a. I =
∆
∆
Q
t
1
=
45 ×
1
1
5
0
s
−3
C
=
b. N ==
N = 1.1 × 10
18
electrons
(3.0 × 10
−3
A)(1.0 min)(60 s/min)
1.60 × 10
−19
C/electron
I∆t
2
1.60 × 10
−19
C/electron
3.0 × 10
−3
A
74. m
atom
= 3.27 × 10
−25
kg
m
tot
= 1.25 kg
∆t = 2.78 h
Q
atom
= 1.60 × 10
−19
C
∆Q = (number of atoms)(Q
atom
) =
m
m
at
t
o
o
m
t
(Q
atom
)
I =
∆
∆
Q
t
=
I ==61.1 A
3.27
1
×
.2
1
5
0
k
−
g
25
kg
(1.60 × 10
−19
C)
(2.78 h)(3600 s/h)
m
m
at
t
o
o
m
t
(Q
atom
)
∆t
Section One—Student Edition Solutions I Ch. 17–11
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
75. P = 90.0 W
∆V = 120 V
∆t = 1.0 h
E = P∆t = (90.0 W)(1.0 h)(3600 s/h) = 3.2 × 10
5
J
76. I = 2.5 A
∆V = 120 V
E = 3.2 × 10
5
J
∆t =
P
E
=
I∆
E
V
=
(2.
3
5
.2
A
×
)(
1
1
0
2
5
0
J
V)
=
or (1.1 × 10
3
s)(1 min/60 s) = 18 min
1.1 × 10
3
s
77. P = 80.0 W
∆V = 12.0 V
Q = 90.0 A
•
h
∆t =
Q
I
=
Q
P
∆V
==13.5 h
(90.0 A
•
h)(12.0 V)
80.0 W
80. ∆V = 12 V
E = 2.0 × 10
7
J
P = 8.0 kW
v = 20.0 m/s
a. I =
∆
P
V
=
8.0 ×
12
1
V
0
3
W
=
b. ∆t =
P
E
∆x = v∆t = v
P
E
==5.0 × 10
4
m
(20.0 m/s)(2.0 × 10
7
J)
8.0 × 10
3
W
670 A
78. ∆t = 5.0 s a. ∆Q = I∆t = (2 A)(2 s) + (4 A)(1 s) + (6 A)(1 s) + (4 A)(1 s)
∆Q = 4 C + 4 C + 6 C + 4C =
b. I =
∆
∆
Q
t
=
1
5
8
.0
C
s
= 3.6 A
18 C
79. I = 50.0 A
R/d = 1.12 × 10
−5
Ω/m
d = 4.0 cm
∆V = IR = (50.0 A)(1.12 × 10
−5
Ω/m)(4.0 × 10
−2
m) = 2.2 × 10
−5
V
1. v
f,1
= 10
7
m/s
q = 1.60 × 10
−19
C
m
e
= 9.109 × 10
−31
kg
v
f,2
= 100 m/s
∆V
1
=
∆P
q
E
=
KE
q
f1
=
∆V
1
=
∆V
1
=
∆V
2
=
∆P
q
E
=
KE
q
f2
=
∆V
1
=
∆V
1
= 3 × 10
−8
V
(9.109 × 10
−31
kg)(100 m/s)
2
2(1.60 × 10
−19
C)
1
2
m
e
v
f2
2
q
300 V
(9.109 × 10
−31
kg)(10
7
m/s)
2
2(1.60 × 10
−19
C)
1
2
m
e
v
f1
2
q
Electrical Energy and Current, Alternative Assessment
Holt Physics Solution ManualI Ch. 17–12
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Electrical Energy and Current, Standardized Test Prep
Givens Solutions
3. q = 1.6 × 10
−19
C
d = 2.0 × 10
−6
m
E = 2.0 N/C
∆PE
electric
= −qEd = −(1.6 × 10
−19
C)(2.0 N/C)(2.0 × 10
−6
m)
∆PE
electric
= −6.4 × 10
−25
N•m = −6.4 × 10
−25
J
4. d = 2.0 × 10
−6
m
E = 2.0 N/C
∆V = −Ed = −(2.0 N/C)(2.0 × 10
−6
m)
∆V = −4.0 × 10
−6
V
7. ∆V = 10.0 V
Q = 40.0 mC = 40.0 × 10
−6
C
C =
∆
Q
V
=
C = 4.00 × 10
−6
F
(40.0 × 10
−6
C)
(10.0 V)
8. ∆V = 10.0 V
Q = 40.0 mC = 40.0 × 10
−6
C
PE
electric
=
1
2
Q∆V =
1
2
(40.0 × 10
−6
C)(10.0 V)
PE
electric
= 2.00 × 10
−4
J
9. I = 5.0 A
∆Q = 5.0 C
∆t =
∆
I
Q
=
5
5
.
.
0
0
C
A
= 1.0 s
11. P = 50.0 W
∆t = 2.00 s
E = P∆t = (50.0 W)(2.00 s)
E = 1.00 × 10
2
J
10. ∆V = 12 V
I = 0.40 A
R =
∆
I
V
=
0
1
.4
2
0
V
A
= 3.0 × 10
1
Ω
12. I = 7.0 A
∆V = 115 V
P = I∆V = (7.0 A)(115 V) = 8.0 × 10
2
W
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 17–13
16. r =
2.50 ×
2
10
−3
m
d = 1.40 × 10
−4
m
∆V
1
= 0.12 V
∆d
1
= 1.40 × 10
−4
m
Q
2
= (0.707)Q
a. C =
e
0
d
A
=
e
0
p
d
r
2
=
C =
b. Q = C∆V
1
= (3.10 × 10
−13
F)(0.12 V) =
c. PE
electric
=
1
2
Q∆V
1
= (0.5)(3.7 × 10
−14
C)(0.12 V) =
d. ∆V
1
= E∆d
1
E =
∆
∆
V
d
1
1
=
1.40
0
×
.1
1
2
0
V
−4
m
= 860 V/m
∆d
2
= 1.10 × 10
−4
m −
1.40 ×
2
10
−4
m
= 4.00 × 10
−5
m
∆V
2
= E∆d
2
= (860 V/m)(4.00 × 10
−5
m) =
e. ∆V
3
=
Q
C
2
Because the capacitance has not changed, ∆V
3
= (0.707)(∆V
1
).
∆V
3
= (0.707)(∆V
1
) = (0.707)(0.12 V) = 8.5 × 10
−2
V
3.4 × 10
−2
V
2.2 × 10
−15
J
3.7 × 10
−14
C
3.10 × 10
−13
F
(8.85 × 10
−12
C
2
/N
•
m
2
)(p)(2.50 × 10
−3
m/2)
2
1.40 × 10
−4
m
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 18–1
1. R
1
= 6.75 Ω
R
2
= 15.3 Ω
R
3
= 21.6 Ω
∆V = 12.0 V
a. R
eq
= R
1
+ R
2
+ R
3
R
eq
= 6.75 Ω+15.3 Ω+21.6 Ω=
b. I =
R
∆
e
V
q
=
4
1
3
2
.
.
6
0
Ω
V
= 0.275 A
43.6 Ω
Circuits and Circuit Elements, Practice A
Givens Solutions
2. R
1
= 4.0 Ω
R
2
= 8.0 Ω
R
3
= 12.0 Ω
∆V = 24.0 V
a. R
eq
= R
1
+ R
2
+ R
3
= 4.0 Ω+8.0 Ω+12.0 Ω=
b. I =
R
∆
e
V
q
=
2
2
4
4
.
.
0
0
Ω
V
=
c. I = 1.00 A
1.00 A
24.0 Ω
3. I = 0.50 A
R
1
= 2.0 Ω
R
2
= 4.0 Ω
R
3
= 5.0 Ω
R
4
= 7.0 Ω
∆V
1
= IR
1
= (0.50 A)(2.0 Ω) =
∆V
2
= IR
2
= (0.50 A)(4.0 Ω) =
∆V
3
= IR
3
= (0.50 A)(5.0 Ω) =
∆V
4
= IR
4
= (0.50 A)(7.0 Ω) = 3.5 V
2.5 V
2.0 V
1.0 V
4. ∆V = 9.00 V
R
1
= 7.25 Ω
R
2
= 4.03 Ω
a. R
eq
= R
1
+ R
2
= 7.25 Ω+4.03 Ω=
I =
R
∆
e
V
q
=
1
9
1
.
.
0
2
0
8
V
Ω
=
b. ∆V
1
= IR
1
= (0.798 A)(7.25 Ω) =
∆V
2
= IR
2
= (0.798 A)(4.03 Ω) = 3.22 V
5.79 V
0.798 A
11.28 Ω
5. R
1
= 7.0 Ω
∆V = 4.5 V
I = 0.60 A
R
eq
= R
1
+ R
2
=
∆
I
V
R
2
=
∆
I
V
− R
1
=
0
4
.
.
6
5
0
V
A
− 7.0 Ω
R
2
= 7.5 Ω−7.0 Ω= 0.5 Ω
6. ∆V = 115 V
I = 1.70 A
R = 1.50 Ω
a. R
eq
=
∆
I
V
=
1
1
.
1
7
5
0
V
A
=
b. NR = R
eq
N =
R
R
eq
=
6
1
7
.5
.6
0
Ω
Ω
= 45 bulbs
67.6 Ω
Circuits and
Circuit Elements
Student Edition Solutions
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualI Ch. 18–2
1. ∆V = 9.0 V
R
1
= 2.0 Ω
R
2
= 4.0 Ω
R
3
= 5.0 Ω
R
4
= 7.0 Ω
I
1
=
∆
R
V
1
=
2
9
.
.
0
0
Ω
V
=
I
2
=
∆
R
V
2
=
4
9
.
.
0
0
Ω
V
=
I
3
=
∆
R
V
3
=
5
9
.
.
0
0
Ω
V
=
I
4
=
∆
R
V
4
=
7
9
.
.
0
0
Ω
V
= 1.3 A
1.8 A
2.2 A
4.5 A
Circuits and Circuit Elements, Practice B
Givens Solutions
2. R
eq
= 2.00 Ω
Parallel: R
eq
=
R
1
+
R
1
+
R
1
+
R
1
+
R
1
−1
=
R
5
−1
R = 5R
eq
= 5(2.00 Ω) = 10.0 Ω
Series: R
eq
= 5R = 5(10.0 Ω) = 50.0 Ω
3. R
1
= 4.0 Ω
R
2
= 8.0 Ω
R
3
= 12.0 Ω
∆V = 24.0 V
a. R
eq
=
R
1
1
+
R
1
2
+
R
1
3
−1
=
4.0
1
Ω
+
8.0
1
Ω
+
12.
1
0 Ω
−1
R
eq
=
0.25
Ω
1
+ 0.12
Ω
1
+ 0.0833
Ω
1
−1
=
0.45
Ω
1
−1
R
eq
=
b. I
1
=
∆
R
V
1
=
2
4
4
.0
.0
Ω
V
=
I
2
=
∆
R
V
2
=
2
8
4
.0
.0
Ω
V
=
I
3
=
∆
R
V
3
=
1
2
2
4
.
.
0
0
Ω
V
= 2.00 A
3.0 A
6.0 A
2.2 Ω
4. R
1
= 18.0 Ω
R
2
= 9.00 Ω
R
3
= 6.00 Ω
I
2
= 4.00 A
a. R
eq
=
R
1
1
+
R
1
2
+
R
1
3
−1
=
18.
1
0 Ω
+
9.0
1
0 Ω
+
6.0
1
0 Ω
−1
R
eq
=
0.0555
Ω
1
+ 0.111
Ω
1
+ 0.167
Ω
1
−1
=
0.334
Ω
1
−1
R
eq
=
b. ∆V = I
2
R
2
= (4.00 A)(9.00 Ω) =
c. I
1
=
∆
R
V
1
=
1
3
8
6
.
.
0
0
Ω
V
=
I
3
=
∆
R
V
3
=
6
3
.
6
0
.
0
0
Ω
V
= 6.00 A
2.00 A
36.0 V
2.99 Ω
Section One—Student Edition Solutions I Ch. 18–3
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
4. R
1
= 2.0 Ω
R
2
= 4.0 Ω
∆V = 12 V
R
1
= 2.0 Ω
R
2
= 4.0 Ω
∆V = 12 V
a. R
eq
= R
1
+ R
2
= 2.0 Ω+4.0 Ω=6.0 Ω
I
1
= I
2
= I =
R
∆
e
V
q
=
6
1
.
2
0
V
Ω
=
∆V
1
= I
1
R
1
= (2.0 A)(2.0 Ω) =
∆V
2
= I
2
R
2
= (2.0 A)(4.0 Ω) =
b. R
eq
=
R
1
1
+
R
1
2
−1
=
2.0
1
Ω
+
4.0
1
Ω
−1
R
eq
=
0.50
Ω
1
+ 0.25
Ω
1
−1
=
0.75
Ω
1
−1
= 1.3 Ω
∆V
1
=∆V
2
=∆V =
I
1
=
∆
R
V
1
1
=
2
1
.
2
0
V
Ω
=
I
2
=
∆
R
V
2
2
=
4
1
.
2
0
V
Ω
= 3.0 A
6.0 A
12 V
8.0 V
4.0 V
2.0 A
1. R
a
= 25.0 Ω
R
b
= 3.0 Ω
R
c
= 40.0 Ω
R
a
= 12.0 Ω
R
b
= 35.0 Ω
R
c
= 25.0 Ω
R
a
= 15.0 Ω
R
b
= 28.0 Ω
R
c
= 12.0 Ω
a. R
bc
=
R
1
b
+
R
1
c
−1
=
3.0
1
Ω
+
40.
1
0 Ω
−1
R
bc
=
0.33
Ω
1
+ 0.0250
Ω
1
−1
=
0.36
Ω
1
−1
R
bc
= 2.8 Ω
R
eq
= R
a
+ R
bc
= 25.0 Ω+2.8 Ω=
b. R
bc
=
R
1
b
+
R
1
c
−1
=
35.
1
0 Ω
+
25.
1
0 Ω
−1
R
bc
=
0.0286
Ω
1
+ 0.0400
Ω
1
−1
=
0.0686
Ω
1
−1
R
bc
= 14.6 Ω
R
eq
= R
a
+ R
bc
= 12.0 Ω+14.6 Ω=
c. R
bc
=
R
1
b
+
R
1
c
−1
=
28.
1
0 Ω
+
12.
1
0 Ω
−1
R
bc
=
0.0357
Ω
1
+ 0.0833
Ω
1
−1
=
0.0119
Ω
1
−1
R
bc
= 8.40 Ω
R
eq
= R
a
+ R
bc
= 15.0 Ω+8.40 Ω= 23.4 Ω
26.6 Ω
27.8 Ω
Circuits and Circuit Elements, Practice C
Circuits and Circuit Elements, Section 2 Review
Givens Solutions
Holt Physics Solution ManualI Ch. 18–4
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
2. R
a
= 25.0 Ω
R
b
= 3.0 Ω
R
c
= 40.0 Ω
R
d
= 15.0 Ω
R
e
= 18.0 Ω
R
a
= 12.0 Ω
R
b
= 35.0 Ω
R
c
= 25.0 Ω
R
d
= 50.0 Ω
R
e
= 45.0 Ω
a. R
ab
=
R
1
a
+
R
1
b
−1
=
25.
1
0 Ω
+
3.0
1
Ω
−1
R
ab
=
0.0400
Ω
1
+ 0.33
Ω
1
−1
=
0.37
Ω
1
−1
R
ab
= 2.7 Ω
R
de
=
R
1
d
+
R
1
e
−1
=
15.
1
0 Ω
+
18.
1
0 Ω
−1
R
de
=
0.0667
Ω
1
+ 0.0556
Ω
1
−1
=
0.1223
Ω
1
−1
R
de
= 8.177 Ω
R
eq
= R
ab
+ R
c
+ R
de
= 2.7 Ω+40.0 Ω+8.177 Ω=
b. R
ab
=
R
1
a
+
R
1
b
−1
=
12.
1
0 Ω
+
35.
1
0 Ω
−1
R
ab
=
0.0833
Ω
1
+ 0.0286
Ω
1
−1
=
0.1119
Ω
1
−1
R
ab
= 8.937 Ω
R
de
=
R
1
d
+
R
1
e
−1
=
50.
1
0 Ω
+
45.
1
0 Ω
−1
R
de
=
0.0200
Ω
1
+ 0.0222
Ω
1
−1
=
0.0422
Ω
1
−1
R
de
= 23.7 Ω
R
eq
= R
ab
+ R
c
+ R
de
= 8.937 Ω+25.0 Ω+23.7 Ω= 57.6 Ω
50.9 Ω
Section One—Student Edition Solutions I Ch. 18–5
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
R
a
= 5.0 Ω
R
b
= 7.0 Ω
R
c
= 4.0 Ω
R
d
= 4.0 Ω
R
e
= 4.0 Ω
R
f
= 2.0 Ω
∆V = 14.0 V
R
ab
= R
a
+ R
b
= 5.0 Ω+7.0 Ω = 12.0 Ω
R
abc
=
R
1
ab
+
R
1
c
−1
=
12.
1
0 Ω
+
4.0
1
Ω
−1
R
abc
=
0.0833
Ω
1
+ 0.25
Ω
1
−1
=
0.33
Ω
1
−1
= 3.0 Ω
R
de
=
R
1
d
+
R
1
e
−1
=
4.0
1
Ω
+
4.0
1
Ω
−1
R
de
=
0.25
Ω
1
+ 0.25
Ω
1
−1
=
0.50
Ω
1
−1
= 2.0 Ω
R
eq
= R
abc
+ R
de
+ R
f
= 3.0 Ω+2.0 Ω+2.0 Ω=7.0 Ω
I =
R
∆
e
V
q
=
1
7
4
.0
.0
Ω
V
= 2.0 A
∆V
abc
= IR
abc
= (2.0 A)(3.0 Ω) = 6.0 V
I
ab
=
∆
R
V
a
a
b
bc
=
1
6
2
.
.
0
0
V
Ω
= 0.50 A
R
a
:I
a
= I
ab
=
∆V
a
= I
a
R
a
= (0.50 A)(5.0 Ω) =
R
b
:I
b
= I
ab
=
∆V
b
= I
b
R
b
= (0.50 A)(7.0 Ω) =
R
c
: ∆V
c
=∆V
abc
=
I
c
=
∆
R
V
c
c
=
4
6
.
.
0
0
Ω
V
=
∆V
de
= IR
de
= (2.0 A)(2.0 Ω) = 4.0 V
R
d
: ∆V
d
=∆V
de
=
I
d
=
∆
R
V
d
d
=
4
4
.
.
0
0
Ω
V
=
R
e
: ∆V
e
=∆V
de
=
I
e
=
∆
R
V
e
e
=
4
4
.
.
0
0
Ω
V
=
R
f
:I
f
= I =
∆V
f
= I
f
R
f
= (2.0 A)(2.0 Ω) = 4.0 V
2.0 A
1.0 A
4.0 V
1.0 A
4.0 V
1.5 A
6.0 V
3.5 V
0.50 A
2.5 V
0.50 A
Circuits and Circuit Elements, Practice D
Givens Solutions
Holt Physics Solution ManualI Ch. 18–6
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Circuits and Circuit Elements, Section 3 Review
Givens Solutions
1. R
1
= 5.0 Ω
R
2
= 5.0 Ω
R
3
= 5.0 Ω
R
4
= 5.0 Ω
R
5
= 1.5 Ω
R
23
= R
2
+ R
3
= 5.0 Ω+5.0 Ω=10.0 Ω
R
234
=
R
1
23
+
R
1
4
−1
=
10.
1
0 Ω
+
5.0
1
Ω
−1
R
234
=
0.100
Ω
1
+ 0.20
Ω
1
−1
=
0.30
Ω
1
−1
= 3.3 Ω
R
eq
= R
1
+ R
234
+ R
5
= 5.0 Ω+3.3 Ω+1.5 Ω= 9.8 Ω
2. R
eq
= 9.8 Ω
∆V = 18.0 V
I
5
= I =
R
∆
e
V
q
=
1
9
8
.8
.0
Ω
V
= 1.8 A
3. I
5
= 1.8 A
R
5
= 1.5 Ω
∆V
5
= I
5
R
5
= (1.8 A)(1.5 Ω) = 2.7 V
4. R = 15.0 Ω
∆V = 120.0 V
N = 35 bulbs
n = 3 strands
R
eq, strand
= NR = (35)(15.0 Ω) = 525 Ω
R
eq
=
R
eq,
1
strand
+
R
eq,
1
strand
+
R
eq,
1
strand
−1
=
525
1
Ω
+
525
1
Ω
+
525
1
Ω
−1
R
eq
=
0.0019
Ω
1
+ 0.0019
Ω
1
+ 0.0019
Ω
1
−1
=
0.0057
Ω
1
−1
= 175 Ω
5. ∆V = 120.0 V
R
eq, strand
= 525 Ω
R = 15.0 Ω
∆V
strand
=∆V = 120.0 V
I
strand
=
R
∆
e
V
q,
s
s
t
t
r
r
a
a
n
n
d
d
=
1
5
2
2
0
5
.0
Ω
V
=
∆V = I
strand
R = (0.229 A)(15.0 Ω) = 3.44 V
0.229 A
R
1
R
2
R
4
R
5
R
3
18.0 V
6. R
eq, strand
= 510. Ω
∆V = 120.0 V
R = 15.0 Ω
∆V
strand
=∆V = 120.0 V
I
strand
=
R
∆
e
V
q,
s
s
t
t
r
r
a
a
n
n
d
d
=
1
5
2
1
0
0
.
.
0
Ω
V
=
∆V = I
strand
R = (0.235 A)(15.0 Ω) = 3.52 V
0.235 A
7. ∆V = 120 V
R
T
= 16.9 Ω
R
M
= 8.0 Ω
R
P
= 10.0 Ω
R
C
= 0.01 Ω
d. R
TMP
=
R
1
T
+
R
1
M
+
R
1
P
−1
=
16.
1
9 Ω
+
8.0
1
Ω
+
10.
1
0 Ω
−1
TMP
=
0.0592
Ω
1
+ 0.12
Ω
1
+ 0.100
Ω
1
−1
=
0.28
Ω
1
−1
= 3.6 Ω
R
eq
= R
TMP
+ R
C
= 3.6 Ω+0.01 Ω= 3.6 Ω
Section One—Student Edition Solutions I Ch. 18–7
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
16. R = 0.15 Ω
R
eq
= 5R = 5(0.15 Ω) = 0.75 Ω
Circuits and Circuit Elements, Chapter Review
17. R
1
= 4.0 Ω
R
2
= 8.0 Ω
R
3
= 12 Ω
∆V = 24 V
a. R
eq
= R
1
+ R
2
+ R
3
= 4.0 Ω+8.0 Ω+12 Ω=
b. I =
R
∆V
eq
=
2
2
4
4
Ω
V
= 1.0 A
24 Ω
18. R
1
= 4.0 Ω
R
2
= 8.0 Ω
R
3
= 12 Ω
∆V = 24 V
a. R
eq
=
R
1
1
+
R
1
2
+
R
1
3
−1
=
4.0
1
Ω
+
8.0
1
Ω
+
12
1
Ω
−1
R
eq
=
0.25
Ω
1
+ 0.12
Ω
1
+ 0.083
Ω
1
−1
=
0.45
Ω
1
−1
=
b. I =
R
∆
e
V
q
=
2
2
.
4
2
V
Ω
= 11 A
2.2 Ω
19. R
1
= 18.0 Ω
R
2
= 9.00 Ω
R
3
= 6.00 Ω
∆V = 12 V
a. R
eq
=
R
1
1
+
R
1
2
+
R
1
3
−1
=
18.
1
0 Ω
+
9.0
1
0 Ω
+
6.0
1
0 Ω
−1
R
eq
=
0.0556
Ω
1
+ 0.111
Ω
1
+ 0.167
Ω
1
−1
=
0.334
Ω
1
−1
=
b. I =
R
∆
e
V
q
=
2
1
.9
2
9
V
Ω
= 4.0 A
2.99 Ω
23. R
1
= 12 Ω
R
2
= 18 Ω
R
3
= 9.0 Ω
R
4
= 6.0 Ω
∆V = 30.0 V
R
234
=
R
1
2
+
R
1
3
+
R
1
4
−1
=
18
1
Ω
+
9.0
1
Ω
+
6.0
1
Ω
−1
R
234
=
0.056
Ω
1
+ 0.11
Ω
1
+ 0.17
Ω
1
−1
=
0.34
Ω
1
−1
= 2.9 Ω
R
eq
= R
1
+ R
234
= 12 Ω+2.9 Ω= 15 Ω
24. R
1
= 7.0 Ω
R
2
= 7.0 Ω
R
3
= 7.0 Ω
R
4
= 7.0 Ω
R
5
= 1.5 Ω
∆V = 12.0 V
R
34
= R
3
+ R
4
= 7.0 Ω+7.0 Ω=14.0 Ω
R
234
=
R
1
2
+
R
1
34
−1
=
7.0
1
Ω
+
14.
1
0 Ω
−1
=
0.14
Ω
1
+ 0.0714
Ω
1
−1
= 4.8 Ω
R
eq
= R
1
+ R
234
+ R
5
= 7.0 Ω+4.8 Ω+1.5 Ω= 13.3 Ω
∆V = 120 V
R
eq
= 3.6 Ω
R
TMP
= 3.6 Ω
R
T
= 16.9 Ω
e. I =
R
∆
e
V
q
=
1
3
2
.6
0
Ω
V
= 33 A
∆V
T
=∆V
TMP
= IR
TMP
= (33 A)(3.6 Ω) = 120 V
I
T
=
∆
R
V
T
T
=
1
1
6
2
.
0
9
V
Ω
= 7.1 A
Holt Physics Solution ManualI Ch. 18–8
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
25. R
1
= 6.0 Ω
R
2
= 9.0 Ω
R
3
= 3.0 Ω
∆V = 12 V
Current:
∆V
12
= IR
12
= (1.8 A)(3.6 Ω) = 6.5 V
I
1
=
∆
R
V
1
12
=
6
6
.
.
0
5
Ω
V
=
I
2
=
∆
R
V
2
12
=
9
6
.
.
0
5
Ω
V
=
R
12
=
R
1
1
+
R
1
2
−1
=
6.0
1
Ω
+
9.0
1
Ω
−1
R
12
=
0.17
Ω
1
+ 0.11
Ω
1
−1
=
0.28
Ω
1
−1
= 3.6 Ω
R
eq
= R
12
+ R
3
= 3.6 Ω+3.0 Ω=6.6 Ω
I =
R
∆V
eq
=
6
1
.
2
6
V
Ω
= 1.8 A
I
3
=
Potential difference:
∆V
1
=∆V
2
=∆V
12
=
∆V
3
= I
3
R
3
= (1.8 A)(3.0 Ω) = 5.4 V
6.5 V
1.8 A
0.72 A
1.1 A
26. R
1
= 3.0 Ω
R
2
= 3.0 Ω
R
3
= 6.0 Ω
R
4
= 6.0 Ω
R
5
= 4.0 Ω
R
6
= 12.0 Ω
R
7
= 2.0 Ω
∆V = 18.0 V
a. R
34
=
R
1
3
+
R
1
4
−1
=
6.0
1
Ω
+
6.0
1
Ω
−1
=
0.17
Ω
1
+ 0.17
Ω
1
−1
=
0.34
Ω
1
−1
= 2.9 Ω
R
234
= R
2
+ R
34
= 3.0 Ω+2.9 Ω=5.9 Ω
R
56
=
R
1
5
+
R
1
6
−1
=
4.0
1
Ω
+
12.
1
0 Ω
−1
R
56
=
0.25
Ω
1
+ 0.0833
Ω
1
−1
=
0.33
Ω
1
−1
= 3.0 Ω
R
567
= R
56
+ R
7
= 3.0 Ω+2.0 Ω=5.0 Ω
R
234567
=
R
2
1
34
+
R
5
1
67
−1
=
5.9
1
Ω
+
5.0
1
Ω
−1
R
234567
=
0.17
Ω
1
+ 0.20
Ω
1
−1
=
0.37
Ω
1
−1
= 2.7 Ω
R
eq
= R
1
+ R
234567
= 3.0 Ω+2.7 Ω=5.7 Ω
I =
R
∆V
eq
=
1
5
8
.7
.0
Ω
V
= 3.2 A
∆V
234567
= IR
234567
= (3.2 A)(2.7 Ω) = 8.6 V
I
7
= I
567
=
∆V
R
2
5
3
6
4
7
567
=
5
8
.
.
0
6
Ω
V
= 1.7 A
Section One—Student Edition Solutions I Ch. 18–9
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
27. R
1
= 8.0 Ω
R
2
= 6.0 Ω
∆V
2
= 12 V
R
eq
= R
1
+ R
2
= 8.0 Ω+6.0 Ω=14.0 Ω
I
2
=
∆
R
V
2
2
=
6
1
.
2
0
V
Ω
= 2.0 A
∆V = I
2
R
eq
= (2.0 A)(14.0 Ω) = 28 V
b. ∆V
7
= I
7
R
7
= (1.7 A)(2.0 Ω) =
c. ∆V
56
= I
567
R
56
= (1.7 A)(3.0 Ω) = 5.1 V
∆V
6
=∆V
56
=
d. I
6
=
∆
R
V
6
6
=
1
5
2
.
.
1
0
V
Ω
= 0.42 A
5.1 V
3.4 V
28. R
1
= 9.0 Ω
R
2
= 6.0 Ω
I
1
= 0.25 A
∆V
1
= I
1
R
1
= (0.25 A)(9.0 Ω) = 2.2 V
29. R
1
= 9.0 Ω
R
2
= 6.0 Ω
I
1
= 0.25 A
R
eq
= R
1
+ R
2
= 9.0 Ω+6.0 Ω=15.0 Ω
∆V = I
1
R
eq
= (0.25 A)(15.0 Ω) = 3.8 V
30. R
1
= 9.0 Ω
R
2
= 6.0 Ω
∆V
2
= 12 V
I =
∆
R
V
2
2
=
6
1
.
2
0
V
Ω
= 2.0 A
R
eq
= R
1
+ R
2
= 9.0 Ω+6.0 Ω=15.0 Ω
∆V = IR
eq
= (2.0 A)(15.0 Ω) = 3.0 × 10
1
V
31. R
1
= 18.0 Ω
R
2
= 9.00 Ω
R
3
= 6.00 Ω
I
2
= 4.00 A
a. R
eq
= R
1
+ R
2
+ R
3
= 18.0 Ω+9.00 Ω+6.00 Ω=
b. I = I
2
= 4.00 A
∆V = IR
eq
= (4.00 A)(33.0 Ω) =
c. I
1
= I
3
= I
2
= 4.00 A
132 V
33.0 Ω
33. R
1
= 90.0 Ω
R
2
= 10.0 Ω
R
3
= 10.0 Ω
R
4
= 90.0 Ω
R
eq
= 60.0 Ω
R
12
= R
1
+ R
2
= 90.0 Ω+10.0 Ω=100.0 Ω
R
34
= R
3
+ R
4
= 10.0 Ω+90.0 Ω=100.0 Ω
R
1234
=
R
1
12
+
R
1
34
−1
=
100
1
.0 Ω
+
100
1
.0 Ω
−1
=
0.01000
Ω
1
+ 0.01000
Ω
1
−1
R
1234
=
0.02000
Ω
1
−1
= 50.00 Ω
R
eq
= R + R
1234
R = R
eq
− R
1234
= 60.0 Ω−50.00 Ω= 10.0 Ω
Holt Physics Solution ManualI Ch. 18–10
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
35. R = 6.0 Ω The following equations represent the circuits as listed.
(a) R
eq
= 2R = 2(6.0 Ω) = 12.0 Ω
(b) R
eq
=
R
2
−1
=
6.0
2
Ω
−1
= 3.0 Ω
(c) R
eq
=
R
3
−1
=
6.0
3
Ω
−1
= 2.0 Ω
(d) R
eq
=
R
1
+
2
1
R
−1
=
6.0
1
Ω
+
12.
1
0 Ω
−1
R
eq
=
0.17
Ω
1
+ 0.0833
Ω
1
−1
=
0.25
Ω
1
−1
= 4.0 Ω
(e) R
eq
=
R
2
−1
+ R = 3.0 Ω+6.0 Ω=9.0 Ω
36. ∆V = 9.0 V
R
1
= 4.5 Ω
R
2
= 3.0 Ω
R
3
= 2.0 Ω
a. R
23
=
R
1
2
+
R
1
3
−1
=
3.0
1
Ω
+
2.0
1
Ω
−1
=
0.83
Ω
1
−1
= 1.2 Ω
R
eq
= R
1
+ R
23
= 4.5 Ω+1.2 Ω=
b. I =
R
∆
e
V
q
=
5
9
.
.
7
0
Ω
V
=
c. I
1
= I =
∆V
23
= IR
23
= (1.6 A)(1.2 Ω) = 1.9 V
I
2
=
∆
R
V
2
23
=
3
1
.
.
0
9
Ω
V
=
I
3
=
∆
R
V
3
23
=
2
1
.
.
0
9
Ω
V
=
d. ∆V
1
= I
1
R
1
= (1.6 A)(4.5 Ω) =
∆V
2
=∆V
3
=∆V
23
= 1.9 V
7.2 V
0.95 A
0.63 A
1.6 A
1.6 A
5.7 Ω
34. R
eq
= 150.0 Ω
∆V = 120.0 V
N = 25
R
eq, string
=
N
R
−1
=
2
R
5
−1
=
2
R
5
R
eq
=
2
R
5
+
2
R
5
=
2
2
R
5
= 150.0 Ω
R =
25(15
2
0.0 Ω)
= 1875 Ω
Section One—Student Edition Solutions I Ch. 18–11
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
37. R
1
= 18.0 Ω
R
2
= 6.0 Ω
∆V = 18.0 V
R
eq
= R
1
+ R
2
= 18.0 Ω+6.0 Ω=24.0 Ω
I
1
= I
2
= I =
R
∆
e
V
q
=
2
1
4
8
.
.
0
0
Ω
V
=
∆V
1
= I
1
R
1
= (0.750 A)(18.0 Ω) =
∆V
2
= I
2
R
2
= (0.750 A)(6.0 Ω) = 4.5 V
13.5 V
0.750 A
38. R
1
= 30.0 Ω
R
2
= 15.0 Ω
R
3
= 5.00 Ω
∆V = 30.0 V
b. R
12
=
R
1
1
+
R
1
2
−1
=
30.
1
0 Ω
+
15.
1
0 Ω
−1
R
12
=
0.0333
Ω
1
+ 0.0667
Ω
1
−1
=
0.1000
Ω
1
−1
= 10.00 Ω
R
eq
= R
12
+ R
3
= 10.00 Ω+5.00 Ω=
c. I
3
= I =
R
∆
e
V
q
=
1
3
5
0
.0
.0
0
V
Ω
=
∆V
12
= IR
12
= (2.00 A)(10.00 Ω) = 20.0 V
I
1
=
∆
R
V
1
12
=
3
2
0
0
.
.
0
0
Ω
V
=
I
2
=
∆
R
V
2
12
=
1
2
5
0
.
.
0
0
Ω
V
=
d. ∆V
1
=∆V
2
=∆V
12
=
∆V
3
= I
3
R
3
= (2.00 A)(5.00 Ω) = 10.0 V
20.0 V
1.33 A
0.667 A
2.00 A
15.00 Ω
39. R
2
= 12 Ω
∆V = 12 V
I
1
= 3.0 A
R
1
=
∆
I
1
V
=
3
1
.0
2V
A
= 4.0 Ω
40. R
1
= 18.0 Ω
R
2
= 6.0 Ω
∆V = 18.0 V
R
eq
=
R
1
1
+
R
1
2
−1
=
18.
1
0 Ω
+
6.0
1
Ω
−1
=
0.0556
Ω
1
+ 0.17
Ω
1
−1
=
0.23
Ω
1
−1
R
eq
= 4.3 Ω
∆V
1
=∆V
2
=∆V =
I
1
=
∆
R
V
1
1
=
1
1
8
8
.
.
0
0
Ω
V
=
I
2
=
∆
R
V
2
2
=
1
6
8
.0
.0
Ω
V
= 3.0 A
1.00 A
18.0 V
Holt Physics Solution ManualI Ch. 18–12
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
41. R
1
= 90.0 Ω
R
2
= 10.0 Ω
R
3
= 10.0 Ω
R
4
= 90.0 Ω
R
eq
= 2R
eq,S
Switch open:
R
12
= R
1
+ R
2
= 90.0 Ω+10.0 Ω=100.0 Ω
R
34
= R
3
+ R
4
= 10.0 Ω+90.0 Ω=100.0 Ω
R
1234
=
R
1
12
+
R
1
34
−1
=
100
1
.0 Ω
+
100
1
.0 Ω
−1
=
0.02000
Ω
1
−1
= 50.00 Ω
R
eq
= R + R
1234
= R + 50.00 Ω
Switch closed:
R
13
=
R
1
1
+
R
1
3
−1
=
90.
1
0 Ω
+
10.
1
0 Ω
−1
R
13
=
0.0111
Ω
1
+ 0.100
Ω
1
−1
=
0.111
Ω
1
−1
= 9.01 Ω
R
24
=
R
1
2
+
R
1
4
−1
=
10.
1
0 Ω
+
90.
1
0 Ω
−1
= 9.01 Ω
R
eq,S
= R + R
13
+ R
24
= R + 9.01 Ω+9.01 Ω=R + 18.02 Ω
R
eq
= 2R
eq,S
R + 50.00 Ω=2(R + 18.02 Ω) = 2R + 36.04 Ω
2R − R = 50.00 Ω−36.04 Ω
R = 13.96 Ω
42. R = 20.0 Ω a. Two resistors in series with two parallel resistors:
R
eq
= R + R +
R
2
−1
= 20.0 Ω+20.0 Ω+
20.
2
0 Ω
−1
= 50.0 Ω
b. Four parallel resistors:
R
eq
=
R
4
−1
=
R
4
=
20.
4
0 Ω
= 5.00 Ω
Section One—Student Edition Solutions I Ch. 18–13
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
44. ∆V = 6.0 V
∆V
A
= 4.0 V (series)
I
B
= 2.0 A (parallel)
series:
∆V =∆V
A
+∆V
B
∆V
B
=∆V −∆V
A
= 6.0 V − 4.0 V = 2.0 V
I
B
=
∆
R
V
B
B
=
3
2
.
.
0
0
Ω
V
= 0.67 A
I
A
= I
B
= 0.67 A
R
A
=
∆
I
V
A
A
=
0
4
.
.
6
0
7
V
A
=
parallel:
∆V
A
=∆V
B
= 6.0 V
R
B
=
∆
I
V
B
B
=
6
2
.
.
0
0
V
A
= 3.0 Ω
6.0 Ω
a. R
12
= R
1
+ R
2
= 30.0 Ω+50.0 Ω=80.0 Ω
R
123
=
R
1
12
+
R
1
3
−1
=
80.
1
0 Ω
+
90.
1
0 Ω
−1
R
123
=
0.0125
Ω
1
+ 0.0111
Ω
1
−1
=
0.0236
Ω
1
−1
= 42.4 Ω
R
eq
= R
123
+ R
4
= 42.4 Ω+20.0 Ω=
b. I =
R
∆
e
V
q
=
6
1
2
2
.
.
4
0
Ω
V
=
c. ∆V
123
= IR
123
= (0.192 A)(42.4 Ω) = 8.14 V
I
12
=
∆
R
V
1
1
2
23
=
8
8
0
.1
.0
4
Ω
V
= 0.102 A
I
1
= I
12
=
d. ∆V
2
= I
12
R
2
= (0.102 A)(50.0 Ω) = 5.10 V
P
2
=
(∆
R
V
2
2
)
2
=
(5
5
.
0
1
.
0
0
V
Ω
)
2
=
e. ∆V
4
= IR
4
= (0.192 A)(20.0 Ω) = 3.84 V
P
4
=
(∆
R
V
4
4
)
2
=
(3
2
.
0
8
.
4
0
V
Ω
)
2
= 0.737 W
0.520 W
0.102 A
0.192 A
62.4 Ω
43. ∆V = 12.0 V
R
1
= 30.0 Ω
R
2
= 50.0 Ω
R
3
= 90.0 Ω
R
4
= 20.0 Ω
Holt Physics Solution ManualI Ch. 18–14
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
46. R
1
= 5.0 Ω
R
2
= 10.0 Ω
R
3
= 4.0 Ω
R
4
= 3.0 Ω
R
5
= 10.0 Ω
R
6
= 2.0 Ω
R
7
= 3.0 Ω
R
8
= 4.0 Ω
R
9
= 3.0 Ω
∆V = 28 V
a. R
789
= R
7
+ R
8
+ R
9
= 3.0 Ω+4.0 Ω + 3.0 Ω=10.0 Ω
R
5789
=
R
1
5
+
R
7
1
89
−1
=
10.
1
0 Ω
+
10.
1
0 Ω
−1
=
0.200
Ω
1
−1
= 5.00 Ω
R
456789
= R
4
+ R
5789
+ R
6
= 3.0 Ω+5.00 Ω+2.0 Ω=10.0 Ω
R
2456789
=
R
1
2
+
R
45
1
6789
−1
=
10.
1
0 Ω
+
10.
1
0 Ω
−1
=
0.200
Ω
1
−1
= 5.00 Ω
R
eq
= R
1
+ R
2456789
+ R
3
= 5.0 Ω+5.00 Ω+4.0 Ω=
b. I =
R
∆
e
V
q
=
1
2
4
8
.0
V
Ω
= 2.0 A
I
1
= I = 2.0 A
14.0 Ω
47. P = 4.00 W
R
1
= 3.0 Ω
R
2
= 10.0 Ω
R
3
= 5.0 Ω
R
4
= 4.0 Ω
R
5
= 3.0 Ω
a. R
23
=
R
1
2
+
R
1
3
−1
=
10.
1
0 Ω
+
5.0
1
Ω
−1
R
23
=
0.100
Ω
1
+ 0.20
Ω
1
−1
=
0.30
Ω
1
−1
= 3.3 Ω
R
234
= R
23
+ R
4
= 3.3 Ω+4.0 Ω=7.3 Ω
R
2345
=
R
2
1
34
+
R
1
5
−1
=
7.3
1
Ω
+
3.0
1
Ω
−1
R
2345
=
0.14
Ω
1
+ 0.33
Ω
1
−1
=
0.47
Ω
1
−1
= 2.1 Ω
R
eq
= R
1
+ R
2345
= 3.0 Ω+2.1 Ω=
b. ∆V =
P
R
eq
=
(4
.0
0
W
)(
5.
1
Ω
)
= 4.5 V
5.1 Ω
48. P
T
= 1200 W
P
C
= 1200 W
∆V = 120 V
I
max
= 15 A
P = I∆V
P
T
+ P
C
= I∆V
I =
2(1
1
2
2
0
0
0
V
W)
= 20 A
no, because 20 A > 15 A
49. P
H
= 1300 W
P
T
= 1100 W
P
G
= 1500 W
∆V = 120 V
a. heater: I =
∆
P
V
H
=
1
1
3
2
0
0
0
V
W
=
toaster: I =
∆
P
V
T
=
1
1
1
2
0
0
0
V
W
=
grill: I =
∆
P
V
G
=
1
1
5
2
0
0
0
V
W
=
b. I
tot
= 11 A + 9.2 A + 12 A = 32.2 A
12 A
9.2 A
11 A
Section One—Student Edition Solutions I Ch. 18–15
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Circuits and Circuit Elements, Standardized Test Prep
Givens Solutions
8. R
1
= 2.0 Ω
R
2
= 2.0 Ω
R
3
= 2.0 Ω
∆V
tot
= 12 V
R
eq
= R
1
+ R
2
+ R
3
= 2.0 Ω+2.0 Ω+2.0 Ω=6.0 Ω
I
R
=
∆
R
V
e
t
q
ot
=
6
1
.
2
0
V
Ω
= 2.0 A
∆V
R
= I
R
R = 2.0 A × 2.0 Ω = 4.0 V
10. R
bulb
= 3.0 Ω
∆V = 9.0 V
I =
R
∆
b
V
ulb
=
3
9
.
.
0
0
Ω
V
= 3.0 A
11. R
bulb
= 3.0 Ω
∆V = 9.0 V
R
eq
=
R
b
1
ulb
× 6
−1
=
3.0
1
Ω
× 6
−1
= 0.50 Ω
I
tot
=
R
∆V
eq
=
0
9
.5
.0
0
V
Ω
= 18 A
17. R
1
= 1.5 Ω
R
bulb
= 3.0 Ω
∆V
tot
= 12 V
a. R
eq
= R
1
+ R
bulb
= 1.5 Ω+3.0 Ω=4.5 Ω
b. I =
R
∆V
eq
=
4
1
.
2
5
V
Ω
= 2.7 A
I
bulb
= 2.7 A
16. R
1
= 1.5 Ω
R
2
= 6.0 Ω
R
bulb
= 3.0 Ω
∆V = 12 V
a. R
12
=
R
1
1
+
R
1
2
−1
=
1.5
1
Ω
+
6.0
1
Ω
−1
= 1.2 Ω
R
eq
= R
12
+ R
bulb
= 1.2 Ω+3.0 Ω=
b. I =
R
∆V
eq
=
4
1
.
2
2
V
Ω
= 2.9 A
I
bulb
= 2.9 A
4.2 Ω
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualI Ch. 18–16
19. R
1
= 150 Ω
R
2
= 180 Ω
∆V = 12 V
R
1
= 150 Ω
R
2
= 180 Ω
∆V = 12 V
a. R
eq
= R
1
+ R
2
= 150 Ω+180 Ω=330 Ω
I
1
= I
2
= I =
R
∆
e
V
q
=
3
1
3
2
0
V
Ω
=
∆V
1
= I
1
R
1
= (0.036 A)(150 Ω) =
∆V
2
= I
2
R
2
= (0.036 A)(180 Ω) =
b. ∆V
1
=∆V
2
=∆V =
I
1
=
∆
R
V
1
1
=
1
1
5
2
0
V
Ω
=
I
2
=
∆
R
V
2
2
=
1
1
8
2
0
V
Ω
= 0.067 A
0.080 A
12 V
6.5 V
5.4 V
0.036 A
18. R
1
= 4.0 Ω
R
2
= 12.0 Ω
∆V = 4.0 V
R
1
= 4.0 Ω
R
2
= 12.0 Ω
∆V = 4.0 V
a. R
eq
= R
1
+ R
2
= 4.0 Ω+12.0 Ω=16.0 Ω
I
1
= I
2
= I =
R
∆
e
V
q
=
1
4
6
.
.
0
0
V
Ω
=
∆V
1
= I
1
R
1
= (0.25 A)(4.0 Ω) =
∆V
2
= I
2
R
2
= (0.25 A)(12.0 Ω) =
b. R
eq
=
R
1
1
+
R
1
2
−1
=
4.0
1
Ω
+
12.
1
0 Ω
−1
R
eq
=
0.25
Ω
1
+ 0.0833
Ω
1
−1
=
0.33
Ω
1
−1
= 3.0 Ω
∆V
1
=∆V
2
=∆V =
I
1
=
∆
R
V
1
1
=
4
4
.
.
0
0
Ω
V
=
I
2
=
∆
R
V
2
2
=
1
4
2
.
.
0
0
V
Ω
= 0.33 A
1.0 A
4.0 V
3.0 V
1.0 V
0.25 A
Section One—Student Edition Solutions I Ch. 19–1
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Magnetism
Student Edition Solutions
I
1. B = 4.20 × 10
−2
T
F
magnetic
= 2.40 × 10
−14
N
q = 1.60 × 10
−19
C
3. B = 1.5 T north
v = 2.5 × 10
7
m/s
downward
q = 1.60 × 10
−19
C
v =
F
m
q
ag
B
netic
= = 3.57 × 10
6
m/s
2.40 × 10
−14
N
(1.60 × 10
−19
C)(4.20 × 10
−2
T)
F
magnetic
= qvB = (1.60 × 10
−19
C)(2.5 × 10
7
m/s)(1.5 T) = 6.0 × 10
−12
m/s N west
Magnetism, Practice A
Givens Solutions
2. F
magnetic
= 2.0 × 10
−14
downward
B = 8.3 × 10
−2
T west
q = 1.60 × 10
−19
C
v =
F
m
q
ag
B
netic
==1.5 × 10
6
m/s north
2.0 × 10
−14
N
(1.60 × 10
−19
C)(8.3 × 10
−2
T)
Magnetism, Practice B
1.
l
= 6.0 m
I = 7.0 A
F
magnetic
= 7.0 × 10
−6
N
B =
F
ma
I
g
l
netic
=
(7
7
.
.
0
0
A
×
)
1
(
0
6
−
.0
6
m
N
)
= 1.7 × 10
−7
T in the +z direction
2.
l
= 1.0 m
F
magnetic
= 0.50 N
I = 10.0 A
B ==
(10.0
0
A
.5
)
0
(1
N
.0 m)
= 0.050 T
F
magnetic
I
l
3.
l
= 0.15 m
I = 4.5 A
F
magnetic
= 1.0 N
B =
F
ma
I
g
l
netic
=
(4.5 A
1
)
.0
(0
N
.15 m)
= 1.5 T
4. B = 1.5 T
F
magnetic
= 4.4 N
I = 5.0 A
l
=
F
ma
I
g
B
netic
=
(5.0
4
A
.4
)(
N
1.5 T)
= 0.59 m
Holt Physics Solution ManualI Ch. 19–2
Copyright © by Holt, Rinehart and Winston. All rights reserved.
I
1. q = 0.030 C
F
magnetic
= 1.5 N
v = 620 m/s
B =
F
ma
q
g
v
netic
=
(0.030 C
1.
)
5
(6
N
20 m/s)
= 0.081 T
3.
l
= 25 cm
I = 5.0 A
B = 0.60 T
F
magnetic
= BI
l
= (0.60 T)(5.0 A)(0.25 m) = 0.75 N
Magnetism, Chapter Review
30. B = 5.0 × 10
−5
T North
F
magnetic
= 3.0 × 10
−11
N
upward
q = 4.0 × 10
−8
C
v =
F
m
q
ag
B
netic
==15 m/s
3.0 × 10
−11
N
(4.0 × 10
−8
C)(5.0 × 10
−5
T)
31. m = 1.673 × 10
−27
kg
B = 5.0 × 10
−5
T
q = 1.60 × 10
−19
C
g = 9.81 m/s
2
mg = qvB
v =
m
qB
g
==2.1 × 10
−3
m/s
(1.673 × 10
−27
kg)(9.81 m/s
2
)
(1.60 × 10
−19
C)(5.0 × 10
−5
T)
32. I = 10.0 A
l
= 5.00 m
F
magnetic
= 15.0 N
B =
F
ma
I
g
l
netic
=
(10.0
1
A
5
)
.0
(5
N
.00 m)
= 0.300 T
33.
l
= 1.00 m
m = 50.0 g = 0.0500 kg
I = 0.245 A
g = 9.81 m/s
2
mg = BI
l
B
=
m
Il
g
=
= 2.00 T
(0.0500 kg)(9.81 m/s
2
)
(0.245 A)(1.00 m)
Magnetism, Section 3 Review
Givens Solutions
34. v = 2.50 × 10
6
m/s
m = 1.673 × 10
−27
kg
q = 1.60 × 10
−19
C
g = 9.81 m/s
2
a. mg = qvB
B =
m
qv
g
==4.10 × 10
−14
T
(1.673 × 10
−27
kg)(9.81 m/s
2
)
(1.60 × 10
−19
C)(2.50 × 10
6
m/s)
38. v = 2.0 × 10
7
m/s
B = 0.10 T
m = 1.673 × 10
−27
kg
q = 1.60 × 10
−19
C
ma = qvB
a =
q
m
vB
==1.9 × 10
14
m/s
2
(1.60 × 10
−19
C)(2.0 × 10
7
m/s)(0.10 T)
1.673 × 10
−27
kg
Section One—Student Edition Solutions I Ch. 19–3
Copyright © by Holt, Rinehart and Winston. All rights reserved.
I
Givens Solutions
39. q = 1.60 × 10
−19
C
a = 2.0 × 10
13
m/s
2
v = 1.0 × 10
7
m/s
m = 1.673 × 10
−27
kg
ma = qvB
B =
m
qv
a
=
B = 2.1 × 10
−2
T, in the negative y direction
(1.673 × 10
−27
kg)(2.0 × 10
13
m/s
2
)
(1.60 × 10
−19
C)(1.0 × 10
7
m/s)
40. v = 3.0 × 10
6
m/s
q = 37°
B = 0.30 T
q = 1.60 × 10
−19
C
m = 1.673 × 10
−27
kg
a. F
magnetic
= qvB(sin q) = (1.60 × 10
−19
C)(3.0 × 10
6
m/s)(0.30 T)(sin 37°)
F
magnetic
=
c. a =
m
F
=
1.
8
6
.
7
7
3
×
×
1
1
0
0
−
−
1
2
4
7
N
kg
= 5.2 × 10
13
m/s
2
8.7 × 10
−14
N
41.
l
= 15 cm
I = 5.0 A
m = 0.15 kg
g = 9.81 m/s
2
mg = BI
l
B == =2.0 T, out of the page
(0.15 kg)(9.81 m/s
2
)
(5.0 A)(0.15 m)
mg
I
l
42. I = 15 A
= 0.12 N/m
F
magnetic
l
Consider the force on a 1.0 m length of wire.
F
magnetic
=
(
l
) = (0.12 N/m)(1.0 m) = 0.12 N
F
magnetic
= BI
l
B ==
(15
0
A
.1
)(
2
1
N
.0 m)
= 8.0 × 10
−3
T, in the positive z direction
F
magnetic
I
l
F
magnetic
l
43. B = 3.5 mT = 3.5 × 10
−3
T
F
magnetic
= 4.5 × 10
−21
N
q = q
p
= 1.60 × 10
−19
C
m = m
p
= 1.67 × 10
−27
kg
a. v =
q
F
B
=
v =
b. KE =
1
2
mv
2
=
1
2
(1.67 × 10
−27
kg)(8.0 m/s)
2
KE = 5.4 × 10
−26
J
8.0 m/s
4.5 × 10
−21
N
(1.60 × 10
−19
C)(3.5 mT)
44. m = 6.68 × 10
−27
kg
r = 3.00 cm
v = 1.00 × 10
4
m/s
q = 1.60 × 10
−19
C
Use the equation for the force that maintains circular motion from Chapter 7.
F
c
= F
magnetic
m
v
r
2
= qvB
B =
m
qr
v
==1.39 × 10
−2
T, toward the observer
(6.68 × 10
−27
kg)(1.00 × 10
4
m/s)
(1.60 × 10
−19
C)(0.0300 m)
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualI Ch. 19–4
45. r = 1000.0 km
B = 4.00 × 10
−8
T
q = 1.60 × 10
−19
C
m = 1.673 × 10
−27
kg
r
E
= 6.37 × 10
6
m
Use the equation for the force that maintains circular motion from Chapter 7.
F
c
= F
magnetic
m
r +
v
2
r
E
= qvB
v =
(r +
m
r
E
)qB
=
v = 2.82 × 10
7
m/s
(1.0000 × 10
6
m + 6.37 × 10
6
m)(1.60 × 10
−19
C)(4.00 × 10
−8
T)
1.673 × 10
−27
kg
46. q
e
=−1.6 × 10
−19
C
m
e
= 9.1 × 10
−31
kg
q
p
= 1.6 × 10
−19
C
c = 3.0 × 10
8
m/s
k
c
= 9.0 × 10
9
N
•
m
2
/C
2
a. v = 2.0% c = (0.02)(3.8 × 10
8
m/s) = (6.0 × 10
6
m/s)
B = 3.0 T
F
magnetic
= qvB = (−1.6 × 10
−19
C)(6.0 × 10
6
m/s)(3.0 T)
F
magnetic =
b. r = 3.0 × 10
−6
m
F
electric
= kc
q
r
e
q
2
p
= (9.0 × 10
9
N
•
m
2
/C
2
)
F
electric
=
c. g = 9.81 m/s
2
F
gravitational
= mg = (9.1 × 10
−31
kg)(9.81 m/s
2
)
F
gravitational
= 8.9 × 10
−30
N
−2.6 × 10
−17
N
(−1.6 × 10
−19
C)(1.6 × 10
−19
C)
(3.0 × 10
−6
m)
2
−2.9 × 10
−12
N
7. q = 3.2 × 10
−19
C
v = 2.5 × 10
6
m/s
B = 2.0 × 10
−4
T
F
magnetic
= qvB = (3.2 × 10
−19
C)(2.5 × 10
6
m/s)(2.0 × 10
−4
T)
F
magnetic
= 1.6 × 10
−16
N
Magnetism, Standardized Test Prep
8.
l
= 25 cm = 0.25 m
I = 12 A (east to west)
B = 4.8 × 10
−5
T (south to
north)
F
magnetic
= BI
l
= (4.8 × 10
−5
T)(12 A)(0.25 m)
F
magnetic
= 1.4 × 10
−4
N
16. q = 1.6 × 10
−19
C
m = 1.7 × 10
−27
kg
B = 0.25 T
v = 2.8 × 10
5
m/s
F
centripetal
= F
magnetic
m
v
r
2
= qvB
r = m
q
v
v
2
B
=
m
qv
v
B
2
=
m
qB
v
r =
r = 1.2 × 10
−2
m = 1.2 cm
(1.7 × 10
−27
kg)(2.8 × 10
5
m/s)
(1.6 × 10
−19
C)(0.25 T)
Section One—Student Edition Solutions I Ch. 20–1
Electromagnetic
Induction
Student Edition Solutions
I
1. r = 22 cm
B
i
= 0.50 T
B
f
= 0.00 T
∆t = 0.25 s
N = 1
q = 0.0°
emf =−NA(cos q)
∆
∆
B
t
∆B = B
f
− B
i
= 0.00 T − 0.50 T =−0.50 T
A = pr
2
emf =−Npr
2
(cos q)
∆
∆
B
t
=−(1)(p)(0.22 m)
2
(cos 0.0°)
−
0
0
.2
.5
5
0
s
T
emf = 0.30 V
Electromagnetic Induction, Practice A
Givens Solutions
Copyright © Holt, Rinehart and Winston. All rights reserved.
2. N = 205
R = 23 Ω
A = 0.25 m
2
q = 0.0°
∆t = 0.25 s
B
i
= 1.6 T
B
f
= 0.0 T
I =
em
R
f
emf =−NA(cos q)
∆
∆
B
t
∆B = B
f
− B
i
= 0.0 T − 1.6 T =−1.6 T
I =
−NA(
∆
co
tR
s q)∆B
=
I = 14 A
−(205)(0.25 m
2
)(cos 0.0°)(−1.6 T)
(0.25 s)(23 Ω)
3. r = 0.33 m
B
i
= 0.35 T
q = 0.0°
B
f
=−0.25 T
∆t = 1.5 s
N = 1
emf =−NA(cos q)
∆
∆
B
t
∆B = B
f
− B
i
=−0.25 T − 0.35 T =−0.60 T
A = pr
2
emf =−Npr
2
(cos q)
∆
∆
B
t
=
emf = 0.14 V
−(1)(p)(0.33 m)
2
(cos 0.0°)(−0.60 T)
1.5 s
4. N = 505
d = 15.5 cm
q
i
= 0.0°
∆t = 2.77 ms
q
f
= 90.0°
emf = 0.166 V
∆cos q = cos q
f
− cos q
i
= cos 90.0°−cos 0.0°=0 − 1 =−1
A = p
d
2
2
B =
−N
(e
A
m
(
f
∆
)
c
(
o
∆
s
t)
q)
=
B = 4.83 × 10
−5
T
(0.166 V)(2.77 × 10
−3
s)
−(505)(p)
0.15
2
5m
2
(−1)
Holt Physics Solution ManualI Ch. 20–2
I
Copyright © Holt, Rinehart and Winston. All rights reserved.
3. N = 256
A = 0.0025 m
2
B
i
= 0.25 T
q = 0.0°
∆t = 0.75 s
B
f
= 0.00 T
∆B = B
f
− B
i
= 0.00 T − 0.25 T =−0.25 T
emf =−NA(cos q)
∆
∆
B
t
=
emf = 0.21 V
−(256)(0.0025 m
2
)(cos 0.0°)(−0.25 T)
0.75 s
Electromagnetic Induction, Section 1 Review
Givens Solutions
2. I
rms
= 5.5 A
I
max
=
0
I
.
r
7
m
0
s
7
=
0
5
.
.
7
5
0
A
7
= 7.8 A
3. ∆V
rms
= 110 V
I
max
= 10.5 A
a. I
rms
= (0.707)(I
max
) = (0.707)(10.5 A) =
b. R =
∆
I
V
rm
rm
s
s
=
7
1
.
1
4
0
2
V
A
= 14.8 Ω
7.42 A
4. ∆V
rms
= 15.0 V
R = 10.4 Ω
I
rms
=
∆V
R
rms
=
1
1
0
5
.
.
4
0
Ω
V
=
I
max
=
0
I
.
r
7
m
0
s
7
=
1
0
.
.
4
7
4
07
A
=
∆V
max
=
∆
0.
V
7
r
0
m
7
s
=
1
0
5
.7
.0
07
V
= 21.2 V
2.04 A
1.44 A
1. A = 0.33 m
2
w = 281 rad/s
B = 0.035 T
N = 37
maximum emf = NABw = (37)(0.33 m
2
)(0.035 T)(281 rad/s)
maximum emf = 1.2 × 10
2
V
Electromagnetic Induction, Section 2 Review
2. maximum emf = 2.8 V
N = 25
A = 36 cm
2
f = 60.0 Hz
B =
maxi
N
m
A
u
w
memf
=
max
N
im
A
u
2p
m
f
emf
=
B = 8.3 × 10
−2
T
2.8 V
(25)(0.0036 m
2
)(2p)(60.0 Hz)
1. R = 25 Ω
∆V
rms
= 120 V
I
rms
=
∆V
R
rms
=
1
2
2
5
0
Ω
V
=
I
max
=
0
I
.
r
7
m
0
s
7
=
0
4
.
.
7
8
0
A
7
=
∆V
max
=
∆
0.
V
7
r
0
m
7
s
=
1
0
2
.7
0
0
V
7
= 170 V
6.8 A
4.8 A
Electromagnetic Induction, Practice B
Section One—Student Edition Solutions I Ch. 20–3
I
Copyright © Holt, Rinehart and Winston. All rights reserved.
5. ∆V
max
= 155 V
R = 53 Ω
a. ∆V
rms
= (0.707)(∆V
max
) = (0.707)(155 V) =
b. I
rms
=
∆V
R
rms
=
1.10
5
×
3 Ω
10
2
V
= 2.1 A
1.10 × 10
2
V
6. ∆V
max
= 451 V
∆V
rms
= (0.707)(∆V
max
) = (0.707)(451 V) = 319 V
Givens Solutions
1. N
1
= 2680 turns
∆V
1
= 5850 V
∆V
2
= 120 V
N
2
=
N
∆
1
∆
V
V
1
2
==55.0 turns
(2680 turns)(120 V)
5850 V
Electromagnetic Induction, Practice C
2. ∆V
1
= 12 V
∆V
2
= 2.0 × 10
4
V
N
1
= 21 turns
N
2
=
N
∆
1
∆
V
V
1
2
==3.5 × 10
4
turns
(21 turns)(2.0 × 10
4
V)
12 V
3. ∆V
1
= 117 V
∆V
2
= 119 340 V
N
2
= 25 500 turns
N
1
=
N
∆
2
V
∆V
2
1
==25.0 turns
(25 500 turns)(117 V)
119 340 V
4. ∆V
1
= 117 V
∆V
2
= 0.750 V
N
N
2
1
=
∆
∆
V
V
2
1
=
0
1
.7
1
5
7
0
V
V
=
15
1
6
5. N
1
= 12 500 turns
N
2
= 525 turns
∆V
1
= 3510 V
∆V
2
=
N
2
N
∆
1
V
1
==147 V
(525 turns)(3510 V)
12 500 turns
1. I
rms
= 0.025 mA
R = 4.3 kΩ
I
max
=
0
I
.
r
7
m
0
s
7
=
0.0
0
2
.7
5
0
m
7
A
=
∆V
rms
= I
rms
R = (0.025 × 10
−3
A)(4.3 × 10
3
Ω) =
∆V
max
= I
max
R = (0.035 × 10
−3
A)(4.3 × 10
3
Ω) = 0.15 V
0.11 V
0.035 mA
Electromagnetic Induction, Section 3 Review
2. N
1
= 50 turns
N
2
= 7000 turns
∆V
1
= 120 V
∆V
2
=
N
2
N
∆
1
V
1
==1.7 × 10
4
V
(7000 turns)(120 V)
50 turns
3. N
1
= 12 turns
N
2
= 2550 turns
∆V
1
= 120 V
∆V
2
=
N
2
N
∆
1
V
1
==2.6 × 10
4
V
(2550 turns)(120 V)
12 turns
I
Copyright © Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualI Ch. 20–4
12. N = 52
A = 5.5 × 10
−3
m
2
B
i
= 0.00 T
B
f
= 0.55 T
∆t = 0.25 s
q = 0.0°
emf =
−NA(c
∆
o
t
s q)∆B
∆B = B
f
− B
i
= 0.55 T − 0.00 T = 0.55 T
emf ==−0.63 V
−(52)(5.5 × 10
−3
m
2
)(cos 0.0°)(0.55 T)
0.25 s
26. ∆V
rms
= 220 000 V
∆V
max
=
∆
0.
V
7
r
0
m
7
s
=
22
0
0
.7
0
0
0
7
0V
= 310 000 V = 3.1 × 10
5
V
10. N = 1
r
i
= 0.12 m
B = 0.15 T
A
f
= 3 × 10
−3
m
2
∆t = 0.20 s
q = 0.0°
emf =
−N(co
∆
s
t
q)B∆A
∆A = A
f
− A
i
= Af − pr
i
2
= (3 × 10
−3
m
2
) − (p)(0.12 m)
2
∆A = (3 × 10
−3
m
2
) − 0.045 m
2
=−0.042 m
2
emf ==3.2 × 10
−2
V
−(1)(cos 0.0°)(0.15 T)(−0.042 m
2
)
0.20 s
27. ∆V
max
= 340 V
R = 120 Ω
a. ∆V
rms
= (0.707)(∆V
max
) = (0.707)(340 V) =
b. I
rms
=
∆V
R
rms
=
2.40
12
×
0
1
Ω
0
2
V
= 2.0 A
2.4 × 10
2
V
Electromagnetic Induction, Chapter Review
Givens Solutions
11. A = (0.055 m)(0.085 m)
q = 0.0°
N = 75
R = 8.7 Ω
−
∆
∆
t
B
= 3.0 T/s
emf =−N
∆[AB(
∆
c
t
os q)]
=−NA(cos q)
∆
∆
B
t
emf =−(75)(0.055 m)(0.085 m)(cos 0.0°)(−3.0 T/s) = 1.05 V
I =
em
R
f
=
1
8
.
.
0
7
5
Ω
V
= 0.12 A
28. I
max
= 0.909 A
R = 182 Ω
a. I
rms
= (0.707)(I
max
) = (0.707)(0.909 A) =
b. ∆V
rms
= I
rms
R = (0.643 A)(182 Ω) =
c. P = I
rms
2
R = (0.643 A)
2
(182 Ω) = 75.2 W
117 V
0.643 A
29. P = 996 W
I
max
= 11.8 A
a. I
rms
= (0.707)(I
max
) = (0.707)(11.8 A) =
b. ∆V
rms
=
I
r
P
ms
=
9
8
9
.3
6
4
W
A
= 119 V
8.34 A
Section One—Student Edition Solutions I Ch. 20–5
I
Givens Solutions
Copyright © Holt, Rinehart and Winston. All rights reserved.
34. ∆V
1
= 120 V
∆V
2
= 9.0 V
N
1
= 640 turns
N
2
=
∆
∆
V
V
2
N
1
1
=
(9.0 V)
1
(
2
6
0
40
V
turns)
= 48 turns
35. ∆V
2
= 9.00 V
N
N
2
1
=
24
1
.6
∆V
1
=∆V
2
N
N
2
1
∆V
1
=(9.00 V)
24
1
.6
=
221 V
36. ∆V
1
= 120 V
∆V
2
= 6.3 V
N
1
= 210 turns
N
2
=
∆
∆
V
V
2
N
1
1
=
(6.3 V)
1
(
2
2
0
10
V
turns)
= 11 turns
37. ∆V
1
= 24 000 V
N
1
= 60 turns
N
2
= 3 turns
b. ∆V
1
=∆V
2
N
N
2
1
∆V
1
=(24 000 V)
6
3
0
= 1200 V =
1.2 × 10
3
V
43. A = 1.886 × 10
−3
m
2
B
i
= 2.5 × 10
−2
T
∆t = 0.25 s
emf = 149 mV
B
f
= 0.000 T
q = 0.0°
N =
−A
(e
(
m
co
f
s
)(
q
∆
)
t
∆
)
B
∆B = B
f
− B
i
= 0.000 T − 2.5 × 10
−2
T =−2.5 × 10
−2
T
N ==7.9 × 10
2
turns
(149 × 10
−3
V)(0.25 s)
−(1.886 × 10
−3
m
2
)(cos 0.0°)(−2.5 × 10
−2
T)
42. N = 1
B
i
= 2.5 × 10
−2
T
A = 7.54 × 10
−3
m
2
emf = 1.5 V
q = 0.0°
B
f
= 0.000 T
∆t =
−NA(
e
c
m
os
f
q)∆B
∆B = B
f
− B
i
= 0.000 T − 2.5 × 10
−2
T =−2.5 × 10
−2
T
∆t ==1.3 × 10
−4
s
−(1)(7.54 × 10
−3
m
2
)(cos 0.0°)(−2.5 × 10
−2
T)
1.5 V
44. N = 325
A = 19.5 × 10
−4
m
2
q = 45°
∆t = 1.25 s
emf = 15 mV
B
f
= 0.0 T
∆B =
−
(
N
em
A(
f
c
)
o
(∆
s
t
q
)
)
==−4.2 × 10
−2
T
B
i
= B
f
−∆B = 0.0 T − (−4.2 × 10
−2
T) = 4.2 × 10
−2
T
(15 × 10
−3
V)(1.25 s)
−(325)(19.5 × 10
−4
m
2
)(cos 45°)
Holt Physics Solution ManualI Ch. 20–6
45. N
1
= 22 turns
N
2
= 88 turns
∆V
1
= 110 V
b. ∆V
2
=
N
2
N
∆
1
V
1
=
(88 tu
22
rn
t
s
u
)
r
(
n
1
s
10 V)
= 4.4 × 10
2
V
I
Givens Solutions
Copyright © Holt, Rinehart and Winston. All rights reserved.
47. ∆V
1
= 20.0 kV
∆V
2
= 117 V
N
N
2
1
=
∆
∆
V
V
2
1
=
20.0
11
×
7
1
V
0
3
V
=
17
1
1
46. N = 105
q = 0.0°
r = 0.833 m
B
i
= 4.72 × 10
−3
T
B
f
= 0.00 T
∆t = 10.5 ms
emf =
−NA(c
∆
o
t
s q)∆B
=
−Npr
2
(
∆
co
t
s q)∆B
∆B = B
f
− B
i
= 0.00 T − 4.72 × 10
−3
T =−4.72 × 10
−3
T
emf =
emf = 1.03 × 10
5
V
−(105)(p)(0.833 m)
2
(cos 0.0°)(−4.72 × 10
−3
T)
10.5 × 10
−6
s
48. emf = (245 V)sin 560t
f =
5
2
6
p
0
=
maximum potential difference = 245 V
89 Hz
49. −M = 1.06 H
∆I = 9.50 A
∆t = 0.0336 s
emf =−M
∆
∆
I
t
= 1.06 H ×
0
9
.0
.5
3
0
36
A
s
= 300 V
50. P = 5.0 × 10
3
kW
∆V
1
= 4500 V
∆V
2
= 510 kV
R = (4.5 × 10
−4
Ω/m)
(6.44 × 10
5
m)
a. I =
∆
P
V
2
P
dissipated
= I
2
R =
∆
P
V
2
2
R =
5
5
.
1
0
0
×
×
1
1
0
0
6
3
W
V
2
(4.5 × 10
−4
Ω/m)(6.44 × 10
5
m)
P
dissipated
= 28 × 10
3
W =
b. If the generator’s output were not stepped up,
I =
∆
P
V
1
P
dissipated
= I
2
R =
∆
P
V
1
2
R =
5.0
45
×
0
1
0
0
V
6
W
2
(4.5 × 10
−4
Ω/m)(6.44 × 10
5
m)
P
dissipated
= 3.6 × 10
8
W = 3.6 × 10
5
kW
28 kW
Section One—Student Edition Solutions I Ch. 20–7
I
Copyright © Holt, Rinehart and Winston. All rights reserved.
4.
∆V
rms
=
∆V
m
2
ax
∆
∆
V
V
m
rm
ax
s
=
1
2
6. A
2
= 1.5A
1
B
2
= B
1
N
2
= 2N
1
cos q
2
= cos q
1
∆t
2
= 0.5∆t
1
∆V
1
=−
N
1
∆[A
∆
1
B
t
1
1
cosq
1
]
∆V
2
=−
N
2
∆[A
∆
2
B
t
2
2
cosq
2
]
∆
∆
V
V
2
1
=
N
N
2
1
∆
∆
[
[
A
A
2
1
B
B
2
1
c
c
o
o
s
s
q
q
2
1
]
]
∆
∆
t
t
1
2
∆
∆
V
V
2
1
=
N
N
2
1
A
A
2
1
∆
∆
t
t
1
2
=
N
N
2
1
A
A
2
1
∆
∆
t
t
1
2
∆
∆
V
V
2
1
=
2
N
N
1
1
1.
A
5A
1
1
0.
∆
5∆
t
1
t
1
=
2
1
1
1
.5
0
1
.5
= 6
∆V
2
= 6 ×∆V
1
Electromagnetic Induction, Standardized Test Prep
Givens Solutions
8. ∆V
1
= 240 000 V
N
1A
= 1000 turns
N
2A
= 50 turns
N
1B
= 600 turns
N
2B
= 20 turns
∆V
2
= ∆V
1
N
N
2
1
A
A
N
N
2
1
B
B
∆V
2
= (240 000V)
1
5
0
0
00
tu
tu
rn
rn
s
s
6
2
0
0
0
t
t
u
u
r
r
n
n
s
s
= 400 V
10. I
max
= 3.5 A
∆V
max
= 340 V
I
rms
= 0.707I
max
= (0.707)(3.5 A) = 2.5 A
∆V
rms
= 0.707∆V
max
= (0.707)(340 V) = 240 V
P
dissipated
=∆V
rms
I
rms
= (240 V)(2.5 A) = 600 W
11. I
max
= 12.0 A
I
rms
= 0.707I
max
= (0.707)(12.0 A) = 8.48 A
14. N
1
= 150 turns
N
2
= 75 000 turns
∆V
1
= 120 V
∆V
2
=∆V
1
N
N
2
1
= (120 V)
75
15
0
0
00
tu
t
r
u
n
r
s
ns
∆V
2
= 6.0 × 10
4
V
18.
∆
∆
B
t
= 0.10 T/s
r = 2.4 cm = 0.024 m
N = 1
q = 180° (for maximum
emf)
emf = − N
∆
∆
Φ
t
M
= −
N∆[AB
∆t
cos q]
emf = − NA cos q
∆
∆
B
t
= − Nπr
2
cos q
∆
∆
B
t
emf = − (1)(π)(0.024 m)
2
(cos 180°)(0.10 T/s)
emf = 1.8 × 10
−4
V
I
Copyright © Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 21–1
1. E = 8.1 × 10
−15
eV
f =
E
h
= = 2.0 Hz
(8.1 × 10
−15
eV)(1.60 × 10
−
19
J/eV)
6.63 × 10
−34
J
•
s
Atomic Physics, Practice A
Givens Solutions
2. f = 0.56 Hz
E = hf = (6.63 × 10
−34
J
•
s)(0.56 Hz) = 3.7 × 10
−34
J
3. E = 5.0 eV
f =
h
E
==1.2 × 10
15
Hz
(1.60 × 10
−19
J/eV)(5.0 eV)
6.63 × 10
−34
J
•
s
4. l = 940 µm
a. f =
l
c
==
c. E = hf ==1.32 × 10
−3
eV
(6.63 × 10
−34
J
•
s)(3.19 × 10
11
Hz)
1.60 × 10
−19
J/eV
3.19 × 10
11
Hz
3.00 × 10
8
m/s
940 × 10
−6
m
1. E = 5.00 eV
KE
max
= E hf
t
f
t
=
E K
h
E
max
=
f
t
= 4.83 × 10
14
Hz
[5.00 eV 3.00 eV](1.60 × 10
−19
J/eV)
6.63 × 10
−34
J
•
s
Atomic Physics, Practice B
Atomic Physics
Student Edition Solutions
2. l = 350 nm
KE
max
= 1.3 eV
work function = hf − KE
max
f =
l
c
work function = h
l
c
− KE
max
work function =−1.3 eV
work function = 3.6 eV − 1.3 eV =
f
t
=
work f
h
unction
=
f
t
= 5.6 × 10
14
Hz
(2.3 eV)(1.60 × 10
−19
J/eV)
6.63 × 10
−34
J
•
s
2.3 eV
(6.63 × 10
−34
J
•
s)(3.00 × 10
8
m/s)
(1.60 × 10
−19
J/eV)(350 × 10
−9
m)
I
Copyright © Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualI Ch. 21–2
4. f = 7.0 × 10
14
Hz
hf
t,lithium
= 2.3 eV
hf
t,silver
= 4.7 eV
hf
t,cesium
= 2.14 eV
E = hf ==2.9 eV
The photoelectric effect will be observed if E > hf
t
, which holds true for
and .cesium
lithium
(6.63 × 10
−34
J
•
s)(7.0 × 10
14
Hz)
1.60 × 10
−19
J/eV
3. f = 1.00 × 10
15
Hz
KE
max
= 2.85 10
–19
J
KE
max
= hf − hf
t
hf
t
= hf − KE
max
hf
t
= (6.63 × 10
−34
J
•
s)(1.00 × 10
15
Hz) − 2.85 × 10
−19
J
hf
t
= 6.63 × 10
−19
J − 2.85 × 10
−19
J
hf
t
= 3.78 × 10
−19
J
Converting to electron-volts, hf
t
=
1.
3
6
.
0
78
×
×
10
1
−
0
1
−
9
1
J
9
/e
J
V
= 2.36 eV
Givens Solutions
2. l = 4.5 × 10
−7
m
E = hf =
h
l
c
=
E = 2.8 eV
(6.63 × 10
−34
J
•
s)(3.00 × 10
8
m/s)
(1.60 × 10
−19
J/eV)(4.5 × 10
−7
m)
Atomic Physics, Section 1 Review
5. l = 1.00 × 10
−7
m
hf
t
= 4.6 eV
f =
l
c
=
3
1
.
.
0
0
0
0
×
×
1
1
0
0
8
−7
m
m
/s
= 3.00 × 10
15
Hz
f
t
=
4.6
h
eV
=
f
t
= 1.1 × 10
15
Hz
Because f > f
t
, electrons are ejected.
KE
max
= hf − hf
t
KE
max
=−4.6 eV
KE
max
= 12.4 eV − 4.6 eV = 7.8 eV
(6.63 × 10
−34
J
•
s)(3.00 × 10
15
Hz)
1.60 × 10
−19
J/eV
(4.6 eV)(1.60 × 10
−19
J/eV)
6.63 × 10
−34
J
•
s
1. E
3
= −1.51 eV
E
2
= −3.40 eV
E = E
3
− E
2
= (−1.51 eV) − (−3.40 eV) = 1.89 eV
f =
E
h
=
f = 4.56 × 10
14
Hz
(1.89 eV)(1.60 × 10
−19
J/eV)
6.63 × 10
−34
J
•
s
Atomic Physics, Practice C
2. E
6
= −0.378 eV
E
3
= −1.51 eV
E = E
6
− E
3
= (−0.378 eV) − (−1.51 eV) = 1.13 eV
f =
E
h
=
f = 2.73 × 10
14
Hz
(1.13 eV)(1.60 × 10
−19
J/eV)
6.63 × 10
−34
J
•
s
Section One—Student Edition Solutions I Ch. 21–3
I
1. m = 50.0g = 5.00 × 10
−2
kg
l = 3.32 × 10
−34
m
v =
l
h
m
==39.9 m/s
6.63 × 10
−34
J
•
s
(5.00 × 10
−2
kg)(3.32 × 10
−34
m)
Atomic Physics, Practice D
2. l = 5.00 × 10
−7
m
m = 9.109 × 10
−31
kg
v =
l
h
m
==1.46 × 10
3
m/s
6.63 × 10
−34
J
•
s
(5.00 × 10
−7
m)(9.109 × 10
−31
kg)
3. m = 0.15 kg
l = 5.00 × 10
−7
m
v =
l
h
m
==8.84 × 10
−27
m/s
6.63 × 10
−34
J
•
s
(5.00 × 10
−7
m)(0.15 kg)
5. v = 3.5 µm/s
l = 1.9 × 10
−13
m
m =
l
h
v
==1.0 × 10
−15
kg
6.63 × 10
−34
J
•
s
(1.9 × 10
−13
m)(3.5 × 10
−6
m/s)
Givens Solutions
3. v = 1.00 × 10
4
m/s
m = 1.673 × 10
−27
kg
l =
m
h
v
==3.96 × 10
−11
m
6.63 × 10
−34
J
•
s
(1.673 × 10
−27
kg)(1.00 × 10
4
m/s)
Atomic Physics, Section 3 Review
4. m = 1375 kg
v = 43 km/h
l =
m
h
v
==4.0 × 10
−38
m
6.63 × 10
−34
J
•
s
(1375 kg)(43 × 10
3
m/h)(1 h/3600 s)
Copyright © Holt, Rinehart and Winston. All rights reserved.
3. E
5
= 6.67 eV
E
1
= 0 eV
E = E
5
− E
1
= (6.67 eV) − (0 eV) = 6.67 eV
f =
E
h
=
f = 1.61 × 10
15
Hz
(6.67 eV)(1.60 × 10
−19
J/eV)
6.63 × 10
−34
J
•
s
5. f = 7.29 × 10
14
Hz E = hf = (6.63 × 10
−34
J
•
s)(7.29 × 10
14
Hz) = 4.83 × 10
−19
J
E = 4.83 × 10
−19
J × 1 eV/1.60 × 10
−19
J = 3.02 eV
11. E = 2.0 keV
f =
h
E
==4.8 × 10
17
Hz
(2.0 × 10
3
eV)(1.60 × 10
−19
J/eV)
6.63 × 10
−34
J
•
s
Atomic Physics, Chapter Review
12. l
1
= 5.00 cm
l
2
= 5.00 × 10
−7
m
l
3
= 5.00 × 10
−8
m
a. E
1
= hf
1
=
l
h
1
c
==
b. E
2
= hf
2
=
l
h
2
c
==
c. E
3
= hf
3
=
l
h
3
c
==24.9 eV
(6.63 × 10
−34
J
•
s)(3.00 × 10
8
m/s)
(1.60 × 10
−19
J/eV)(5.00 × 10
−8
m)
2.49 eV
(6.63 × 10
−34
J
•
s)(3.00 × 10
8
m/s)
(1.60 × 10
−19
J/eV)(5.00 × 10
−7
m)
2.49 × 10
−5
eV
(6.63 × 10
−34
J
•
s)(3.00 × 10
8
m/s)
(1.60 × 10
−19
J/eV)(5.00 × 10
−2
m)
Holt Physics Solution ManualI Ch. 21–4
I
Copyright © Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
34. m = 0.15 kg
v = 45 m/s
l =
m
h
v
==9.8 × 10
−35
m
6.63 × 10
−34
J
•
s
(0.15 kg)(45 m/s)
33. l = 5.2 × 10
−11
m
v =
m
h
l
==1.4 × 10
7
m/s
6.63 × 10
−34
J
•
s
(9.109 × 10
−31
kg)(5.2 × 10
−11
m)
13. f = 1.5 × 10
15
Hz
KE
max
= 1.2 eV
f
t
=
hf − K
h
E
max
f
t
=
f
t
==1.2 × 10
15
Hz
(9.9 × 10
–19
J − 1.9 × 10
–19
J)
6.63 × 10
–34
J
•
s
(6.63 × 10
−34
J
•
s)(1.5 × 10
15
Hz) − (1.2 eV)(1.60 × 10
−19
J/eV)
6.63 × 10
−34
J
•
s
14. f
t
= 1.14 × 10
15
Hz
work function = hf
t
=
work function = 4.72 eV
(6.63 × 10
−34
J
•
s)(1.14 × 10
15
Hz)
1.60 × 10
−19
J/eV
23. E
1
= −13.6 eV
E
2
= −3.40 eV
E
1
= −13.6 eV
E
3
= −1.51 eV
E
1
= −13.6 eV
E
4
= −0.850 eV
E
1
= −13.6 eV
E
5
= −0.544 eV
a. E = E
2
− E
1
=−3.40 eV − (−13.6 eV) = 10.2 eV
f =
E
h
=
f =
b. E = E
3
− E
1
=−1.51 eV − (−13.6 eV) = 12.1 eV
f =
E
h
=
f =
c. E = E
4
− E
1
=−0.850 eV − (−13.6 eV) = 12.8 eV
f =
E
h
=
f =
d. E = E
5
− E
1
=−0.544 eV − (−13.6 eV) = 13.1 eV
f =
E
h
=
f = 3.16 × 10
15
Hz
(13.1 eV)(1.60 × 10
−19
J/eV)
6.63 × 10
−34
J
•
s
3.09 × 10
15
Hz
(12.8 eV)(1.60 × 10
−19
J/eV)
6.63 × 10
−34
J
•
s
2.92 × 10
15
Hz
(12.1 eV)(1.60 × 10
−19
J/eV)
6.63 × 10
−34
J
•
s
2.46 × 10
15
Hz
(10.2 eV)(1.60 × 10
−19
J/eV)
6.63 × 10
−34
J
•
s
Section One—Student Edition Solutions I Ch. 21–5
I
Copyright © Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
35. l
1
= l
KE
max,1
= 1.00 eV
l
2
=
1
2
l
KE
max,2
= 4.00 eV
work function = hf − KE
max
=
h
l
c
− KE
max
h
l
c
− KE
max,1
=−KE
max,2
=
2
l
hc
− KE
max,2
KE
max,2
− KE
max,1
=
h
l
c
h
l
c
= 4.00 eV − 1.00 eV = 3.00 eV
work function =
h
l
c
− KE
max,1
= 3.00 eV − 1.00 eV = 2.00 eV
hc
1
2
l
36. m = 0.50 kg
h
m
= 3.0 m
l = 5.0 × 10
−7
m
PE = mgh
m
= nhf =
n
l
hc
n =
lm
h
g
c
h
m
=
n = 3.7 × 10
19
photons
(5.0 × 10
−7
m)(0.50 kg)(9.81 m/s
2
)(3.0 m)
(6.63 × 10
−34
J
•
s)(3.00 × 10
8
m/s)
37. l
1
= 670.0 nm
l
2
= 520.0 nm
KE
max,2
= (1.50)(KE
max,1
)
KE
max
= hf − hf
t
=
h
l
c
− hf
t
For wavelength l
1
,KE
max,1
=
l
h
1
c
− hf
t
For wavelength l
2
,KE
max,2
=
l
h
2
c
− hf
t
KE
max,2
= (1.50)(KE
max,1
)
l
h
2
c
− hf
t
= (1.50)
l
h
1
c
− hf
t
l
h
2
c
− hf
t
=
(1.5
l
0)
1
(hc)
− (1.50)(hf
t
)
(1.50)(hf
t
) − hf
t
=
(1.5
l
0)
1
(hc)
−
l
h
2
c
(0.50)(hf
t
) =
(1.5
l
0)
1
(hc)
−
l
h
2
c
hf
t
= (2.0)
(1.5
l
0)
1
(hc)
−
l
h
2
c
hf
t
= (2.0)(hc)
1
l
.5
1
0
−
l
1
2
hf
t
= (2.0)(6.63 × 10
−34
J
•
s)(3.00 × 10
8
m/s)
−
hf
t
= (2.0)(6.63 × 10
−34
J
•
s)(3.00 × 10
8
m/s)(2.24 × 10
6
m
−1
− 1.923 × 10
6
m
−1
)
hf
t
=
hf
t
= 0.80 eV
(2.0)(6.63 × 10
−34
J
•
s)(3.00 × 10
8
m/s)(0.32 × 10
6
m
−1
)
1.60 × 10
−19
J/eV
1
520.0 × 10
−9
m
1.50
670.0 × 10
−9
m
Holt Physics Solution ManualI Ch. 21–6
I
Copyright © Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
38. m = 0.200 kg
∆y = 50.0 m
l =
m
h
v
v =
2g
∆
y
l == =1.06 × 10
−34
m
6.63 × 10
−34
J
•
s
(0.200 kg)
(2
)(
9.
81
m
/s
2
)
(5
0.
0
m
)
h
m
2g
∆
y
7. E
5
= −0.544 eV
E
2
= −3.40 eV
E = E
5
− E
2
= (−0.544 eV) − (−3.40 eV) = 2.86 eV
f =
E
h
=
f = 6.90 × 10
14
Hz
(2.86 eV)(1.60 × 10
−19
J/eV)
6.63 × 10
−34
J
•
s
Atomic Physics, Standardized Test Prep
11. l = 4.00 × 10
−14
m
m
p
= 1.67 × 10
−27
kg
v =
m
h
l
==9.93 × 10
6
m/s
6.63 × 10
−34
J
•
s
(1.67 × 10
−27
kg)(4.00 × 10
−14
m)
8. E
3
= −1.51 eV
E
2
= −3.40 eV
E = E
3
− E
2
= (−1.51 eV) − (−3.40 eV) = 1.89 eV
f =
E
h
=
f = 4.56 × 10
14
Hz
(1.89 eV)(1.60 × 10
−19
J/eV)
6.63 × 10
−34
J
•
s
13. f = 2.80 × 10
14
Hz
E = hf = (6.63 × 10
−34
J
•
s)(2.80 × 10
14
Hz) =
E = 1.86 × 10
−19
J × 1 eV/1.60 × 10
−19
J = 1.16 eV
1.86 × 10
−19
J
14. l = 3.0 × 10
−7
m
hf
t,lithium
= 2.3 eV
hf
t,iron
= 3.9 eV
hf
t,mercury
= 4.5 eV
a. E = hf =
h
l
c
==4.1 eV
The photoelectric effect will be observed if E > hf
t
, which holds true for
and .
b. For lithium, KE
max
= E − hf
t,lithium
= 4.1 eV − 2.3 eV =
For iron, KE
max
= E − hf
t,iron
= 4.1 eV − 3.9 eV = 0.2 eV
1.8 eV
ironlithium
(6.63 × 10
−34
J
•
s)(3.00 × 10
8
m/s)
(1.60 × 10
−19
J/eV)(3.0 × 10
−7
m)
I
Givens Solutions
Copyright © Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 21–7
17. v
max
= 4.6 × 10
5
m/s
l = 625 nm
m = 9.109 × 10
−31
kg
a. hf
t
= hf − KE
max
=
h
l
c
−
2
1
m(v
max
)
2
hf
t
=−(0.5)(9.109 × 10
−31
kg)(4.6 × 10
5
m/s)
2
hf
t
= (3.18 × 10
−19
J) − (9.6 × 10
−20
J) = 22.2 × 10
−20
J
hf
t
==
b. f
t
=
work f
h
unction
==3.35 × 10
14
Hz
22.2 × 10
−20
J
6.63 × 10
−34
J
•
s
1.39 eV
22.2 × 10
−20
J
1.60 × 10
−19
J/eV
(6.63 × 10
−34
J
•
s)(3.00 × 10
8
m/s)
625 × 10
−9
m
18. l = 1.0 × 10
−11
m
m = 9.109 × 10
−31
kg
a. l =
m
h
v
v =
l
h
m
KE =
2
1
mv
2
=
1
2
m
l
h
m
2
=
2l
h
2
2
m
KE =
KE =
b. E = hf ==
E = 1.2 × 10
5
eV (120 keV)
(6.63 × 10
−34
J
•
s)(3.00 × 10
8
m/s)
(1.60 × 10
−19
J/eV)(1.0 × 10
−11
m)
hc
l
1.5 × 10
4
eV (15 keV)
(6.63 × 10
−34
J
•
s)
2
(2)(1.0 × 10
−11
m)
2
(9.109 × 10
−31
kg)(1.60 × 10
−19
J/eV)
Section One—Student Edition Solutions I Ch. 22–1
Subatomic Physics
Student Edition Solutions
I
1. For
20
10
Ne:
Z = 10
A = 20
atomic mass of Ne-20 =
19.992 435 u
atomic mass of H =
1.007 825 u
m
n
= 1.008 665 u
For
40
20
Ca:
Z = 20
A = 40
atomic mass of Ca-40 =
39.962 591 u
N = A − Z = 20 − 10 = 10
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of Ne-20
∆m = 10(1.007 825 u) + 10(1.008 665 u) − 19.992 435 u
∆m = 10.078 250 u + 10.086 650 u − 19.992 435 u
∆m = 0.172 465 u
E
bind
= (0.172 465 u)(931.49 MeV/u) =
N = A − Z = 40 − 20 = 20
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of Ca-40
∆m = 20(1.007 825 u) + 20(1.008 665 u) − 39.962 591 u
∆m = 20.156 500 u + 20.173 300 u − 39.962 591 u
∆m = 0.367 209 u
E
bind
= (0.367 209 u)(931.49 MeV/u) = 342.05 MeV
160.65 MeV
Copyright © Holt, Rinehart and Winston. All rights reserved.
Subatomic Physics, Practice A
Givens Solutions
2. For
3
1
H:
Z = 1
A = 3
atomic mass of H-3 =
3.016 049 u
atomic mass of H =
1.007 825 u
m
n
= 1.008 665 u
For
3
2
He:
Z = 2
A = 3
atomic mass of He-3 =
3.016 029 u
N = A − Z = 3 − 1 = 2
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of H-3
∆m = 1(1.007 825 u) + 2(1.008 665 u) − 3.016 049 u
∆m = 1.007 825 u + 2.017 330 u − 3.016 049 u
∆m = 0.009 106 u
E
bind
= (0.009 106 u)(931.49 MeV/u) = 8.482 MeV
N = A − Z = 3 − 2 = 1
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of He-3
∆m = 2(1.007 825 u) + 1(1.008 665 u) − 3.016 029 u
∆m = 2.015 650 u + 1.008 665 u − 3.016 029 u
∆m = 0.008 286 u
E
bind
= (0.008 286 u)(931.49 MeV/u) = 7.718 MeV
The difference in binding energy is 8.482 MeV − 7.718 MeV = .0.764 MeV
Holt Physics Solution ManualI Ch. 22–2
I
4. For
238
92
U:
Z = 92
A = 238
atomic mass of U-238 =
238.050 784 u
atomic mass of H =
1.007 825 u
m
n
= 1.008 665 u
N = A − Z = 238 − 92 = 146
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of U-238
∆m = 92(1.007 825 u) + 146(1.008 665 u) − 238.050 784 u
∆m = 92.719 900 u + 147.265 090 u − 238.050 784 u
∆m = 1.934 206 u
nu
E
c
b
l
i
e
n
o
d
n
=
E
b
A
ind
==7.5701 MeV/nucleon
(1.934 206 u)(931.49 MeV/u)
238
Givens Solutions
Copyright © Holt, Rinehart and Winston. All rights reserved.
3. atomic mass of Ca-43 =
42.958 767 u
m
n
= 1.008 665 u
atomic mass of Ca-42 =
41.958 618 u
∆m = m
unbound
− m
bound
∆m = (atomic mass of Ca-42 + m
n
) − (atomic mass of Ca-43)
∆m = 41.958 618 u + 1.008 665 u − 42.958 767 u
∆m = 0.008 516 u
E
bind
of the last neutron = (0.008 516 u)(931.49 MeV/u) = 7.933 MeV
6. atomic mass of H =
1.007 825 u
m
n
= 1.008 665 u
For
93
41
Nb:
Z = 41
A = 93
atomic mass of Nb-93 =
92.906 376 u
For
197
79
Au:
Z = 79
A = 197
atomic mass of Au-197 =
196.996 543 u
For
27
13
Al:
Z = 13
A = 27
atomic mass of Al-27 =
26.981 534 u
a. N = A − Z = 93 − 41 = 52
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of Nb-93
∆m = 41(1.007 825 u) + 52(1.008 665 u) − 92.906 376 u
∆m = 41.320 825 u + 52.450 580 u − 92.906 376 u
∆m = 0.865 029 u
E
bind
= (0.865 029 u)(931.49 MeV/u) =
b. N = A − Z = 197 − 79 = 118
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of Au-197
∆m = 79(1.007 825 u) + 118(1.008 665 u) − 196.966 543 u
∆m = 79.618 175 u + 119.022 470 u − 196.966 543 u
∆m = 1.674 102 u
E
bind
= (1.674 102 u)(931.49 MeV/u) =
c. N = A − Z = 27 − 13 = 14
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of Al-27
∆m = 13(1.007 825 u) + 14(1.008 665 u) − 26.981 534 u
∆m = 13.101 725 u + 14.121 310 u − 26.981 534 u
∆m = 0.241 501 u
E
bind
= (0.241 501 u)(931.49 MeV/u) = 224.96 MeV
1559.4 MeV
805.77 MeV
Subatomic Physics, Section 1 Review
Section One—Student Edition Solutions I Ch. 22–3
I
Copyright © Holt, Rinehart and Winston. All rights reserved.
8. For
23
11
Na:
Z = 11
A = 23
atomic mass of Na-23 =
22.989 767 u
atomic mass of H =
1.007 825 u
m
n
= 1.008 665 u
For
23
12
Mg:
Z = 12
A = 23
atomic mass of Mg-23 =
22.994 124 u
N = A − Z = 23 − 11 = 12
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of Na-23
∆m = 11(1.007 825 u) + 12(1.008 665 u) − 22.989 767 u
∆m = 11.086 08 u + 12.103 98 u − 22.989 767 u
∆m = 0.200 29 u
nu
E
c
b
l
i
e
n
o
d
n
=
E
b
A
ind
==8.1117 MeV/nucleon
N = A − Z = 23 − 12 = 11
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of Mg-23
∆m = 12(1.007 825 u) + 11(1.008 665 u) − 22.994 124 u
∆m = 12.093 900 u + 11.095 315 u − 22.994 124 u
∆m = 0.195 091 u
nu
E
c
b
l
i
e
n
o
d
n
=
E
b
A
ind
==7.9011 MeV/nucleon
The difference in binding energy per nucleon is
8.1117 MeV − 7.9011 MeV = .0.2106 MeV
(0.195 091 u)(931.49 MeV/u)
23
(0.200 29 u)(931.49 MeV/u)
23
1.
12
5
B → ? +
−
0
1
e + v
2.
212
83
Bi → ? +
4
2
He
3. ? →
14
7
N +
−
0
1
e + v
4.
225
89
Ac →
221
87
Fr + ?
A = 12 − 0 = 12
Z = 5 − (−1) = 6, which is carbon, C
? =
A = 212 − 4 = 208
Z = 83 − 2 = 81, which is thallium, Tl
? =
A = 14 + 0 = 14
Z = 7 + (−1) = 6, which is carbon, C
? =
A = 225 − 221 = 4
Z = 89 − 87 = 2, which is helium, He
? =
4
2
He
14
6
C
208
81
Tl
12
6
C
Subatomic Physics, Practice B
Givens Solutions
5. Nickel-63 decays by b
−
to
copper-63.
b
−
decay involves an electron and an antineutrino.
63
28
Ni →
63
29
Cu +
−
0
1
e + v
Holt Physics Solution ManualI Ch. 22–4
I
Givens Solutions
Copyright © Holt, Rinehart and Winston. All rights reserved.
6.
56
26
Fe →
56
27
Co + ?
a. A = 56 − 56 = 0
Z = 26 − 27 =−1
? =
−
0
1
e, so the decay is
b. b
−
decay involves an electron and an antineutrino.
56
26
Fe →
56
27
Co +
−
0
1
e + v
b
−
1. T
1/2
= 164 × 10
–6
s
N = 2.0 × 10
6
l =
0
T
.6
1
9
/2
3
=
164
0
×
.6
1
9
0
3
–6
s
=
activity = lN ==0.23 Ci
(4.23 × 10
3
s
–1
)(2.0 × 10
6
)
3.7 × 10
10
s
–1
/Ci
4.23 × 10
3
s
–1
Subatomic Physics, Practice C
2. T
1/2
= 19.7 min
N = 2.0 × 10
9
l =
0
T
.6
1
9
/2
3
==
activity = lN ==3.2 × 10
–5
Ci
(5.86 × 10
–4
s
–1
)(2.0 × 10
9
)
3.7 × 10
10
s
–1
/Ci
5.86 × 10
–4
s
–1
0.693
(19.7 min)(60 s/min)
3. T
1/2
= 8.07 days
N = 2.5 × 10
10
l =
0
T
.6
1
9
/2
3
=
l =
activity = lN ==6.7 × 10
−7
Ci
(9.94 × 10
−7
s
−1
)(2.5 × 10
10
)
3.7 × 10
10
s
−1
/Ci
9.94 × 10
−7
s
−1
0.693
(8.07 days)(24 h/day)(3600 s/h)
4. m
i
= 1.00 × 10
−3
g
t = 2.0 h
m
f
= 0.25 × 10
−3
g
m
m
f
i
=
0
1
.
.
2
0
5
0
×
×
1
1
0
0
−
−
3
3
g
g
=
1
4
2 ×
1
4
=
1
2
, so we know that 2 half-lives have passed in 2.0 h.
T
1
/
2
=
2.0
2
h
= 1.0 h
5. T
1
/
2
= 3.82 days
N = 4.0 × 10
8
a.
3
1
.8
2
2
d
d
a
a
y
y
s
s
≈ 3 half-lives
1
2
×
1
2
×
1
2
=
1
8
1
8
(4.0 × 10
8
) =
b. N
decayed
= N − N
remaining
N
decayed
= 4.0 × 10
8
atoms − 5.0 × 10
7
atoms
N
decayed
= 3.5 × 10
8
atoms
5.0 × 10
7
atoms
Section One—Student Edition Solutions I Ch. 22–5
I
Copyright © Holt, Rinehart and Winston. All rights reserved.
? →
4
2
He +
145
60
Nd
c. A = 4 + 145 = 149
Z = 2 + 60 = 62, which is samarium, Sm
? =
149
62
Sm
Subatomic Physics, Section 2 Review
Givens Solutions
3. N = 5.3 × 10
5
nuclei
activity = 1 decay/4.2 h
4. T
1/2
= 5715 years
14
C = (0.125)(original
14
C)
The
14
C has been reduced by 0.125 =
1
8
=
1
2
3
= 3 half-lives. Thus, the age of the site is
3T
1/2
= (3)(5715 years) = .17 140 years
7. For
12
6
C:
Z = 6
A = 12
atomic mass of C-12 =
12.000 000 u
atomic mass of H =
1.007 825 u
m
n
= 1.008 665 u
N = A − Z = 12 − 6 = 6
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of C-12
∆m = 6(1.007 825 u) + 6(1.008 665 u) − 12.000 000 u
∆m = 6.046 950 u + 6.051 990 u − 12.000 000 u
∆m = 0.098 940 u
E
bind
= (0.098 940 u)(931.49 MeV/u) = 92.162 MeV
Subatomic Physics, Chapter Review
a. l =
act
N
ivity
=
l =
b. T
1/2
=
0.6
l
93
==
or (5.8 × 10
9
s)(1 h/3600 s)(1 day/24 h)(1 year/365.25 days) = 180 years
5.8 × 10
9
s
0.693
1.2 × 10
−10
s
−1
1.2 × 10
−10
s
−1
(1 decay/4.2 h)(1 h/3600 s)
5.3 × 10
5
2.
232
90
Th → ? +
4
2
He
12
5
B → ? +
−
0
1
e + v
a. A = 232 − 4 = 228
Z = 90 − 2 = 88, which is radium, Ra
? =
b. A = 12 − 0 = 12
Z = 5 − (−1) = 6, which is carbon, C
? =
12
6
C
228
88
Ra
8. For
3
1
H:
Z = 1
A = 3
atomic mass of H-3 =
3.016 049 u
atomic mass of H =
1.007 825 u
m
n
= 1.008 625 u
N = A − Z = 3 − 1 = 2
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of H-3
∆m = 1(1.007 825 u) + 2(1.008 665 u) − 3.016 049 u
∆m = 1.007 825 u + 2.017 330 u − 3.016 049 u
∆m = 0.009 106 u
E
bind
= (0.009 106 u)(931.49 MeV/u) = 8.482 MeV
Holt Physics Solution ManualI Ch. 22–6
22. T
1/2
= 2.42 min
N = 1.67 × 10
11
l =
0
T
.6
1
9
/2
3
==
activity = lN ==2.2 × 10
−2
Ci
(4.77 × 10
−3
s
−1
)(1.67
× 10
11
)
3.7 × 10
10
s
−1
/Ci
4.77 × 10
−3
s
−1
0.693
(2.42 min)(60.0 s/min)
I
Givens Solutions
Copyright © Holt, Rinehart and Winston. All rights reserved.
20.
7
3
Li +
4
2
He → ? +
1
0
n
A = 7 + 4 − 1 = 10
Z = 3 + 2 = 5, which is Boron, B
? =
10
5
B
21. ? +
14
7
N →
1
1
H +
17
8
O
7
3
Li +
1
1
H →
4
2
He + ?
a. A = 1 + 17 − 14 = 4
Z = 1 + 8 − 7 = 2, which is helium, He
? =
b. A = 7 + 1 − 4 = 4
Z = 3 + 1 − 2 = 2, which is helium, He
? =
4
2
He
4
2
He
9. For
24
12
Mg:
Z = 12
A = 24
atomic mass of Mg-24 =
23.985 042 u
atomic mass of H =
1.007 825 u
m
n
= 1.008 665 u
For
85
37
Rb:
Z = 37
A = 85
atomic mass of Rb-85 =
84.911 793 u
N = A − Z = 24 − 12 = 12
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of Mg-24
∆m = 12(1.007 825 u) + 12(1.008 665 u) − 23.985 042 u
∆m = 12.093 900 u + 12.103 980 u − 23.985 042 u
∆m = 0.212 838 u
nu
E
c
b
l
i
e
n
o
d
n
=
E
b
A
ind
==
N = A − Z = 85 − 37 = 48
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of Rb-85
∆m = 37(1.007 825 u) + 48(1.008 665 u) − 84.911 793 u
∆m = 37.289 525 u + 48.415 920 u − 84.911 793 u
∆m = 0.793 652 u
nu
E
c
b
l
i
e
n
o
d
n
=
E
b
A
ind
==8.6974 MeV/nucleon
(0.793 652 u)(931.49 MeV/u)
85
8.2607 MeV/nucleon
(0.212 838 u)(931.49 MeV/u)
24
For
3
2
He:
Z = 2
A = 3
atomic mass of He-3 =
3.016 029 u
N = A − Z = 3 − 2 = 1
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of He-3
∆m = 2(1.007 825 u) + 1(1.008 665 u) − 3.016 029 u
∆m = 2.015 650 u + 1.008 665 u − 3.016 029 u
∆m = 0.008 286 u
E
bind
= (0.008 286 u)(931.49 MeV/u) = 7.718 MeV
Section One—Student Edition Solutions I Ch. 22–7
I
Givens Solutions
Copyright © Holt, Rinehart and Winston. All rights reserved.
23. T
1/2
= 140 days
N
f
=
1
1
6
N
i
1
1
6
=
1
2
4
, so 4 half-lives have passed.
4T
1/2
= (4)(140 days) = 560 days
24.
14
6
C = (0.0625)(original
14
6
C)
T
1/2
= 5715 years
1
2
x
= 0.0625
x = 4, so 4 half-lives have passed.
4T
1/2
= (4)(5715 years) = 22 860 years
34. m = 1.99 × 10
30
kg
r = 2.3 × 10
17
kg/m
3
m = Vr =
4
3
pr
3
r
r =
4
3
p
m
r
1/3
=
1/3
= 1.3 × 10
4
m
(3)(1.99 × 10
30
kg)
(4)(p)(2.3 × 10
17
kg/m
3
)
33. r
H
= 0.53 × 10
−10
m
r
nuclear
= 2.3 × 10
17
kg/m
3
m
H
≈ m
p
= 1.673 × 10
−27
kg
r
r
n
a
u
to
c
m
lea
ic
r
== =
r
r
n
a
u
to
c
m
lea
ic
r
==1.2 × 10
−14
(3)(1.673 × 10
−27
kg)
(4p)(0.53 × 10
−10
m)
3
(2.3 × 10
17
kg/m
3
)
3m
H
4p(r
H
)
3
r
nuclear
4
–
3
p
m
(r
H
H
)
3
r
nuclear
m
V
H
H
r
nuclear
32.
27
13
Al +
4
2
He → ? +
30
15
P
a. A = 27 + 4 − 30 = 1
Z = 13 + 2 − 15 = 0
? =
1
0
n
35. atomic mass of H =
1.007 825 u
m
n
= 1.008 665 u
atomic mass of O-15 =
15.003 065 u
For
15
8
O:
Z = 8
A = 15
atomic mass of N-15 =
15.000 108 u
For
15
7
N:
Z = 7
A = 15
N = A − Z = 15 − 8 = 7
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of O-15
∆m = 8(1.007 825 u) + 7(1.008 665 u) − 15.003 065 u
∆m = 8.062 600 u + 7.060 655 u − 15.003 065 u
∆m = 0.120 190 u
E
bind
= (0.120 190 u)(931.49 MeV/u) = 111.96 MeV
N = A − Z = 15 − 7 = 8
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of N-15
∆m = 7(1.007 825 u) + 8(1.008 665 u) − 15.000 108 u
∆m = 7.054 775 u + 8.069 320 u − 15.000 108 u
∆m = 0.123 987 u
E
bind
= (0.123 987 u)(931.49 MeV/u) = 115.49 MeV
The difference in binding energy is 115.49 MeV − 111.96 MeV = .3.53 MeV
Holt Physics Solution ManualI Ch. 22–8
I
Givens Solutions
Copyright © Holt, Rinehart and Winston. All rights reserved.
38.
140
Xe and
94
Sr are released
as fission fragments.
132
Sn and
101
Mo are re-
leased as fission fragments.
a.
235
U +
1
0
n →
140
Xe +
94
Sr + ?
A = 235 + 1 − (140 + 94) = 2
? =
b.
235
U +
1
0
n →
132
Sn +
101
Mo + ?
A = 235 + 1 − (132 + 101) = 3
? = 3
1
0
n
2
1
0
n
37.
1
0
n +
197
79
Au → ? +
−
0
1
e + v
atomic mass of Au-197 =
196.966 543 u
atomic mass of Hg-198 =
197.966 743 u
m
n
= 1.008 665 u
a. A = 197 + 1 = 198
Z = 79 − (−1) = 80, which is mercury, Hg
? =
198
80
Hg
b. ∆m = m
unbound
− m
bound
∆m = (atomic mass of Au-197 + m
n
) − (atomic mass of Hg-198)
∆m = 196.966 543 u + 1.008 665 u − 197.966 743 u
∆m = 0.008 465 u
E = (0.008 465 u)(931.49 MeV/u) = 7.885 MeV
1
0
n +
197
79
Au →
198
80
Hg +
−
0
1
e + v
39.
6
3
Li +
1
1
p Æ
4
2
He + ?
A = 6 + 1 − 4 = 3
Z = 3 + 1 − 2 = 2, which is helium, He
? =
3
2
He
40.
10
5
B +
4
2
He →
1
1
p + ?
A = 10 + 4 − 1 = 13
Z = 5 + 2 − 1 = 6, which is carbon, C
? =
13
6
C
42.
18
8
O +
1
1
p →
18
9
F + ?
A = 18 + 1 − 18 = 1
Z = 8 + 1 − 9 = 0
? =
1
0
n
36. N = 7.96 × 10
10
atoms
T
1/2
= 5715 years
a. l =
0
T
.6
1
9
/2
3
=
l = 2.31 × 10
−10
min
−1
lN = (2.31 × 10
−10
min
−1
)(7.96 × 10
10
) = 18.4 decays/min
0.693
(5715 years)(365.25 days/year)(24 h/day)(60 min/h)
41. P = 2.0 × 10
3
kW
•
h/month
conversion efficiency =
100.0%
E = 208 MeV/fission event
∆t = 1 year
E = P∆t = (N)(208 MeV)
N =
208
P∆
M
t
eV
=
N = 2.6 × 10
21
atoms
(2.0 × 10
6
W
•
h/month)(12 months)(3600 s/h)
(208 × 10
6
eV)(1.60 × 10
−19
J/eV)
I
Givens Solutions
Copyright © Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 22–9
43. 2
4
2
He → nucleus A + g
8
4
Be +
4
2
He → nucleus B + g
a. A = 2(4) = 8
Z = 2(2) = 4, which is beryllium, Be
nucleus A =
b. A = 8 + 4 = 12
Z = 4 + 2 = 6, which is carbon, C
nucleus B =
12
6
C
8
4
Be
44. lN = 240.0 mCi
T
1/2
= 14 days
l =
0
T
.6
1
9
/2
3
=
l = 5.7 × 10
−7
s
−1
N =
l
l
N
=
N = 1.6 × 10
16
nuclei
(240.0 × 10
−3
Ci)(3.7 × 10
10
s
−1
/Ci)
5.7 × 10
−7
s
−1
0.693
(14 days)(24 h/day)(3600 s/h)
45. activity = 5.0 µCi
N = 1.0 × 10
9
l =
act
N
ivity
==1.8 × 10
–4
s
–1
T
1/2
=
0.6
l
93
T
1/2
=
1.8 ×
0.
1
6
0
9
–
3
4
s
–1
= 3.8 × 10
3
s
(5.0 × 10
−6
Ci)(3.7 × 10
10
s
–1
/Ci)
1.0 × 10
9
46. m
tot
=
(9.1 × 10
11
kg)(0.0070)
atomic mass of U-235 =
3.9 × 10
−25
kg
P = 7.0 × 10
12
J/s
E = 208 MeV/fission event
N =
atom
m
ic
to
m
t
ass
E = N(208 MeV)
∆t =
P
E
=
N(208
P
MeV)
=
(
(
a
m
to
to
m
t
)
i
(
c
2
m
08
a
M
ss)
e
(
V
P
)
)
∆t =
∆t =
or (7.8 × 10
10
s)(1 h/3600 s)(1 d/24 h)(1 year/365.25 d) = 2500 years
7.8 × 10
10
s
(9.1 × 10
11
kg)(0.0070)(208 × 10
6
eV)(1.60 × 10
−19
J/eV)
(3.9 × 10
−25
kg)(7.0 × 10
12
J/s)
47. E = 208 MeV/fission event
P = 100.0 W
∆t = 1.0 h
E
tot
= P∆t = N(208 MeV)
N =
208
P∆
M
t
eV
=
N = 1.1 × 10
16
fission events
(100.0 W)(1.0 h)(3600 s/h)
(208 × 10
6
eV)(1.60 × 10
−19
J/eV)
I
Givens Solutions
Copyright © Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualI Ch. 22–10
48. P = 1.0 × 10
3
MW
E = 208 MeV/fission event
conversion efficiency =
30.0%
∆t = 24 h
E = P∆t = (N)(208 MeV)(0.300)
N =
(208 M
P
eV
∆
)
t
(0.300)
=
N = 8.7 × 10
24
atoms
(1.0 × 10
9
W)(24 h)(3600 s/h)
(208 × 10
6
eV)(1.60 × 10
−19
J/eV)(0.300)
2. m = 1.66 × 10
−27
kg
c = 3.00 × 10
8
m/s
5.
4
2
He +
9
4
Be →
12
6
C + X
E
R
= mc
2
= (1.66 × 10
−27
kg)(3.00 × 10
8
m/s)
2
= 1.49 × 10
−10
J
A = 4 + 9 − 12 = 1
Z = 2 + 4 − 6 = 0
X =
1
0
n
Subatomic Physics, Standardized Test Prep
7. age of the material =
23 000 years
T
1/2
= 5715 years
2
5
3
7
0
1
0
5
0
y
y
e
e
a
a
r
r
s
s
≈ 4.0 half-lives
1
2
4
= 0.0625
Approximately 6% of the material remains, hence about 100% − 6% = of the
material has decayed.
94%
15.
1
0
n + ? →
4
2
He +
7
3
Li
A = 4 + 7 − 1 = 10
Z = 2 + 3 − 0 = 5, which is boron, B
? =
10
5
B
8. T
1/2
= 5.76 years
N = 2.0 × 10
9
l =
0
T
.6
1
9
/2
3
==
activity = lN ==2.1 × 10
–10
Ci
(3.81 × 10
−9
s
−1
)(2.0 × 10
9
)
3.7 × 10
10
s
–1
/Ci
3.81 × 10
–9
s
–1
0.693
(5.76 years)(3.156 × 10
7
s/year)
16. T
1/2
= 432 years
It takes 10 half-lives to reach 0.1% of its original activity.
Total length of time to reach 0.1% is (432 years)(10) = 4320 years
17. Z = 26
A = 56
atomic mass of Fe-56 =
55.934 940 u
atomic mass of H =
1.007 825 u
m
n=
1.008 665 u
a. N = A − Z = 56 − 26 = 30
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of Fe-56
∆m = 26(1.007 825 u) + 30(1.008 665 u) − 55.934 940 u
∆m = 26.203 450 u + 30.259 950 u − 55.934 940 u
∆m =
b. E
bind
= (0.528 460 u)(931.49 MeV/u)
E
bind
= 492.26 MeV
0.528 460 u
I
Givens Solutions
Copyright © Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions I Ch. 22–11
18. m of U-238 = 238.050 784 u
m of Th-234 = 234.043 593 u
m of He-4 = 4.002 602 u
∆m = m
unbound
− m
bound
∆m = (m of U-238) − (m of Th-234 + m of He-4)
∆m = 238.050 784 u − (234.043 593 u + 4.002 602 u)
∆m = 0.004 589 u
E = (0.004 589 u)(931.49 MeV/u) = 4.275 MeV
Section One—Student Edition Solutions V Apx I–1
Appendix I
Additional Problems
Student Edition Solutions
I
1. depth = 1.168 × 10
3
cm
2. area = 1 acre
= 4.0469 × 10
3
m
2
3. Volume = 6.4 × 10
4
cm
3
depth = 1.168 × 10
3
cm ×
10
1
2
m
cm
= 1.168 × 10
1
m = 11.68 m
area = 1 acre = 4.0469 × 10
3
m
2
×
1
1
0
k
3
m
m
2
area = 4.0469 × 10
3
m
2
×
1
1
0
k
6
m
m
2
2
= 4.0469 × 10
−3
km
2
volume = 6.4 × 10
4
cm
3
×
10
1
2
m
cm
3
= 6.4 × 10
4
cm
3
×
10
1
6
m
cm
3
3
= 6.4 × 10
−2
m
3
The Science of Physics
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
4. mass = 6.0 × 10
3
kg
mass = 6.0 × 10
3
kg ×
1
1
0
k
3
g
g
×
1
1
0
m
−3
g
g
= 6.0 × 10
9
mg
5. time = 6.7 × 10
−17
s
time = 6.7 × 10
−17
s ×
10
1
12
s
ps
= 6.7 × 10
−5
ps
7. v = 89.5 km/h north
v
avg
= 77.8 km/h north
∆t
rest
= 22.0 min
∆x = v
avg
∆t = v(∆t −∆t
rest
)
∆t(v
avg
− v) =−v∆t
rest
∆t ==
∆t = 2.80 h = 2 h, 48 min
(89.5 km/h)(22.0 min)
60
1
m
h
in
89.5 km/h − 77.8 km/h
v∆t
rest
v − v
avg
8. ∆x = 1220 km
v
i
= 11.1 km/s
v
f
= 11.7 km/s
∆t =
v
2
i
∆
+
x
v
f
= =
2
2
2
4
.
4
8
0
k
k
m
m
/s
= 107 s
(2)(1220 km)
11.1 km/s + 11.7 km/s
6. ∆x = 15.0 km west
∆t = 15.3 s
v
avg
=
∆
∆
x
t
= =
4.2
1
5
5
×
.0
1
k
0
m
−3
h
= 3.53 × 10
3
km/h west
15.0 km
(15.3 s)
36
1
0
h
0s
Motion In One Dimension
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–2
9. v
i
= 4.0 m/s
∆t = 18 s
∆x = 135 m
v
f
=
2
∆
∆
t
x
− v
i
=
(2)(
1
1
8
35
s
m)
− 4.0 m/s = 15 m/s − 4.0 m/s =
v
f
= (11 m/s)
36
1
0
h
0s
1
1
0
k
3
m
m
v
f
= 4.0 × 10
1
km/h
11 m/s
10. v
i
= 7.0 km/h
v
f
= 34.5 km/h
∆x = 95 m
a =
v
f
2
2
−
∆x
v
i
2
=
a =
a ==0.46 m/s
2
(1140 km
2
/h
2
)
36
1
0
h
0 s
2
1
1
0
k
3
m
m
2
190 m
(1190 km
2
/h
2
− 49 km
2
/h
2
)
36
1
0
h
0s
2
1
1
0
k
3
m
m
2
190 m
[(34.5 km/h)
2
− (7.0 km/h)
2
]
36
1
0
h
0s
2
1
1
0
k
3
m
m
2
(2)(95 m)
11. ∆x = 4.0 m
∆t = 5.0 min
v
avg
=
∆
∆
x
t
= = 48 m/h
4.0 m
(5.0 min)
60
1
m
h
in
12. ∆t = 28 s
a = 0.035 m/s
2
v
i
= 0.76 m/s
v
f
= a∆t + v
i
= (0.035 m/s
2
)(28.0 s) + 0.76 m/s = 0.98 m/s + 0.76 m/s = 1.74 m/s
13. ∆t
tot
= 5.10 s
a =−9.81 m/s
2
∆x
tot
= 0 m
∆t
tot
= v
i
∆ t
tot
+
1
2
a∆t
tot
2
Because ∆x
tot
= 0,
v
i
=−
1
2
a∆t
tot
=−
1
2
(−9.81 m/s
2
)(5.10 s) =+25.0 m/s = 25.0 m/s upward
14. a
avg
=−0.870 m/s
2
∆t = 3.80 s
a
avg
=
∆
∆
v
a
t
vg
∆v
avg
= a
avg
∆t = (−0.870 m/s
2
)(3.80 s) = −3.31 m/s
15. ∆x = 55.0 m
∆t = 1.25 s
v
f
= 43.2 m/s
v
i
=
2
∆
∆
t
x
− v
f
=
(2)
1
(5
.2
5
5
.0
s
m)
− 43.2 m/s = 88.0 m/s − 43.2 m/s = 44.8 m/s
16. ∆x = 12.4 m upward
∆t = 2.0 s
v
i
= 0 m/s
Because v
i
= 0 m/s, a =
2
∆
∆
t
2
x
=
(2)
(
(
2
1
.0
2.
s
4
)
2
m)
= 6.2 m/s
2
upward
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–3
17. ∆x =+42.0 m
v
i
=+153.0 km/h
v
f
= 0 km/h
a =
v
f
2
2∆
−
x
v
i
2
=
a ==−21.5 m/s
2
−(2.34 × 10
4
km
2
/h
2
)
36
1
0
h
0 s
2
1
1
0
k
3
m
m
2
(84.0 m)
[(0 km/h)
2
− (153.0 km/h)
2
]
36
1
0
h
0s
2
1
1
0
k
3
m
m
2
(2) (42.0 m)
18. v
i
= 17.5 m/s
v
f
= 0.0 m/s
∆t
tot
= 3.60 s
∆x =
1
2
(v
i
+v
f
)∆t
∆t
top
=
∆t
2
tot
=
3.6
2
0s
= 1.80 s
∆x =
1
2
(17.5 m/s + 0.0 m/s)(1.80 s) = 15.8 m
19. ∆t = 5.50 s
v
i
= 0.0 m/s
v
f
= 14.0 m/s
∆x =
1
2
(v
i
+ v
f
)∆t =
1
2
(0.0 m/s + 14.0 m/s)(5.50 s) = 38.5 m
20. v = 6.50 m/s downward
=−6.50 m/s
∆t = 34.0 s
∆x = v∆t = (−6.50 m/s)(34.0 s) =−221 m = 221 m downward
21. v
t
= 10.0 cm/s
v
h
= 20 v
t
= 2.00 × 10
2
cm/s
∆t
race
=∆t
t
∆t
h
=∆t
t
− 2.00 min
∆x
t
=∆x
h
+ 20.0 cm =∆x
race
∆x
t
= v
t
∆t
t
∆x
h
= v
h
∆t
h
= v
h
(∆t
t
− 2.00 min)
∆x
t
=∆x
race
=∆x
h
+ 20.0 cm
v
t
∆t
t
= v
h
(∆t
t
− 2.00 min) + 20.0 cm
∆t
t
(v
t
− v
h
) =−v
h
(2.00 min) + 20.0 cm
∆t
t
=
∆t
race
=∆t
t
=
∆t
race
= =
∆t
race
= 126 s
−2.40 × 10
4
cm
−1.90 × 10
2
cm/s
20.0 cm − 2.40 × 10
4
cm
−1.90 × 10
2
cm/s
20.0 cm − (2.00 × 10
2
cm/s)(2.00 min)(60 s/min)
10.0 cm/s − 2.00 × 10
2
cm/s
20.0 cm − v
h
(2.00 min)
v
t
− v
h
22. ∆x
race
=∆x
t
v
t
= 10.0 cm/s
∆t
t
= 126 s
∆x
race
=∆x
t
= v
t
∆t
t
= (10.0 cm/s)(126 s) = 1.26 × 10
3
cm = 12.6 m
23. v
i
= 12.5 m/s up,
v
i
=+12.5 m/s
v
f
= 0 m/s
a = 9.81 m/s
2
down,
a =−9.81 m/s
2
v
f
= v
i
+ a∆t
∆t =
v
f
a
− v
i
=
0m
−
/
9
s
.8
−
1
1
m
2.5
/s
2
m/s
= 1.27 s
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–4
24. ∆t = 0.910 s
∆x = 7.19 km
v
i
= 0 km/s
v
f
=
2
∆
∆
t
x
− v
i
=
(2)
0
(7
.9
.1
1
9
0
k
s
m)
− 0 km/s = 15.8 km/s
25. a = 3.0 m/s
2
∆t = 4.1 s
v
f
= 55.0 km/h
v
f
= v
i
+ a∆t
v
i
= v
f
− a∆t =
55.0
h
km
−(3.0 m/s
2
)(4.1 s)
1
1
00
k
0
m
m
36
1
0
h
0s
v
i
= 55.0 km/h − 44 km/h = 11 km/h
26. ∆t = 1.5 s
v
i
= 2.8 km/h
v
f
= 32.0 km/h
a = =
a ==5.4 m/s
2
(29.2 km/h)
36
1
0
h
0s
1
1
0
k
3
m
m
1.5 s
(32.0 km/h − 2.8 km/h)
36
1
0
h
0s
10
k
3
m
m
1.5 s
v
f
− v
i
∆t
27. a = 4.88 m/s
2
∆x = 18.3 m
v
i
= 0 m/s
Because v
i
= 0 m/s,
∆t =
2∆
a
x
=
= 2.74 s
(2)(18.3 m)
(4.88 m/s
2
)
28. a
avg
= 16.5 m/s
2
v
i
= 0 km/h
v
f
= 386.0 km/h
∆t = = =
∆t ==6.50 s
107.2 m/s
16.5 m/s
2
(386.0 km/h − 0 km/h)
36
1
0
h
0s
1
1
0
k
3
m
m
16.5 m/s
2
v
f
− v
i
a
avg
∆v
a
avg
29. v
i
= 50.0 km/h forward
=+50.0 km/h
v
f
= 0 km/h
a = 9.20 m/s
2
backward
=−9.20 m/s
2
∆x =
v
f
2
2
−
a
v
i
2
=
∆x =
∆x = 10.5 m = 10.5 m forward
−(2.50 × 10
3
km
2
/h
2
)
36
1
0
h
0s
2
1
1
0
k
3
m
m
2
−18.4 m/s
2
[(0 km/h)
2
− (50.0 km/h)
2
]
36
1
0
h
0s
2
1
1
0
k
3
m
m
2
(2)(−9.20 m/s
2
)
30. v
i
=−4.0 m/s
a
avg
=−0.27 m/s
2
∆t = 17 s
v
f
= a
avg
∆t + v
i
v
f
= (−0.27 m/s
2
)(17 s) + (−4.0 m/s) =−4.6 m/s − 4.0 m/s =−8.6 m/s
31. v
i
=+4.42 m/s
v
f
= 0 m/s
a =−0.75 m/s
2
∆t =
v
f
−
a
v
i
=
0m
−
/
0
s
.7
−
5
4
m
.42
/s
2
m/s
=
−
−
0
4
.
.
7
4
5
2
m
m
/
/
s
s
2
= 5.9 s
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–5
32. v
i
= 4.42 m/s
a =−0.75 m/s
2
∆t = 5.9 s
∆x = v
i
∆t +
1
2
a∆t
2
= (4.42 m/s)(5.9 s) +
1
2
(−0.75 m/s
2
)(5.9 s)
2
∆x = 26 m − 13 m = 13 m
33. v
i
= 25 m/s west
v
f
= 35 m/s west
∆x = 250 m west
∆t =
v
2
i
∆
+
x
v
f
=
25
(
m
2)
/
(
s
2
+
50
35
m
m
)
/s
=
6
5
.0
.0
×
×
1
1
0
0
1
2
m
m
/s
= 8.3 s
34. a = −7.6 × 10
−2
m/s
2
∆x = 255 m
∆t = 82.0 s
v
i
= v
f
− a∆t = 0.0 m/s − (−7.6 × 10
−2
m/s
2
)(82.0 s) = 6.2 m/s
36. v
i
= 0.0 m/s
v
f
= −49.5 m/s
a = −9.81 m/s
2
∆x =
v
f
2
2
−
a
v
i
2
==
∆x = −125 m or 125 m downward
2.45 × 10
3
m
2
/s
2
−19.6 m/s
2
(−49.5 m/s)
2
− (0.0 m/s)
2
2(−9.81 m/s
2
)
37. v
i
=+320 km/h
v
f
= 0 km/h
∆t = 0.18 s
a
avg
== =
a
avg
==−490 m/s
2
−89 m/s
0.18 s
(0 km/h − 320 km/h)
36
1
0
h
0s
1
1
0
k
3
m
m
0.18 s
v
f
− v
i
∆t
∆v
∆t
38. a = 7.56 m/s
2
∆x = 19.0 m
v
i
= 0 m/s
v
f
=
v
i
2
+
2
a∆
x
=
(0
m
/s
)
2
+
(
2)
(7
.5
6
m
/s
2
)
(1
9.
0
m
)
v
f
=
28
7
m
2
/
s
2
=±16.9 m/s = 16.9 m/s
39. v
i
= 85.1 m/s upward
=+85.1 m/s
a =−9.81 m/s
2
∆x = 0 m
Because ∆x = 0 m, v
i
∆t +
1
2
a∆t
2
= 0
∆t =−−
2
a
v
i
= − −
(
(
2
−
)
9
(
.
8
8
5
1
.1
m
m
/s
/
2
s
)
)
= 17.3 s
40. v
i
= 13.7 m/s forward
=+13.7 m/s
v
f
= 11.5 m/s backward
=−11.5 m/s
∆t = 0.021 s
a
avg
= = = =
a
avg
=−1200 m/s
2
, or 1200 m/s
2
backward
−25.2 m/s
0.021 s
(− 11.5 m/s) − (13.7 m/s)
0.021 s
v
f
− v
i
∆t
∆v
∆t
41. v
i
= 1.8 m/s
v
f
= 9.4 m/s
a = 6.1 m/s
2
∆x =
v
f
2
2
−
a
v
i
2
= =
∆x =
(2)
8
(
5
6.
m
1
2
m
/s
/
2
s
2
)
= 7.0 m
88 m
2
/s
2
− 3.2 m
2
/s
2
(2)(6.1 m/s
2
)
(9.4 m/s)
2
− (1.8 m/s)
2
(2)(6.1 m/s
2
)
35. v
i
= 4.5 m/s
v
f
= 10.8 m/s
a
avg
= 0.85 m/s
2
∆t =
a
∆
a
v
vg
= =
10.8
0
m
.8
/
5
s −
m
4
/s
.5
2
m/s
=
0
6
.8
.3
5
m
m
/
/
s
s
2
= 7.4 s
v
f
− v
i
a
avg
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–6
42. v
i
= 0 m/s
∆t = 2.0 s
a =−9.81 m/s
2
Because v
i
= 0 m/s, ∆x =
1
2
a∆t
2
=
1
2
(−9.81 m/s
2
)(2.0 s)
2
=−2.0 × 10
1
m
distance of bag below balloon = 2.0 × 10
1
m
43. a = 0.678 m/s
2
v
f
= 8.33 m/s
∆x = 46.3 m
v
i
=
v
f
2
−
2
a∆
x
=
(8
.3
3
m
/s
)
2
−
(
2)
(0
.6
78
m
/s
2
)
(4
6.
3
m
)
v
i
=
69
.4
m
2
/
s
2
−
6
2.
8
m
2
/
s
2
=
6.
6
m
2
/
s
2
=±2.6 m/s = 2.6 m/s
44. v
i
= 7.5 m/s
v
f
= 0.0 m/s
a = −9.81 m/s
2
v
f
= v
i
+ a∆t
∆t =
v
f
a
− v
i
=
0.0
−
m
9
/
.8
s
1
−
m
7.
/
5
s
2
m/s
= 0.76 s
45. v
i
= 0.0 m/s
a = −3.70 m/s
2
∆x = −17.6 m
v
f
2
= v
i
2
+ 2a∆x = (0.0 m/s)
2
+ 2(−3.70 m/s
2
)(−17.6m) = 130 m
2
/s
2
v
f
=
130 m
2
/s
2
= 11.4 m/s down
Two-Dimensional Motion and Vectors
46. d = 599 m
∆y = 89 m north
d
2
=∆x
2
+∆y
2
∆x =
d
2
−
∆
y
2
=
(5
99
m
)
2
−
(
89
m
)
2
=
3.
59
×
1
0
5
m
2
−
7
.9
×
1
0
3
m
2
∆x =
3.
51
×
1
0
5
m
2
∆x = 592 m, east
47. d = 599 m
∆y = 89 m north
q = sin
−1
∆
d
y
= sin
−1
5
8
9
9
9
m
m
q = 8.5 ° north of east
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–7
48. d = 478 km
∆y = 42 km, south =−42 km
d
2
=∆x
2
+∆y
2
∆x =
d
2
−
∆
y
2
=
(4
78
k
m
)
2
−
(
−
42
k
m
)
2
2.
28
×
1
0
5
k
m
2
−
1
.8
×
1
0
3
k
m
2
∆x =
2.
26
×
1
0
5
k
m
2
=−475 km
∆x = 475 km, west
49. d = 478 km
∆y = 42 km, south =−42 km
q = sin
−1
∆
d
y
= sin
−1
−
47
4
8
2
k
k
m
m
q = 5.0° south of west
50. d = 7400 km
q = 26° south of west
∆y = 3200 km, south =
−3200 km
d
2
=∆x
2
=∆y
2
∆x =
d
2
−
∆
y
2
=
(7
40
0
km
)
2
−
(
−
32
00
k
m
)
2
=
5.
5
×
1
0
7
k
m
2
−
1
.0
×
1
0
7
k
m
2
∆x =
4.
5
×
1
0
7
k
m
2
=−6700 km
∆x = 6700 km, west
51. d = 5.3 km
q = 8.4° above horizontal
∆y = d(sin q) = (5.3 km)(sin 8.4°)
∆y = 0.77 km = 770 m
the mountain’s height = 770 m
52. d = 113 m
q = 82.4° above the
horizontal south
∆x = d(cos q) = (113 m)(cos 82.4°)
∆x = 14.9 m, south
53. v = 55 km/h
q = 37° below the horizontal
=−37°
v
y
= v(sin q) = (55 km/h)[sin(−37°)]
v
y
=−33 km/h = 33 km/h, downward
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–8
54. d
1
= 55 km
q
1
= 37 north of east
d
2
= 66 km
q
2
= 0.0° (due east)
∆x
1
= d
1
(cos q
1
) = (55 km)(cos 37°) = 44 km
∆y
1
= d
1
(sin q
1
) = (55 km)(sin 37°) = 33 km
∆x
2
= d
2
(cos q
2
) = (66 km)(cos 0.0°) = 66 km
∆y
2
= d
2
(sin q
2
) = (66 km)(sin 0.0°) = 0 km
∆x
tot
=∆x
1
+∆x
2
= 44 km + 66 km = 110 km
∆y
tot
=∆y
1
+∆y
2
= 33 km + 0 km = 33 km
d =
(∆
x
t
ot
)
2
+
(
∆
y
t
ot
)
2
=
(1
10
k
m
)
2
+
(
33
k
m
)
2
=
1.
21
×
1
0
4
k
m
2
+
1
.1
×
1
0
3
k
m
2
=
1.
32
×
1
0
4
k
m
2
d =
q = tan
−1
∆
∆
x
y
t
t
o
o
t
t
= tan
−1
1
3
1
3
0
k
k
m
m
q = 17° north of east
115 km
55. d
1
= 4.1 km
q
1
= 180° (due west)
d
2
= 17.3 km
q
2
= 90.0° (due north)
d
3
= 1.2 km
q
3
= 24.6° west of north
= 90.0°+24.6°=114.6°
∆x
1
= d
1
(cos ∆
1
) = (4.1 km)(cos 180°) =−4.1 km
∆y
1
= d
1
(sin q
1
) = (4.1 km)(sin 180°) = 0 km
∆x
2
= d
2
(cos q
2
) = (17.3 km)(cos 90.0°) = 0 km
∆y
2
= d
2
(sin q
2
) = (17.3 km)(sin 90.0°) = 17.3 km
∆x
3
= d
3
(cos q
3
) = (1.2 km)(cos 114.6°) =−0.42 km
Dy
3
= d
3
(sin q
3
) = (1.2 km)(sin 114.6°) = 1.1 km
∆x
tot
=∆x
1
+∆x
2
+∆x
3
=−4.1 km + 0 km + (−0.42 km) =−4.5 km
∆y
tot
=∆y
1
+∆y
2
+∆y
3
= 0 km + 17.3 km + 1.1 km = 18.4 km
d =
(∆
x
t
ot
)
2
+
(
∆
y
t
ot
)
2
=
(−
4.
5
km
)
2
+
(
18
.4
k
m
)
2
=
2.
0
×
1
0
1
k
m
2
+
3
39
k
m
2
=
35
9
km
2
d =
q = tan
−1
∆
∆
x
y
t
t
o
o
t
t
= tan
−1
−
18
4
.
.
4
5
k
k
m
m
=−76°= 76° north of west
18.9 km
56. ∆x = 125 m
v
x
= 90.0 m/s
∆x = v
x
∆t
∆t == =1.39 s
(125 m)
(90 m/s)
∆x
v
x
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–9
57. v
x
= 10.0 cm/s ∆t =
∆
v
x
x
∆x = 18.6 cm
∆y =−
1
2
g∆t
2
g = 9.81 m/s
2
∆y =−
1
2
g
∆
v
x
x
2
=−
1
2
(9.81 m/s
2
)
1
1
0
8
.0
.6
c
c
m
m
/s
2
=−17.0 m
58. v
i
= 250 m/s At the maximum height
q = 35° v
y,f
= v
y,i
− g∆t = 0
g = 9.81 m/s
2
v
y,i
= v
i
(sin q) = g∆t
∆t =
v
i
(si
g
n q)
=
(250
9
m
.8
/
1
s)
m
(s
/
i
s
n
2
35°)
∆t =
59. v
i
= 23.1 m/s v
y,f
2
− v
y,i
2
=−2g∆y
∆y
max
= 16.9 m At maximum height, v
y,f
g = 9.81 m/s
2
v
y,i
= v
i
(sin q) =
2g
∆
y
m
ax
q = sin
−1
= sin
−1
q =
60. v
bw
= 58.0 km/h, forward v
be
= v
bw
+ v
we
=+58.0 km/h + (−55.0 km/h) =+3.0 km/h
=+58.0 km/h
∆t =
v
∆
b
x
e
=
3
1
.0
.4
k
k
m
m
/h
v
we
= 55.0 km/h, backward
∆t =
=−55.0 km/h
61. v
1e
= 286 km/h, forward v
12
+ v
2e
= v
1e
v
2e
= 252 km/h, forward v
12
= v
1e
− v
2e
∆x = 0.750 km v
12
= v
1e
− v
2e
= 286 km/h − 252 km/h = 34 km/h
∆t =
v
∆
1
x
2
−
0
3
.
4
75
k
0
m
k
/
m
h
= 2.2 × 10
−2
h
∆t = (2.2 × 10
−2
h)
36
1
0
h
0s
= 79 s
0.47 h = 28 min
52.0°
(2
)(
9.
81
m
/s
2
)
(1
6.
9
m
)
23.1 m/s
2g
∆
y
m
ax
v
i
15 s
squirrel’s height = 17.0 m
62. ∆x = 165 m
∆y =−45 m
d =
∆
x
2
+
∆
y
2
=
(1
65
m
)
2
+
(
−
45
m
)
2
2.
72
×
1
0
4
m
2
+
2
.0
×
1
0
3
m
2
=
2.
92
×
1
0
4
m
2
d =
q tan
−1
∆
∆
x
y
= tan
−1
−
16
4
5
5
m
m
q =−15°= 15° below the horizontal
171 m
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–10
63. ∆y =−13.0 m
∆x = 9.0 m
d =
∆
x
2
+
∆
y
2
=
(9
.0
m
)
2
+
(
−
13
.0
m
)
2
=
81
m
2
+
1
69
m
2
=
2.
50
×
1
0
2
m
2
d =
q = tan
−1
∆
∆
x
y
tan
−1
−
9
1
.
3
0
.0
m
m
q =−55°= 55° below the horizontal
15.8 m
64. d = 2.7 m
q = 13° from the table’s
length
∆x = d(cos q) = (2.7 m)(cos 13°)
∆x =
∆y = d(sin q) = (2.7 m)(sin 13°)
∆y = 0.61 m along the table’s width
2.6 m along the table’s length
65. v = 1.20 m/s
q = 14.0° east of north
v
x
= v(sin q) = (1.20 m/s)(sin 14.0°)
v
x
=
v
y
= v(cos q) = (1.20 m/s)(cos 14.0°)
v
y
= 1.16 m/s, north
0.290 m/s, east
66. v = 55.0 km/h
q = 13.0° above horizontal
v
y
= v(sin q) = (55.0 km/h)(sin 13.0°)
v
y
=
v
x
= v(cos q) = (55.0 km/h)(cos 13.0°)
v
x
= 53.6 km/h, forward
12.4 km/h, upward
67. d = 3.88 km
∆x = 3.45 km
h
1
= 0.8 km
d
2
=∆x
2
+∆y
2
∆y =
d
2
−
∆
x
2
=
(3
.8
8
km
)
2
−
(
3.
45
k
m
)
2
=
15
.1
k
m
2
−
1
1.
9
km
2
=
3.
2
km
2
∆y = 1.8 km
height of mountain = h =∆y + h
1
= 1.8 km + 0.8 km
h = 2.6 km
68. d
1
= 850 m
q
1
= 0.0°
d
2
= 640 m
q
2
= 36°
∆x
1
= d
1
(cos q
1
) = (850 m)(cos 0.0°) = 850 m
∆y
1
= d
1
(sin q
1
) = (850 m)(sin 0.0°) = 0 m
∆x
2
= d
2
(cos q
2
) = (640 m)(cos 36°) = 520 m
∆y
2
= d
2
(sin q
2
) = (640 m)(sin 36°) = 380 m
∆x
tot
=∆x
1
+∆x
2
= 850 m + 520 m = 1370 m
∆y
tot
=∆y
1
+∆y
2
= 0 m + 380 m = 380 m
d =
(∆x
tot
)
2
+ (∆y
tot
)
2
=
(1370
m)
2
+
(380 m
)
2
=
1.88 ×
10
6
m
2
+ 1.4 ×
10
5
m
2
=
2.02 ×
10
6
m
2
= 1420 m =
q = tan
−1
∆
∆
x
y
t
t
o
o
t
t
= tan
−1
1
3
3
8
7
0
0
m
m
= 16° to the side of the initial dispacement
1.42 × 10
3
m
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–11
69. d
1
= 46 km
q
1
= 15° south of east
=−15°
d
2
= 22 km
q
2
= 13° east of south
=−77°
d
3
= 14 km
q
3
= 14° west of south
=−90.0°−14°=−104°
∆x
1
= d
1
(cos q
1
) = (46 km)[cos(−15°)] = 44 km
∆y
1
= d
1
(sin q
1
) = (46 km)[sin(−15°)] =−12 km
∆x
2
= d
2
(cos q
2
) = (22 km)[cos(−77°)] = 4.9 km
∆y
2
= d
2
(sin q
2
) = (22 km)[sin(−77°)] =−21 km
∆x
3
= d
3
(cos q
3
) = (14 km)[cos(−104°)] =−3.4 km
∆y
3
= d
3
(sin q
3
) = (14 km)[sin(−104°)] =−14 km
∆x
tot
=∆x
1
+∆x
2
+∆x
3
= 44 km + 4.9 km + (−3.4 km) = 46 km
∆y
tot
=∆y
1
+∆y
2
+∆y
3
=−12 km + (−21 km) + (−14 km) =−47 km
d =
(∆
x
t
ot
)
2
+
(
∆
y
t
ot
)
2
=
(4
6
km
)
2
+
(
−
47
k
m
)
2
=
2.
1
×
1
0
3
k
m
2
+
2
.2
×
1
0
3
k
m
2
=
4.
3
×
1
0
3
k
m
2
d =
q = tan
−1
∆
∆
x
y
t
t
o
o
t
t
= tan
−1
−
4
4
6
7
k
k
m
m
=−46°
q = 46° south of east
66 km
70. v
x
= 9.37 m/s ∆t =
∆
v
x
x
∆x = 85.0 m
∆y =−
1
2
g∆t
2
g = 9.81 m/s
2
∆y =−
1
2
g
∆
v
x
x
2
=−
1
2
(9.81 m/s
2
)
9
8
.3
5
7
.0
m
m
/s
2
=−404 m
71. ∆y =−2.50 × 10
2
m ∆x = v
x
∆t
v
x
= 1.50 m/s
∆y =−
1
2
g∆t
2
g = 9.81 m/s
2
∆t =
2
−
∆
g
y
∆x = v
x
2
−
∆
g
y
= (1.50 m/s)
(2
)(
−
−
2
9
.
.
5
8
0
1
×
m
1
/
0
s
2
2
m
)
∆x =
72. v
x
= 1.50 m/s v
y,f
2
=−2g∆y + v
y,i
2
∆y =−2.50 × 10
2
m v
y,i
= 0 m/s, so
g = 9.81 m/s
2
v
y,f
= v
y
=
−
2g
∆
y
=
−
(2
)(
9.
81
m
/s
2
)
(−
2.
50
×
1
0
2
m
)
v
y
= 70.0 m/s
v =
v
x
2
+
v
y
2
=
(1
.5
0
m
/s
)
2
+
(
70
.0
m
/s
)
2
=
2.
25
m
2
/
s
2
+
4
.9
0
×
1
0
3
m
2
/
s
2
=
4.
90
×
1
0
3
m
2
/
s
2
v =
q = tan
−1
v
v
x
y
= tan
−1
1
7
.
0
5
.
0
0
m
m
/
/
s
s
q = 1.23° from the vertical
70.0 m/s
10.7 m
mountain’s height = 404 m
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–12
73. q =−30.0°∆y = v
i
(sin q)∆t −
1
2
g∆t
2
v
i
= 2.0 m/s
2
g
∆t
2
− [v
i
(sin q)]∆t +∆y = 0
∆y =−45 m
Solving for ∆t using the quadratic equation,
g = 9.81 m/s
2
∆t =
∆t =
∆t ==
∆t =
∆t must be positive, so the positive root must be chosen.
∆t =
9.
2
8
9
1
m
m
/
/
s
s
2
=
74. v
i
= 10.0 m/s ∆x = v
i
(cos q)∆t = (10.0 m/s)(cos 37.0°)(2.5 s)
q = 37.0°∆x =
∆t = 2.5 s
∆y = v
i
(sin q)∆t −
1
2
g∆t
2
= (10.0 m/s)(sin 37.0°)(2.5 s) −
1
2
(9.81 m/s
2
)(2.5 s)
2
g = 9.81 m/s
2
= 15 m − 31 m
∆y =
75. v
aw
= 55.0 km/h, north v
ae
= v
aw
+ v
we
v
we
= 40.0 km/h at 17.0° v
x, ae
= v
x, aw
+ v
x, we
= v
we
(cos q
we
)
north of west v
y, ae
= v
y, aw
+ v
y, w e
= v
aw
+ v
we
(sin q
we
)
q
we
= 180.0°−17.0°=163.0°
v
x, ae
= (40.0 km/h)(cos 163.0°) =−38.3 km/h
v
y, ae
= 55.0 km/h + (40.0 km/h)(sin 163.0°) = 55.0 km/h + 11.7 km/h = 66.7 km/h
v
ae
=
v
x
,a
e
)
2
+
(
v
y
,a
e
0
2
=
(−
38
.3
k
m
/h
)
2
+
(
66
.7
k
m
/h
)
2
v
ae
=
1.
47
×
1
0
3
k
m
2
/
h
2
+
4
.4
5
×
1
0
3
k
m
2
/
h
2
=
5.
92
×
1
0
3
k
m
2
/
h
2
v
ae
=
q = tan
−1
v
v
x
y,
,
a
a
e
e
= tan
−1
=−60.1°
q = 60.1° west of north
66.7 km/h
−38.3 km/h
76.9 km/h
−16 m
2.0 10
1
m
3.0 s
−1.0 m/s ± 3.0 × 10
1
m/s
9.81 m/s
2
−1.0 m/s ±
8.
8
×
1
0
2
m
2
/
s
2
9.81 m/s
2
−1.0 m/s ±
1.
0
m
2
/
s
2
+
8
.8
×
1
0
2
m
2
/
s
2
9.81 m/s
2
(2.0 m/s)[sin(−30.0°)] ±
[(
−
2.
0
m
/s
)[
si
n
(−
30
.0
°)
]
2
−
(
2)
(9
.8
1
m
/s
2
)
(−
45
m
)
9.81 m/s
2
v
i
(sin q) ±
[−
v
i
(s
in
q
)]
2
−
4
2
g
(
∆
y)
2
2
g
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–13
76. v
ae
= 76.9 km/h at 29.9°∆x = v
ae
(cos q
ae
)∆t
west of north
∆y = v
ae
(sin q
ae
)∆t
∆t = 15.0 min
q
ae
= 90.0°+29.9°=119.9°
∆x = (76.9 km/h)(cos 119.9°)(15.0 min)(1 h/60 min) =−9.58 km
∆y = (76.9 km/h)(sin 119.9°)(15.0 min)(1 h/60 min) = 16.7 km
∆x =
∆y = 16.7 km, north
9.58 km, west
77. d
1
= 2.00 × 10
2
m
q
1
= 0.0°
d
2
= 3.00 × 10
2
m
q
2
= 3.0°
d
3
= 2.00 × 10
2
m
q
3
= 8.8°
∆x
1
= d
1
(cos q
1
) = (2.00 × 10
2
m)(cos 0.0
2
) = 2.0 × 10
2
m
∆y
1
= d
1
(sin q
1
) = (2.00 × 10
2
m)(sin 0.0°) = 0 m
∆x
2
= d
2
(cos q
2
) = (3.00 × 10
2
m)(cos 3.0°) = 3.0 × 10
2
m
∆y
2
= d
2
(sin q
2
) = (3.00 × 10
2
m)(sin 3.0°) = 16 m
∆x
3
= d
3
(cos q
3
) = (2.00 × 10
2
m)(cos 8.8°) = 2.0 × 10
2
m
∆y
3
= d
3
(sin q
3
) = (2.00 × 10
2
m)(sin 8.8°) = 31 m
∆x
tot
=∆x
1
+∆x
2
+∆x
3
= 2.0 × 10
2
m + 3.0 × 10
2
m + 2.0 × 10
2
m = 7.0 × 10
2
m
∆y
tot
=∆y
1
+∆y
2
+∆y
3
= 0 m + 16 m + 31 m = 47 m
d =
(∆
x
t
ot
)
2
+
(
∆
y
t
ot
)
2
=
(7
.0
×
1
0
2
m
)
2
+
(
47
m
)
2
=
4.
9
×
1
0
5
m
2
+
2
.2
×
1
0
3
m
2
=
4.
9
×
1
0
5
m
2
d =
q = tan
−1
∆
∆
x
y
t
t
o
o
t
t
= tan
−1
7.0
4
×
7
1
m
0
2
m
q = 3.8° above the horizontal
7.0 × 10
2
m
78. d
1
= 79 km
q
1
= 18° north of west
180.0°−18°=162°
d
2
= 150 km
q
2
= 180.0° due west
d
3
= 470 km
q
3
= 90.0° due north
d
4
= 240 km
q
4
= 15° east of north
90.0°−15°=75°
∆x
1
= d
1
(cos q
1
) = (790 km)(cos 162°) =−750 km
∆y
1
= d
1
(sin q
1
) = (790 km)(sin 162°) = 24 km
∆x
2
= d
2
(cos q
2
) = (150 km)(cos 180.0°) =−150 km
∆y
2
= d
2
(sin q
2
) = (150 km)(sin 180.0°) = 0 km
∆x
3
= d
3
(cos q
3
) = (470 km)(cos 90.0°) = 0 km
∆y
3
= d
3
(sin q
3
) = (470 km)(sin 90.0°) = 470 km
∆x
4
= d
4
(cos q
4
) = (240 km)(cos 75°) = 62 km
∆y
4
= d
4
(sin q
4
) = (240 km)(sin 75°) = 230 km
∆x
tot
=∆x
1
+ ∆x
2
+∆x
3
+ ∆x
4
= (−750 km) + (−150 km) + 0 km + 62 km =−840 km
∆y
tot
=∆y
1
+ ∆y
2
+∆y
3
+ ∆y
4
= 240 km + 0 km + 470 km + 230 km = 940 km
d =
(∆
x
t
ot
)
2
+
(
∆
y
t
ot
)
2
=
(−
84
0
km
)
2
+
(
94
0
km
)
2
=
7.
1
×
1
0
5
k
m
2
+
8
.8
×
1
0
5
k
m
2
=
15
.9
×
1
0
5
k
m
2
d =
q = tan
−1
∆
∆
x
y
t
t
o
o
t
t
= tan
−1
−
9
8
4
4
0
0
k
k
m
m
=−48°
q = 48° north of west
1260 km
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–14
79. v
x
= 85.3 m/s ∆t =
2
−
∆
g
y
=
∆
v
x
x
∆y =−1.50 m
∆x = v
x
2
−
∆
g
y
= (85.3 m/s)
(2
−
)
9
(
.
−
8
1
1
.
5
m
0
/
m
s
2
)
= 47.2 m
g = 9.81 m/s
2
range of arrow = 47.2 m
80. ∆t = 0.50 s
∆x = 1.5 m
q = 33°
∆x = v
i
(cos q)∆t
v
i
=
(cos
∆
q
x
)∆t
=
(cos 3
1
3
.
°
5
)
m
(0.50 s)
= 3.6 m/s
81. ∆x
1
= 0.46 m ∆x
tot
=∆x
1
+∆x
2
∆x
2
= 4.00 m ∆t =
v
i
(c
∆
o
x
s q)
q = 41.0°∆y = v
i
(sin q)∆t −
1
2
g∆t
2
= v
i
(sin q)
∆
v
i
x
(
i
c
+
os
∆
q
x
)
2
−
1
2
g
∆
v
x
i
(
1
co
+
s
∆
q
x
)
2
2
∆y =−0.35 m ∆y = (∆x
1
+∆x
2
)(tan q) −
g
2
(∆
v
x
i
2
1
(c
+
o
∆
s
x
q
2
)
2
)
2
g = 9.81 m/s
2
v
i
=
v
i
=
v
i
=
v
i
=
v
i
= 6.36 m/s
(9.81 m/s
2
)(4.46 m)
2
(2)(cos 41.0°)
2
(4.23 m)
(9.81 m/s
2
)(4.46 m)
2
(2)(cos 41.0°)
2
(3.88 m + 0.35 m)
(9.81 m/s
2
)(0.46 m + 4.00 m)
2
(2)(cos 41.0°)
2
[(0.46 m + 4.00 m)(tan 41.0°) − (−0.35 m)]
g(∆x
1
+∆x
2
)
2
2(cos q)
2
[(∆x
1
+∆x
2
)(tan q) −∆y]
82. v
fc
= 87 km/h, west v
fe
= v
fc
+ v
ce
v
ce
= 145 km/h, north v
x, fe
= v
x, fc
+ v
x, ce
= v
fc
=−87 km/h
∆t = 0.45 s v
y, fe
= v
y, fc
+ v
y, ce
= v
ce
=+145 km/h
∆x = v
x, fe
∆t = (−87 km/h)(10
3
m/km)(1 h/3600 s)(0.45 s) =−11 m
∆x =
∆y = v
y, fe
∆t = (145 km/h)(10
3
m/km)(1 h/3600 s)(0.45 s)
∆y = 18 m, north
11m, west
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–15
83. v
bw
= 12.0 km/h, south v
be
= v
bw
+ v
we
v
we
= 4.0 km/h at 15.0° v
x, be
= v
x, bw
+ v
x, we
= v
we
(cos q
we
)
south of east
v
y, be
= v
y, bw
+ v
y, we
= v
bw
+ v
we
(sin q
we
)
q
we
=−15.0°
v
x, be
= (4.0 km/h)[cos(−15.0°)] = 3.9 km/h
v
y, be
= (−12.0 km/h) + (4.0 km/h)[sin(−15.0°)] = (−12.0 km/h) + (−1.0 km/h)
=−13.0 km/h
v
be
=
(v
x,
b
e
)
2
+
v
y,
be
)
2
=
(3
.9
k
m
/h
)
2
+
(
−
13
.0
k
m
/h
)
2
v
be
=
15
k
m
2
/
h
2
+
1
69
k
m
2
/
h
2
=
18
4
km
2
/
h
2
v
be
=
q = tan
−1
v
v
x
y,
,
b
b
e
e
= tan
−1
−
3
1
.
3
9
.0
km
km
/h
/h
=−73°
q = 73° south of east
13.6 km/h
Forces and the Laws of Motion
84. F
1
= 7.5 × 10
4
N north
F
2
= 9.5 × 10
4
N at 15.0°
north of west
q
1
= 90.0°
q
2
= 180.0° − 15.0° = 165.0°
F
x,net
= F
x
= F
1
(cos q
1
) + F
2
(cos q
2
)
F
x,net
= (7.5 × 10
4
N)(cos 90.0°) + (9.5 × 10
4
N)(cos 165.0°)
F
x,net
= −9.2 × 10
4
N
F
y,net
= F
y
= F
1
(sin q
1
) + F
2
(sin q
2
)
F
y,net
= (7.5 × 10
4
N)(sin 90.0°) + (9.5 × 10
4
N)(sin 165.0°)
F
y,net
= 7.5 × 10
4
N + 2.5 × 10
4
N = 10.0 × 10
4
N
q = tan
−1
= tan
−1
=−47°
q = 47° north of west
10.0 × 10
4
N
−9.2 × 10
4
F
y,net
F
x,net
85. F = 76 N
q = 40.0°
F
x
= F(cos q) = (76 N)(cos 40.0°)
F
x
= 58 N
86. F = 76 N
q = 40.0°
F
y
= F(sin q) = (76 N)(sin 40.0°)
F
y
= 49 N
87. F
1
= 6.0 N
F
2
= 8.0 N
F
max
= F
1
+ F
2
= 6.0 N + 8.0 N
F
max
=
F
min
= F
2
− F
1
= 8.0 N − 6.0 N
F
min
= 2.0 N
14.0 N
88. m = 214 kg
F
buoyant
= 790 N
g = 9.81 m/s
2
F
net
= F
buoyant
− mg = 790 N − (214 kg)(9.81 m/s
2
)
F
net
= 790 N − 2.10 × 10
3
N = −1310 N
a
net
= = = −6.12 m/s
2
−1310 N
214 kg
F
net
m
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–16
89. F
net
= 2850 N
v
f
= 15 cm/s
v
i
= 0 cm/s
∆t = 5.0 s
a
net
= = = 3.0 cm/s
2
= 3.0 × 10
−2
m/s
2
F
net
= m a
net
m = =
m = 9.5 × 10
4
kg
2850 N
3.0 × 10
−2
m/s
2
F
net
a
net
15 cm/s − 0 cm/s
5.0 s
v
f
− v
i
∆t
90. m = 8.0 kg
∆y = 20.0 cm
∆t = 0.50 s
v
i
= 0 m/s
g = 9.81 m/s
2
∆y = v
i
∆t + a
net
∆t
2
Because v
i
= 0 m/s, a
net
= = = 1.6 m/s
2
F
net
= m a
net
= (8.0 kg)(1.6 m/s
2
) = 13 N
F
net
= 13 N upward
(2)(20.0 × 10
−2
m)
(0.50 s)
2
2∆y
∆t
2
1
2
91. m = 90.0 kg
q = 17.0°
g = 9.81 m/s
2
F
net
= mg(sin q) − F
k
= 0
F
k
= mg(sin q) = (90.0 kg)(9.81 m/s
2
)(sin 17.0°) = 258 N
F
k
= 258 N up the slope
92. q = 5.0° F
net
= mg(sin q) − F
k
= 0
F
k
= m
k
F
n
= m
k
mg(cos q)
m
k
=
m
m
g
g
(
(
c
si
o
n
s
q
q
)
)
= tan q = tan 5.0°
m
k
= 0.087
93. m = 2.00 kg
q = 36.0°
a
g
= 9.81 m/s
2
F
n
= ma
g
cos q = (2.00 kg)(9.81 m/s
2
)(cos 36.0°) = 15.9 N
94. m = 1.8 × 10
3
kg
q = 15.0°
F
s,max
= 1.25 × 10
4
N
g = 9.81 m/s
2
F
s,max
= m
s
F
n
= m
s
mg(cos q)
m
s
=
mg
F
(
s
c
,m
o
a
s
x
q)
=
m
s
= 0.73
1.25 × 10
4
N
(1.8 × 10
3
kg)(9.81 m/s
2
)(cos 15.0°)
95. m
k
= 0.20
g = 9.81 m/s
2
F
net
= m a
net
= F
k
F
k
= m
k
F
h
= m
k
mg
a
net
=
m
k
m
mg
= m
k
g = (0.20)(9.81 m/s
2
)
a
net
= 2.0 m/s
2
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–17
96. F
applied
= 5.0 N to the left
m = 1.35 kg
a
net
= 0.76 m/s
2
to the left
F
net
= m a
net
= F
applied
− F
k
F
k
= F
applied
− m a
net
F
k
= 5.0 N − (1.35 kg)(0.76 m/s
2
) = 5.0 N − 1.0 N = 4.0 N
F
k
= 4.0 N to the right
97. F
1
= 15.0 N
q = 55.0°
F
y
= F(sin q) = (15.0 N)(sin 55.0°)
F
y
=
F
x
= F(cos q) = (15.0 N)(cos 55.0°)
F
x
= 8.60 N
12.3 N
98. F
1
= 6.00 × 10
2
N north
F
2
= 7.50 × 10
2
N east
F
3
= 6.75 × 10
2
N at 30.0°
south of east
q
1
= 90.0°
q
2
= 0.00°
q
3
= −30.0°
F
x,net
= F
x
= F
1
(cos q
1
) + F
2
(cos q
2
) + F
3
(cos q
3
) = (6.00 × 10
2
N)(cos 90.0°)
+ (7.50 × 10
2
N)(cos 0.00°) + (6.75 × 10
2
N)[cos(−30.0°)]
F
x,net
= 7.50 × 10
2
N + 5.85 × 10
2
N = 13.35 × 10
2
N
F
y,net
= F
y
= F
1
(sin q
1
) + F
2
(sin q
2
) + F
3
(sin q
3
) = (6.00 × 10
2
N)(sin 90.0°)
+ (7.50 × 10
2
N)(sin 0.00°) + (6.75 × 10
2
N)[sin (−30.0°)]
F
y,net
= 6.00 × 10
2
N + (−3.38 × 10
2
N) = 2.62 × 10
2
N
q = tan
−1
= tan
−1
q = 11.1° north of east
2.62 × 10
2
N
13.35 × 10
2
N
F
y,net
F
x,net
99. F
net
= −65.0 N
m = 0.145 kg
a
net
= = = −448 m/s
2
−65.0 N
0.145 kg
F
net
m
100. m = 2.0 kg
∆y = 1.9 m
∆t = 2.4 s
v
i
= 0 m/s
∆y = v
i
∆t + a
net
∆t
2
Because v
i
= 0 m/s, a
net
= = = 0.66 m/s
2
F
net
= ma
net
= (2.0 kg)(0.66 m/s) = 1.3 N
F
net
= 1.3 N upward
(2)(1.9 m)
(2.4 s)
2
2∆y
∆t
2
1
2
101. ∆t = 1.0 m/s
∆t = 5.0 s
F
downhill
= 18.0 N
F
uphill
= 15.0 N
a
net
== =0.20 m/s
2
F
net
= m a
net
= F
downhill
− F
uphill
= 18.0 N − 15.0 N = 3.0 N
m = = = 15 kg
3.0 N
0.20 m/s
2
F
net
a
net
1.0 m/s
5.0 s
∆v
∆t
102. m
sled
= 47 kg
m
supplies
= 33 kg
m
k
= 0.075
q = 15°
F
k
= m
k
F
n
= m
k
(m
sled
+ m
supplies
)g(cos q) = (0.075)(47 kg + 33 kg)(9.81 m/s
2
)(cos 15°)
F
k
= (0.075)(8.0 × 10
1
kg)(9.81 m/s
2
)(cos 15°) = 57 N
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–18
103. a
net
= 1.22 m/s
2
q = 12.0°
g = 9.81 m/s
2
F
net
= m a
net
= mg(sin q) − F
k
F
k
= m
k
F
n
= m
k
mg(cos q)
m a
net
+ m
k
mg(cos q) = mg(sin q)
m
k
=
g(s
g
in
(c
q
o
)
s
−
q
a
)
net
= =
m
k
= = 0.085
0.82 m/s
2
(9.81 m/s
2
)(cos 12.0°)
2.04 m/s
2
− 1.22 m/s
2
(9.81 m/s
2
)(cos 12.0°)
(9.81 m/s
2
)(sin 12.0°) − 1.22 m/s
2
(9.81 m/s
2
)(cos 12.0°)
104. F
applied
= 1760 N
q = 17.0°
m = 266 kg
g = 9.81 m/s
2
F
net
= F
applied
− mg(sin q) − F
s,max
= 0
F
s,max
= m
s
F
n
= m
s
mg(cos q)
m
s
mg(cos q) = F
applied
− mg(sin q)
m
s
=
F
appl
m
ied
g
−
(c
m
os
g
q
(s
)
in q)
=
1760 − (266 kg)(9.81 m/s
2
)(sin 17°)
(266 kg)(9.81 m/s
2
)(cos 17°)
105. F
downward
= 4.26 × 10
7
N
m
k
= 0.25
F
net
= F
downward
− F
k
= 0
F
k
= m
k
F
n
= F
downward
F
n
= = = 1.7 × 10
8
N
4.26 × 10
7
N
0.25
F
downward
m
k
106. F
n
= 1.7 × 10
8
N
q = 10.0°
g = 9.81 m/s
2
F
n
= mg (cos q)
m = = = 1.8 × 10
7
kg
1.7 × 10
8
N
(9.81 m/s
2
)(cos 10.0°)
F
n
g (cos q)
107. F
applied
= 2.50 × 10
2
N
m = 65.0 kg
q = 18.0°
a
net
= 0.44 m/s
2
F
net
= m a
net
= F
applied
− mg(sin q) − F
k
F
k
= F
applied
− mg(sin q) − ma
net
F
k
= 2.50 × 10
2
N − (65.0 kg)(9.81 m/s
2
)(sin 18.0°) − (65.0 kg)(0.44 m/s
2
)
F
k
= 2.50 × 10
2
N − 197 N − 29 N = 24 N = 24 N downhill
108. F
1
= 2280.0 N upward
F
2
= 2250.0 N downward
F
3
= 85.0 N west
F
4
= 12.0 N east
F
y,net
= F
y
= F
1
+ F
2
= 2280.0 N + (−2250.0 N) =30.0 N
F
x,net
= F
x
= F
3
+ F
4
= −85.0 N + 12.0 N = −73.0 N
q = tan
−1
= tan
−1
=−22.3°
q = 22.3° up from west
30.0 N
−73.0 N
F
y,net
F
x,net
109. F
1
= 7.50 × 10
2
N
q
1
= 40.0°
F
2
= 7.50 × 10
2
N
q
2
=−40.0°
F
y,net
= F
g
= F
1
(cos q
1
) + F
2
(cos q
2
)
F
y,net
= (7.50 × 10
2
N)(cos 40.0°) + (7.50 × 10
2
N) [cos(−40.0°)]
F
g
= 575 N + 575 N = 1.150 × 10
3
N
m
s
= =
m
s
= 0.40
1.00 × 10
3
N
(266 kg)(9.81 m/s
2
)(cos 17°)
1760 − 760 N
(266 kg)(9.81 m/s
2
)(cos 17°)
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–19
110. F
max
= 4.5 × 10
4
N
a
net
= 3.5 m/s
2
g = 9.81 m/s
2
F
net
= m a
net
= F
max
− mg
m(a
net
+ g) = F
max
m == = =3.4 × 10
3
kg
4.5 × 10
4
N
13.3 m/s
2
4.5 × 10
4
N
3.5 m/s
2
+ 9.81 m/s
2
F
max
a
net
+ g
111. F
s,max
= 2400 N
ms = 0.20
q = 30.0°
g = 9.81 m/s
2
F
s,max
= m
s
F
n
F
n
= = = 1.2 × 10
4
N
F
n
= 1.2 × 10
4
N perpendicular to and away from the incline
2400 N
0.20
F
s,max
m
s
112. F
s,max
= 2400 N
ms = 0.20
q = 30.0°
g = 9.81 m/s
2
F
n
= mg(cos q)
m = = = 1400 kg
1.2 × 10
4
N
(9.81 m/s
2
)(cos 30.0°)
F
n
g (cos q)
113. m = 5.1 × 10
2
kg
q = 14°
F
applied
= 4.1 × 10
3
N
g = 9.81 m/s
2
F
net
= F
applied
− mg(sin q) − F
s,max
= 0
F
s,max
= m
s
F
n
= m
s
mg(cos q)
m
s
mg(cos q) = F
applied
− mg(sin q)
m
s
=
F
appl
m
ied
g
−
(c
m
os
g
q
(s
)
in q)
=
m
s
= =
m
s
= 0.60
2.9 × 10
3
N
(5.1 × 10
2
kg)(9.81 m/s
2
)(cos 14°)
4.1 × 10
3
N − 1.2 × 10
3
N
(5.1 × 10
2
kg)(9.81 m/s
2
)(cos 14°)
4.1 × 10
3
N − (5.1 × 10
2
kg)(9.81 m/s
2
)(sin 14°)
(5.1 × 10
2
kg)(9.81 m/s
2
)(cos 14°)
Work and Energy
114. d = 3.00 × 10
2
m
W = 2.13 × 10
6
J
q = 0°
F =
d(c
W
os q)
==7.10 ×
3
N
2.13 × 10
6
J
(3.00 × 10
2
m)(cos 0°)
115. F = 715 N
W = 2.72 × 10
4
J
q = 0°
d =
F (c
W
os q)
=
(7
2
1
.
5
72
N
×
)(
1
co
0
s
4
0
J
°)
= 38.0 m
116. v
1
= 88.9 m/s
v
f
= 0 m/s
∆t = 0.181 s
d = 8.05 m
m = 70.0 kg
q = 180°
W = Fd(cos q)
F = ma
a =
∆
∆
v
t
=
v
f
∆
−
t
v
i
W =
m (v
∆
f
t
− v
i
)
d (cos q) = (8.05 m)(cos 180°)
W =
W = 2.77 × 10
5
J
(70.0 kg)(88.9 m/s)(8.05 m)
(0.181 s)
(70.0 kg)(0 m/s − 88.9 m/s)
(0.181 s)
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–20
118. v = 35.0 km/h KE =
1
2
mv
2
=
1
2
(9.00 × 10
2
kg) [(35.0 km/h)(10
3
m/km)(1 h/3600 s)]
2
m = 9.00 × 10
2
kg KE = 4.25 × 10
4
J
119. KE = 1433 J
m = 47.0 g
v =
2
m
KE
=
47
(
.
2
0
)(
×
1
4
1
3
0
3
−3
J)
k
g
= 247 m/s
m =
2
v
K
2
E
=
(2)
(
(
9
6
.
.
7
0
8
8
m
×
/
1
s
0
)
2
4
J)
= 1.27 × 10
3
kg
120. v = 9.78 m/s
KE = 6.08 × 10
4
J
121. m = 50.0 kg
v
i
= 47.00 m/s
v
f
= 5.00 m/s
W
net
=∆KE = KE
f
− KE
i
=
1
2
mv
f
2
−
1
2
mv
i
2
W
net
=
1
2
m(v
f
2
− v
i
2
) =
1
2
(50.0 kg)[(5.00 m/s)
2
− (47.00 m/s)
2
]
W
net
=
1
2
(50.0 kg)(25.0 m
2
/s
2
− 2209 m
2
/s
2
) =
1
2
(50.0 kg)(−2184 m
2
/s
2
)
W
net
=−5.46 × 10
4
J
122. m = 1100 kg
v
i
= 48.0 km/h
v
f
= 59.0 km/h
d = 100 m
v
i
=
48.0
h
km
1
1
00
k
0
m
m
36
1
0
h
0s
= 13.3 m/s
v
f
=
59.0
h
km
1
1
00
k
0
m
m
36
1
0
h
0s
= 16.4 m/s
∆KE =
1
2
m(v
f
2
− v
i
2
) =
1
2
(1100 kg)[(16.4)
2
− (13.3)
2
]
∆KE = (550 kg)(269 m
2
/s
2
− 177 m
2
/s
2
) = (550 kg)(92 m
2
/s
2
) = 5.1 × 10
4
J
F =
W
d
=
∆K
d
E
=
5.1
10
×
0
1
m
0
4
J
= 5.1 × 10
2
N
123. h = 5334 m
m = 64.0 kg
g = 9.81 m/s
2
PE
g
= mgh = (64.0 kg)(9.81 m/s
2
)(5334 m) = 3.35 × 10
6
J
124. k = 550 N/m
x =−1.2 cm
PE
elastic
=
1
2
kx
2
=
1
2
(550 N/m)(–1.2 × 10
−2
m)
2
= 4.0 × 10
−2
J
125. m = 0.500 g
h = 0.250 km
g = 9.81 m/s
2
PE
i
= KE
f
mgh = KE
f
KE
f
= (0.500 × 10
−3
kg)(9.81 m/s
2
)(0.250 × 10
3
m) = 1.23 J
117. v = 15.8 km/s
m = 0.20 g
KE =
1
2
mv
2
=
1
2
(0.20 × 10
−3
kg)(15.8 × 10
3
m/s)
2
KE = 2.5 × 10
4
J
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–21
126. m = 50.0 g
v
i
= 3.00 × 10
2
m/s
v
f
= 89.0 m/s
ME
i
+∆ME = ME
f
ME
i
= KE
i
=
1
2
mv
i
2
ME
f
= KE
f
=
1
2
mv
f
2
∆ME = ME
f
− ME
i
=
1
2
m(v
f
2
− v
i
2
)
∆ME =
1
2
(50.0 × 10
−3
kg)[(89.0 m/s)
2
− (3.00 × 10
2
m/s)
2
]
∆ME =
1
2
(5.00 × 10
−2
kg)(7.92 × 10
3
m
2
/s
2
− 9.00 × 10
4
m
2
/s
2
)
∆ME =
1
2
(5.00 × 10
−2
kg) (−8.21 × 10
4
m
2
/s
2
)
∆ME =−2.05 × 10
3
J
127. P = 380.3 kW
W = 4.5 × 10
6
J
∆t =
W
P
=
38
4
0
.
.
5
3
×
×
1
1
0
0
6
3
J
W
= 12 s
128. P = 13.0 MW
∆t = 15.0 min
W = P ∆t = (13.0 × 10
6
W)(15.0 min)(60 s/min) = 1.17 × 10
10
J
129. F
net
= 7.25 × 10
−2
N
W
net
= 4.35 × 10
−2
J
q = 0°
d =
F
net
W
(c
n
o
et
s q)
==0.600 m
4.35 × 10
−2
J
(7.25 × 10
−2
N)(cos 0°)
130. d = 76.2 m
W
net
= 1.31 × 10
3
J
q = 0°
F
net
=
d(
W
co
n
s
et
q )
=
(76
1
.
.
2
31
m
×
)(
1
c
0
o
3
s
J
0°)
= 17.2 N
131. d = 15.0 m
F
applied
= 35.0 N
q
1
= 20.0°
F
k
= 24.0 N
q
2
= 180°
W
net
= F
applied
d (cos q
1
) + F
k
d (cos q
2
)
W
net
= (35.0 N) (15.0 m) (cos 20.0°) + (24.0 N) (15.0 m) (cos 180°)
W
net
= 493 J + (−3.60 × 10
2
J)
W
net
= 133J
132. m = 7.5 × 10
7
kg
v = 57 km/h
KE =
1
2
mv
2
=
1
2
(7.5 × 10
7
kg) [(57 km/h)(10
3
m/km)(1h/3600 s)]
2
KE = 9.4 × 10
9
J
133. KE = 7.81 × 10
4
J
m = 55.0 kg
v =
2
m
KE
=
(2)(7
5
.8
5
1
.0
×
kg
10
4
J)
= 53.3 m/s
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–22
134. v
i
= 8.0 m/s
v
f
= 0 m/s
d = 45 m
F
k
= 0.12 N
q = 180°
W
net
=∆KE = KE
f
− KE
i
=
1
2
mv
f
2
−
1
2
mv
i
2
W
net
= F
net
d(cos q) = F
k
d(cos q)
1
2
m(v
f
2
− v
i
2
) = F
k
d(cos q)
m =
2 F
v
k
f
2
d(
−
co
v
i
s
2
q)
==
−(2)(
−
0
6
.1
4
2
m
N
2
)
/
(
s
4
2
5m)
m = 0.17 kg
(2)(0.12 N)(45 m)(cos 180°)
(0 m/s)
2
− (8.0 m/s)
2
135. v
i
= 2.40 × 10
2
km/h
v
f
= 0 km/h
a
net
= 30.8 m/s
2
m = 1.30 × 10
4
kg
q = 180°
W
net
=∆KE = KE
f
− KE
i
=
1
2
mv
f
2
− v
i
2
W
net
= F
net
d (cos q) = ma
net
d(cos q)
ma
net
d(cos q) =
1
2
m(v
f
2
− v
i
2
)
d =
2 a
v
n
f
e
2
t
(
−
c
v
o
i
s
2
q)
=
d ==72.2 m
(−5.76 × 10
4
km
2
/h
2
)(10
3
m/km)
2
(1h/3600 s)
2
−(2)(30.8 m/s
2
)
[(0 km/h)
2
− (2.40 × 10
2
km/h)
2
] (10
3
m/km)
2
(1h/3600 s)
2
(2)(30.8 m/s
2
)(cos 180°)
136. h = 7.0 m
PE
g
= 6.6 × 10
4
J
g = 9.81 m/s
2
PE
g
= mgh
m =
P
g
E
h
g
=
(9.81
6.
m
6
/
×
s
2
1
)
0
(
4
7.
J
0m)
m = 9.6 × 10
2
kg
137. k = 1.5 × 10
4
N/m
PE
elastic
= 120 J
PE
elastic
=
1
2
kx
2
x =±
2
P
E
k
el
as
tic
=±
1.
5
(2
×
)
(
1
1
0
2
4
0
N
J)
/
m
Spring is compressed, so negative root is selected.
x =−0.13 m =−13 cm
138. m = 100.0 g
x = 30.0 cm
k = 1250 N/m
PE
elastic
= KE
1
2
kx
2
=
1
2
mv
2
v =
k
m
x
2
=
v = 33.5 m/s
(1250 N/m)(30.0 × 10
−2
m)
2
100.0 × 10
−3
kg
139. h = 3.0 m
g = 9.81 m/s
2
PE
i
= KE
f
mgh =
1
2
mv
f
2
v
f
=
2g
h
=
(2
)(
9.
81
m
/s
2
)
(3
.0
m
)
v
f
= 7.7 m/s
140. W = 1.4 × 10
13
J
∆t = 8.5 min
P =
∆
W
t
= = 2.7 × 10
10
W = 27 GW
1.4 × 10
13
J
(8.5 min)(60 s/min)
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–23
141. F = 334 N
d = 50.0 m
q = 0°
P = 2100 W
W = Fd(cos q)
∆t =
W
P
=
Fd(c
P
os q)
==8.0 s
(334 N)(50.0 m)(cos 0°)
2100 W
142. P = (4)(300.0 kW)
∆t = 25 s
W = P ∆t = (4)(300.0 × 10
3
W)(25 s) = 3.0 × 10
7
J
143. F
applied
= 92 N
m = 18 kg
m
k
= 0.35
d = 7.6 m
g = 9.81 m/s
2
q = 0°
KE
i
= 0 J
W
net
=∆KE = KE
f
− KE
i
= KE
f
W
net
= F
net
d (cos q)
F
net
= F
applied
− F
k
= F
applied
− m
k
mg
KE
f
= (F
applied
− m
k
mg) d (cos q)
= [92 N − (0.35)(18 kg)(9.81 m/s
2
)](7.6 m)(cos 0°)
KE
f
= (92 N − 62 N)(7.6 m) = (3.0 × 10
1
N)(7.6 m)
KE
f
= 230 J
144. x = 5.00 cm
KE
car
= 1.09 × 10
−4
J
Assuming all of the kinetic energy becomes stored elastic potential energy,
KE
car
= PE
elastic
=
1
2
kx
2
k =
2 PE
x
e
2
lastic
=
(
(
5
2
.
)
0
(
0
1.
×
09
10
×
−
1
2
0
m
4
)
J
2
)
k = 8.72 × 10
6
N/m
145. m = 25.0 kg
v = 12.5 m/s
g = 9.81 m/s
2
PE
i
= KE
f
mgh =
1
2
mv
2
h =
2
v
2
g
=
(2
(
)
1
(
2
9
.
.
5
81
m
m
/s
/
)
s
2
2
)
= 7.96 m
146. m = 5.0 kg
q = 25.0°
PE
g
= 2.4 × 10
2
J
PE
g
= mgh = mgd(sin q)
d =
mg
P
(
E
si
g
n q)
=
d = 12 m
2.4 × 10
2
J
(5.0 kg)(9.81 m/s
2
)(sin 25.0°)
147. m = 2.00 × 10
2
kg
F
wind
= 4.00 × 10
2
N
d = 0.90 km
v
i
= 0 m/s
q = 0°
W
net
=∆KE = KE
f
− KE
i
=
1
2
mv
f
2
−
1
2
mv
i
2
W
net
= F
net
d (cos q) = F
wind
d(cos q)
1
2
mv
f
2
−
1
2
mv
i
2
= F
wind
d (cos q)
v
f
=
2F
w
in
d
m
d
(
co
s
q
)
+
v
i
2
=
+
(
0
m
/s
)
2
v
f
=
v
f
= 6.0 × 10
1
m/s
(2)(4.00 × 10
2
N)(9.0 × 10
2
m)
2.00 × 10
2
kg
(2)(4.00 × 10
2
N)(0.90 × 10
3
m)(cos 0°)
2.00 × 10
2
kg
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–24
148. m = 50.0 kg
k = 3.4 × 10
4
N/m
x = 0.65 m
h
f
= 1.00 m − 0.65 m
= 0.35 m
PE
g,i
= PE
elastic,f
+ PE
g,f
mgh
i
=
1
2
kx
2
+ mgh
f
h
i
= h
f
+
2
kx
m
2
g
= 0.35 m + = 0.35 m + 15 m
h
i
= 15 m
(3.4 × 10
4
N/m)(0.65 m)
2
(2)(50.0 kg)(9.81 m/s
2
)
149. ∆x = 274 m to the north
∆t = 8.65 s
m = 50.0 kg
v
avg
=
∆
∆
x
t
=
2
8
7
.6
4
5
m
s
= 31.7 m/s to the north
p = mv
p
avg
= mv
avg
= (50.0 kg)(31.7 m/s) = 1.58 × 10
3
kg
•
m/s to the north
Momentum and Collisions
150. m = 1.46 × 10
5
kg
p = 9.73 × 10
5
kg
•
m/s to
the south
v =
m
p
=
v = 6.66 m/s to the south
9.73 × 10
5
kg
•
m/s
1.46 × 10
5
kg
151. v = 255 km/s
p = 8.62 × 10
36
kg
•
m/s
m =
p
v
= = 3.38 × 10
31
kg
8.62 × 10
36
kg
•
m/s
255 × 10
3
m/s
152. m = 5.00 g
v
i
= 255 m/s to the right
v
f
= 0 m/s
∆t = 1.45 s
∆p = mv
f
− mv
i
= F∆t
F == =−0.879 N
F = 0.879 N to the left
(5.00 × 10
−3
kg)(0 m/s) − (5.00 × 10
−3
kg)(255 m/s)
1.45 s
mv
f
− mv
i
∆t
153. m = 0.17 kg
∆v =−9.0 m/s
g = 9.81 m/s
2
m
k
= 0.050
F∆t =∆p = m∆v
F = F
k
=−mgm
k
∆t =
−
m
m
∆
gm
v
k
=
−
∆
gm
v
k
=
−(9.81
−9
m
.0
/s
m
2
)
/
(
s
0.050)
∆t = 18 s
154. v
i
= 382 km/h to the right
v
f
= 0 km/h
m
c
= 705 kg
m
d
= 65 kg
∆t = 12.0 s
F =
∆
∆
p
t
=
F =
F = = − 6.81 × 10
3
N
F = 6.81 × 10
3
N to the left
−(7.70 × 10
2
kg)(382 km/h)(10
3
m/km)(1 h/3600 s)
12.0 s
[(705 kg + 65 kg)(0 km/h) − (705 kg + 65 kg)(382 km/h)](10
3
m//km)(1 h/3600 s)
12.0 s
(m
c
+ m
d
)v
f
− (m
c
+ m
d
)v
i
∆t
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–25
155. v
i
= 382 km/h to the right
v
f
= 0 km/h
∆t = 12.0 s
∆x =
1
2
(v
i
+ v
f
)∆t =
1
2
(382 km/h + 0 km/h)(10
3
m/km)(1 h/3600 s)(12.0 s)
∆x = 637 m to the right
156. m
1
= 50.0 g
v
1, i
= 0 m/s
v
1, f
= 400.0 m/s forward
m
2
= 3.00 kg
v
2, i
= 0 m/s
Because the initial velocities for both rifle and projectile are zero, the momentum con-
servation equation takes the following form:
m
1
v
1, f
+ m
2
v
2, f
= 0
v
2, f
= = = −6.67 m/s
v
2, f
= 6.67 m/s backward
−(50.0 × 10
−3
kg)(400.0 m/s)
3.00 kg
−m
1
v
1, f
m
2
157. v
1, i
= 0 cm/s
v
1, f
= 1.2 cm/s forward
=+1.2 cm/s
v
2, i
= 0 cm/s
v
2, f
= 0.40 cm/s backward
=−0.40 cm/s
m
1
= 2.5 g
m
1
v
1, f
+ m
2
v
2, f
= 0
m
2
= =
m
2
= 7.5 g
−(2.5 g)(1.2 cm/s)
−0.40 cm/s
−m
1
v
1, f
v
2, f
158. m
s
= 25.0 kg
m
c
= 42.0 kg
v
1, i
= 3.50 m/s
v
2, i
= 0 m/s
v
f
= 2.90 m/s
m
1
= mass of child and sled = m
s
+ m
c
= 25.0 kg + 42.0 kg = 67.0 kg
m
1
v
1, i
+ m
2
v
2, i
= (m
1
+ m
2
)v
f
m
2
= =
m
2
===14 kg
40 kg
•
m/s
2.90 m/s
234 kg
•
m/s + 938 kg
•
m/s
2.90 m/s
(67.0 kg)(3.50 m/s) − (67.0 kg)(2.90 m/s)
2.90 m/s − 0 m/s
m
1
v
1, i
− m
1
v
f
v
f
− v
2, i
159. m
1
= 8500 kg
v
1, i
= 4.5 m/s to the
right =+4.5 m/s
m
2
= 9800 kg
v
2, i
= 3.9 m/s to the left
=−3.9 m/s
v
f
=
v
f
= =
v
f
= 0.0 m/s
3.8 × 10
4
kg
•
m/s − 3.8 × 10
4
kg
•
m/s
1.83 × 10
4
kg
(8500 kg)(4.5 m/s) + (9800 kg)(−3.9 m/s)
8500 kg + 9800 kg
m
1
v
1, i
+ m
2
v
2, i
m
1
+ m
2
160. m
1
= 8500 kg
v
1, i
= 4.5 m/s
m
2
= 9800 kg
v
2, i
=−3.9 m/s
v
f
= 0 m/s
KE
i
=
1
2
m
1
v
1, i
2
+
1
2
m
2
v
2, i
2
=
1
2
(8500 kg)(4.5 m/s)
2
+
1
2
(9800 kg)(−3.9 m/s)
2
KE
i
= 8.6 × 10
4
J + 7.5 × 10
4
J = 16.1 × 10
4
J = 1.61 × 10
5
J
KE
f
=
1
2
(m
1
+ m
2
)v
f
2
=
1
2
(8500 kg + 9800 kg)(0 m/s)
2
= 0 J
∆KE = KE
f
− KE
i
= 0 J − 1.61 × 10
5
J =−1.61 × 10
5
J
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–26
161. m
1
= 55 g
v
1, i
= 1.5 m/s
m
2
= 55 g
v
2, i
= 0 m/s
v
f
= = =
v
f
= 0.75 m/s
percent decrease of KE =×100 = × 100 =
− 1
× 100
KE
i
=
1
2
m
1
v
1, i
2
+
1
2
m
2
v
2, i
=
1
2
(55 × 10
−3
kg)(1.5 m/s)
2
+
1
2
(55 × 10
−3
kg)(0 m/s)
2
KE
i
= 6.2 × 10
−2
J + 0 J = 6.2 × 10
−2
J
KE
f
=
1
2
(m
1
+ m
2
)v
f
2
=
1
2
(55 g + 55 g)(10
−3
kg/g)(0.75 m/s)
3
KE
f
= 3.1 × 10
−2
J
percent decrease of KE =
− 1
× 100 = (0.50 − 1) × 100 = (−0.50) × 100
percent decrease of KE =−5.0 × 10
1
percent
3.1 × 10
−2
J
6.2 × 10
−2
J
KE
f
KE
i
KE
f
− KE
i
KE
i
∆KE
KE
i
(55 g)(1.5 m/s)
1.10 × 10
2
g
(55 g)(1.5 m/s) + (55 g)(0 m/s)
55 g + 55 g
m
1
v
1, i
+ m
2
v
2, i
m
1
+ m
2
162 m
1
= m
2
= 45 g
v
2, i
= 0 m/s
v
1, f
= 0 m/s
v
2, f
= 3.0 m/s
Momentum conservation
m
1
v
1, i
+ m
2
v
2, i
= m
1
v
1, f
+ m
2
v
2, f
v
1, i
= v
1, f
+ v
2, f
− v
2, i
= 0 m/s + 3.0 m/s − 0 m/s
v
1, i
=
Conservation of kinetic energy (check)
1
2
m
1
v
1, i
2
+
1
2
m
2
v
2, i
2
=
1
2
m
1
v
1, f
2
+
1
2
m
2
v
2, f
2
v
1, i
2
+ v
2, i
2
= v
1, f
2
+ v
2, f
2
(3.0 m/s)
2
+ (0 m/s)
2
= (0 m/s)
2
+ (3.0 m/s)
2
9.0 m
2
/s
2
= 9.0 m
2
/s
2
3.0 m/s
163. m = 5.00 × 10
2
kg
p = 8.22 × 10
3
kg
•
m/s to
the west
v =
m
p
=
v = 16.4 m/s to the west
8.22 × 10
3
kg
•
m/s
5.00 × 10
2
kg
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–27
164. m
1
= 3.0 × 10
7
kg
m
2
= 2.5 × 10
7
kg
v
2, i
= 4.0 km/h to the
north =+4.0 km/h
v
1, f
= 3.1 km/h to the
north =+3.1 km/h
v
2, f
= 6.9 km/h to the
south =−6.9 km/h
Momentum conservation
m
1
v
1, i
+ m
2
v
2, i
= m
1
v
1, f
+ m
2
v
2, f
v
1, i
=
v
1, i
=
v
1, i
==−6.0 km/h
v
1, i
=
Conservation of kinetic energy (check)
1
2
m
1
v
1, i
2
+
1
2
m
2
v
2, i
2
=
1
2
m
1
v
1, f
2
+
1
2
m
2
v
2, f
2
1
2
(3.0 × 10
7
kg)[(−6.0 × 10
3
m/h)(1 h/3600 s)]
2
+
1
2
(2.5 × 10
7
kg)[(4.0 × 10
3
m/h)(1 h/3600 s)]
2
=
1
2
(3.0 × 10
7
kg)[(3.1 × 10
3
m/h)(1 h/3600 s)]
2
+
1
2
(2.7 × 10
7
kg)[(−6.9 × 10
3
m/h)(1 h/3600 s)]
2
4.2 × 10
7
J + 1.5 × 10
7
J = 1.1 × 10
7
J + 4.6 × 10
7
J
5.7 × 10
7
J = 5.7 × 10
7
J
6.0 km/h to the south
−1.8 × 10
8
kg
•
km/h
3.0 × 10
7
kg
9.3 × 10
7
kg
•
km/h − 1.7 × 10
8
kg
•
km/h − 1.0 × 10
8
kg
•
km/h
3.0 × 10
7
kg
(3.0 × 10
7
kg)(3.1 km/h) + (2.5 × 10
7
kg)(−6.9 km/h) − (2.5 × 10
7
kg)(4.0 km/h)
3.0 × 10
7
kg
m
1
v
1, f
+ m
2
v
2, f
− m
2
v
2, i
m
1
165. m = 7.10 × 10
5
kg
v = 270 km/h
p = mv = (7.10 × 10
5
kg)(270 km/h)(10
3
m/km)(1 h/3600 s)
p = 5.33 × 10
7
kg
•
m/s
166. v = 50.0 km/h
p = 0.278 kg
•
m/s
m =
p
v
=
m = 2.00 × 10
−2
kg = 20.0 g
0.278 kg
•
m/s
(50.0 km/h)(10
3
m/km)(1 h/3600 s)
167. F = 75 N
m = 55 kg
∆t = 7.5 s
v
i
= 0 m/s
∆p = mv
f
− mv
i
= F∆t
v
f
=
F∆t
m
+ mv
i
=
v
f
= 1.0 × 10
1
m/s
(75 N)(7.5 s) + (55 kg)(0 m/s)
55 kg
168. m = 60.0 g
F =−1.5 N
∆t = 0.25 s
v
f
= 0 m/s
∆p = mv
f
− mv
i
= F∆t
v
i
=
mv
f
m
− F∆t
= =
v
i
= 6.2 m/s
(1.5 N)(0.25 s)
60.0 × 10
−3
kg
(60.0 × 10
−3
kg)(0 m/s) − (−1.5 N)(0.25 s)
60.0 × 10
−3
kg
169. m = 1.1 × 10
3
kg
v
f
= 9.7 m/s to the east
v
i
= 0 m/s
∆t = 19 s
F =
∆
∆
p
t
=
mv
f
∆
−
t
mv
i
F = = 560 N
F = 560 N to the east
(1.1 × 10
3
kg)(9.7 m/s) − (1.1 × 10
3
kg)(0 m/s)
19 s
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–28
170. m = 12.0 kg
F
applied
= 15.0 N
q = 20.0°
F
friction
= 11.0 N
v
i
= 0 m/s
v
f
= 4.50 m/s
F = F
applied
(cos q) − F
friction
∆t =
∆
F
p
= =
∆t ==
∆t = 17 s
54.0 kg
•
m/s
3.1 N
54.0 kg
•
m/s − 0 kg
•
m/s
14.1 N − 11.0 N
(12.0 kg)(4.50 m/s) − (12.0 kg)(0 m/s)
(15.0 N)(cos 20.0°) − 11.0 N
mv
f
− mv
i
F
applied
(cos q) − F
friction
171. v
i
= 7.82 × 10
3
m/s
v
f
= 0 m/s
m = 42 g
∆t = 1.0 × 10
−6
s
F ==
mv
f
∆
−
t
mv
i
F =
F =
F =−3.3 × 10
8
N
−(42 × 10
−3
kg)(7.82 × 10
3
m/s)
1.0 × 10
−6
s
(42 × 10
−3
kg)(0 m/s) − (42 × 10
−3
kg)(7.82 × 10
3
m/s)
1.0 × 10
−6
s
∆p
∆t
172. m = 455 kg
∆t = 12.2 s
m
k
= 0.071
g = 9.81 m/s
2
v
f
= 0 m/s
∆p = F∆t
F = F
k
=−mgm
k
∆p =−mgm
k
∆t =−(455 kg)(9.81 m/s
2
)(0.071)(12.2 s) =−3.9 × 10
3
kg
•
ms
∆p = 3.9 × 10
3
kg
•
ms opposite the polar bear’s motion
173. m = 455 kg
∆t = 12.2 s
m
k
= 0.071
g = 9.81 m/s
2
v
f
= 0 m/s
v
i
=
mv
f
m
−∆p
=
v
i
==8.6 m/s
∆x =
1
2
(v
i
+ v
f
)∆t =
1
2
(8.6 m/s + 0 m/s)(12.2 s)
∆x = 52 m
3.9 × 10
3
kg
•
ms
455 kg
(455 kg)(0 m/s) − (−3.9 × 10
3
kg
•
ms)
455 kg
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–29
174. m = 2.30 × 10
3
kg
v
i
= 22.2 m/s
v
f
= 0 m/s
F =−1.26 × 10
4
N
∆t =
∆
F
p
=
mv
f
−
F
mv
i
∆t = =
∆t = 4.06 s
−5.11 × 10
4
kg
•
m/s
−1.26 × 10
4
N
(2.30 × 10
3
kg)(0 m/s) − (2.30 × 10
3
kg)(22.2 m/s)
−1.26 × 10
4
N
175. v
1, i
= 0 m/s
v
2, i
= 5.4 m/s to the north
v
1, f
= 1.5 m/s to the north
v
2, f
= 1.5 m/s to the north
m
1
= 63 kg
m
1
v
1, i
+ m
2
v
2, i
= m
1
v
1, f
+ m
2
v
2, f
m
2
= = =
m
2
= 24 kg
(63 kg)(1.5 m/s)
3.9 m/s
(63 kg)(1.5 m/s) − (63 kg)(0 m/s)
5.4 m/s − 1.5 m/s
m
1
v
1, f
− m
1
v
1, i
v
2, i −
v
2, f
176. m
i
= 1.36 × 10
4
kg
m
2
= 8.4 × 10
3
kg
v
2, i
= 0 m/s
v
1, f
= v
2, f
= 1.3 m/s
m
1
v
1, i
+ m
2
v
2, i
= m
1
v
1, f
+ m
2
v
2, f
v
1, i
=
v
1, i
=
v
1, i
= =
v
1, i
= 2.1 m/s
2.9 × 10
4
kg
•
m/s
1.36 × 10
4
kg
1.8 × 10
4
kg
•
m/s + 1.1 × 10
4
kg
•
m/s
1.36 × 10
4
kg
(1.36 × 10
4
kg)(1.3 m/s) + (8.4 × 10
3
kg)(1.3 m/s) − (8.4 × 10
3
kg)(0 m/s)
1.36 × 10
4
kg
m
1
v
1,
f
+ m
2
v
2,
f
− m
2
v
2, i
m
1
177. m
i
= 1292 kg
v
i
= 88.0 km/h to the east
m
f
= 1255 kg
m
i
v
i
= m
f
v
f
v
f
=
m
m
i
v
f
i
=
v
f
= 90.6 km/h to the east
(1292 kg)(88.0 km/h)
1255 kg
178. m
1
= 68 kg
m
2
= 68 kg
v
2, i
= 0 m/s
v
1, f
= 0.85 m/s to the west
=−0.85 m/s
v
2, f
= 0.85 m/s to the west
=−0.85 m/s
m
1
v
1, i
+ m
2
v
2, i
= m
1
v
1, f
+ m
2
v
2, f
v
1, i
==
v
1, i
=−0.85 m/s + (−0.85 m/s) =−1.7 m/s
v
1, i
= 1.7 m/s to the west
(68 kg)(−0.85 m/s) + (68 kg)(−0.85 m/s) − (68 kg)(0 m/s)
68 kg
m
1
v
1, f
+ m
2
v
2, f
− m
2
v
2, i
m
i
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–30
179. m
1
= 1400 kg
v
1, i
= 45 km/h to the north
m
2
= 2500 kg
v
2, i
= 33 km/h to the east
v
f
=
The component of v
f
in the x-direction is given by
v
f, x
= = =
v
f, x
= 21 km/h
The component of v
f
in the y-direction is given by
v
f, y
== =
v
f, y
= 16 km/h
v
f
=
v
f
,x
2
+
v
f,
y
2
=
(2
1
km
/h
)
2
+
(
16
k
m
/h
)
2
v
f
=
44
0
km
2
/
h
2
+
2
60
k
m
2
/
h
2
=
7.
0
×
1
0
2
k
m
2
/
h
2
v
f
= 26 km/h
q = tan
−1
v
v
f
f
,
,
x
y
= tan
−1
1
2
6
1
k
k
m
m
/
/
h
h
= 37°
v
f
= 26 km/h at 37° north of east
(1400 kg)(45 km/h)
3900 kg
(1400 kg)(45 km/h)
1400 kg + 2500 kg
m
1
v
1, i
m
1
+ m
2
(2500 kg)(33 km/h)
3900 kg
(2500 kg)(33 km/h)
1400 kg + 2500 kg
m
2
v
2, i
m
1
+ m
2
m
1
v
1, i
+ m
2
v
2, i
m
1
+ m
2
180. m
1
= 4.5 kg
v
1, i
= 0 m/s
m
2
= 1.3 kg
v
f
= 0.83 m/s
v
2, i
= =
v
2, i
= = 3.7 m/s
KE
i
=
1
2
m
1
v
1, i
2
+
1
2
m
2
v
2, i
2
=
1
2
(4.5 kg)(0 m/s)
2
+
1
2
(1.3 kg)(3.7 m/s)
2
KE
i
= 0 J + 8.9 J = 8.9 J
KE
f
=
1
2
(m
1
+ m
2
)v
f
2
=
1
2
(4.5 kg + 1.3 kg)(0.83 m/s)
2
=
1
2
(5.8 kg)(0.83 m/s)
2
KE
f
= 2.0 J
∆KE = KE
f
− KE
i
= 2.0 J − 8.9 J =−6.9 J
(5.8 kg)(0.83 m/s)
1.3 kg
(4.5 kg + 1.3 kg)(0.83 m/s) − (4.5 kg)(0 m/s)
1.3 kg
(m
1
+ m
2
)v
f
− m
1
v
1, i
m
2
181. m
1
= 0.650 kg
v
1, i
= 15.0 m/s to the right
=+15.0 m/s
m
2
= 0.950 kg
v
2, i
= 13.5 m/s to the left
=−13.5 m/s
v
f
==
v
f
= = = −1.91 m/s
v
f
= 1.91 m/s to the left
KE
i
=
1
2
m
1
v
1, i
2
+
1
2
m
2
v
2, i
2
=
1
2
(0.650 kg)(15.0 m/s)
2
+
1
2
(0.950 kg)(−13.5 m/s)
2
KE
i
= 73.1 J + 86.6 J = 159.7 J
KE
f
=
1
2
(m
1
+ m
2
)v
f
2
=
1
2
(0.650 kg + 0.950 kg)(1.91 m/s)
2
=
1
2
(1.600 kg)(1.91 m/s)
2
KE
f
= 2.92 J
∆KE = KE
f
− KE
i
= 2.92 J − 159.7 J =−1.57 × 10
2
J
−3.0 kg
•
m/s
1.600 kg
9.75 kg
•
m/s − 12.8 kg
•
m/s
1.600 kg
(0.650 kg)(15.0 m/s) + (0.950 kg)(−13.5 m/s)
0.650 kg + 0.950 kg
m
1
v
1, i
+ m
2
v
2, i
m
1
+ m
2
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–31
182. m
1
= 10.0 kg
m
2
= 2.5 kg
v
1,i
= 6.0 m/s
v
2,i
=−3.0 m/s
v
f
=
m
1
v
m
1,
1
i
+
+
m
m
2
2
v
2,i
=
v
f
===4.2 m/s
52 kg
•
m/s
12.5 kg
6.0 × 10
1
kg
•
m/s − 7.5 kg
•
m/s
12.5 kg
(10.0 kg)(6.0 m/s) + (2.5 kg)(−3.0 m/s)
10.0 kg + 2.5 kg
183. v
1, i
= 6.00 m/s to the right
=+6.00 m/s
v
2, i
= 0 m/s
v
1, f
= 4.90 m/s to the left
=−4.90 m/s
v
2, f
= 1.09 m/s to the right
=+1.09 m/s
m
2
= 1.25 kg
Momentum conservation
m
1
v
1, i
+ m
2
v
2, i
= m
1
v
1, f
+ m
2
v
2, f
m
1
= = =
m
1
=
Conservation of kinetic energy (check)
1
2
m
1
v
1, i
2
+
1
2
m
2
v
2, i
2
=
1
2
m
1
v
1, f
2
+
1
2
m
2
v
2, f
2
1
2
(0.125 kg)(6.00 m/s)
2
+
1
2
(1.25 kg)(0 m/s)
2
=
1
2
(0.125 kg)(−4.90 m/s)
2
+
1
2
(1.25 kg)(1.09 m/s)
2
2.25 J + 0 J = 1.50 J + 0.74 J
2.25 J = 2.24 J
The slight difference arises from rounding.
0.125 kg
1.36 kg
•
m/s
10.90 m/s
(1.25 kg)(1.09 m/s) − (1.25 kg)(0 m/s)
6.00 m/s − (−4.90 m/s)
m
2
v
2, f
− m
2
v
2, i
v
1, i
− v
1, f
184. m
1
= 2150 kg
v
1,i
= 10.0 m/s to the east
m
2
= 3250 kg
v
f
= 5.22 m/s to the east
v
2,i
=
v
2,i
=
v
2,i
=
v
2,i
==
v
2,i
= 2.1 m/s to the east
6700 kg
•
m/s
3250 kg
2.82 × 10
4
kg
•
m/s − 2.15 × 10
4
kg
•
m/s
3250 kg
(5.40 × 10
3
kg)(5.22 m/s) − (2150 kg)(10.0 m/s)
3250 kg
(2150 kg + 3250 kg)(5.22 m/s) − (2150 kg)(10.0 m/s)
3250 kg
(m
1
+ m
2
)v
f
− m
1
v
1,i
m
2
185. m
1
= 2150 kg
v
1,i
= 10.0 m/s to the east
m
2
= 3250 kg
v
f
= 5.22 m/s to the east
v
2,i
= 2.1 m/s to the east
∆KE = KE
f
− KE
i
KE
i
=
1
2
m
1
v
1,i
2
+
1
2
m
2
v
2,i
2
=
1
2
(2150 kg)(10.0 m/s)
2
+
1
2
(3250 kg)(2.1 m/s)
2
KE
i
= 1.08 × 10
5
J + 7.2 × 10
3
J = 1.15 × 10
5
J
KE
f
=
1
2
(m
1
+ m
2
)v
f
2
=
1
2
(2150 kg + 3250 kg)(5.22 m/s)
2
KE
f
=
1
2
(5.40 × 10
3
kg)(5.22 m/s)
2
= 7.36 × 10
4
J
∆KE = KE
f
− KE
i
= 7.36 × 10
4
J − 1.15 × 10
5
J =−4.1 × 10
4
J
The kinetic energy decreases by .4.1 × 10
4
J
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–32
186. m
1
= 15.0 g
v
1,i
= 20.0 cm/s to the
right = +20.0 cm/s
m
2
= 20.0 g
v
2,i
= 30.0 cm/s to the left
= −30.0 cm/s
v
1,f
= 37.1 cm/s to the left
= −37.1 cm/s
v
2,f
=
v
2,f
=
v
2,f
=
v
2,f
==12.8 cm/s to the right
256 g
•
cm/s
20.0 g
3.00 × 10
2
g
•
cm/s − 6.00 × 10
2
g
•
cm/s + 5.56 × 10
2
g
•
cm/s
20.0 g
(15.0 g)(20.0 cm/s) + (20.0 g)(−30.0 cm/s) − (15.0 g)(−37.1 cm/s)
20.0 g
m
1
v
1,i
+ m
2
v
2,i
− m
1
v
1,f
m
2
187. v
1, i
= 5.0 m/s to the
right =+5.0 m/s
v
2, i
= 7.00 m/s to the
left =−7.00 m/s
v
f
= 6.25 m/s to the left
=−6.25 m/s
m
2
= 150.0 kg
m
1
==
m
1
= =
m
1
= 9.8 kg
−110 kg
•
m/s
−11.2 m/s
−1050 kg
•
m/s + 938 kg
•
m/s
−11.2 m/s
(150.0 kg)(−7.00 m/s) − (150.0 kg)(−6.25 m/s)
−6.25 m/s − 5.0 m/s
m
2
v
2, i
− m
2
v
f
v
f
− v
1, i
188. m
1
= 6.5 × 10
12
kg
v
1
= 420 m/s
m
2
= 1.50 × 10
13
kg
v
2
= 250 m/s
Conservation of Momentum gives:
m
1
v
1i
+ m
2
v
2i
= (m
1
+ m
2
)v
f
v
f
=
The change in Kinetic Energy is:
∆KE = KE
f
− KE
i
=
1
2
(m
1
+ m
2
)v
f
2
−
1
2
m
1
v
1i
2
+
1
2
m
2
v
2f
2
2∆KE = (m
1
+ m
2
)
2
− (m
1
v
1i
2
+ m
2
v
2i
2
)
(m
1
+ m
2
)2∆KE = m
1
2
v
1i
2
+ 2m
1
m
2
v
1i
v
2i
+ m
2
2
v
2i
2
− (m
1
+ m
2
)m
1
v
1i
2
+ (m
1
+ m
2
)m
2
v
2i
2
2(m
1
+ m
2
)∆KE = 2m
1
m
2
v
1i
v
2i
− m
1
m
2
v
1i
2
− m
1
m
2
v
2i
2
2(m
1
+ m
2
)∆KE = −m
1
m
2
(v
1i
2
− 2v
1i
v
2i
+ v
2i
2
) = −m
1
m
2
(v
1i
− v
2i
)
2
∆KE = −
1
2
(v
1i
− v
2i
)
2
∆KE = −
1
2
(420 m/s − 250 m/s)
2
∆KE = −
1
2
(170 m/s)
2
= −6.6 × 10
16
kg
•
m
2
/s
2
∆KE =−6.6 × 10
16
J
(6.5 × 10
12
kg)(1.50 × 10
13
kg)
2.15 × 10
13
kg
(6.5 × 10
12
kg)(1.50 × 10
13
kg)
6.5 × 10
12
kg + 1.50 × 10
13
kg
m
1
m
2
m
1
+ m
2
m
1
v
1i
+ m
2
v
2i
m
1
+ m
2
m
1
v
1i
+ m
2
v
2i
m
1
+ m
2
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–33
189. m
1
= 7.00 kg
v
1, i
= 2.00 m/s to the east
(at 0°)
m
2
= 7.00 kg
v
1, i
= 0 m/s
v
1, f
= 1.73 m/s at 30.0°
north of east
Momentum conservation
In the x-direction:
m
1
v
1, i
(cos q
1, i
) + m
2
v
2, i
(cos q
2, i
) = m
1
v
1, f
(cos q
1, f
) + m
2
v
2, f
(cos q
2, f
)
v
2, f
(cos q
2, f
) = v
1, i
(cos q
1, i
) + v
2, i
(cos q
2, i
) − v
i, f
(cos q
1, f
)
v
2, f
(cos q
2, f
) = (2.00 m/s)(cos 0°) + 0 m/s − (1.73 m/s)(cos 30.0°)
v
2, f
= 2.00 m/s − 1.50 m/s = 0.50 m/s
In the y-direction:
m
1
v
1, i
(sin q
1, i
) + m
2
v
2, i
(sin q
2, i
) = m
1
v
1, f
(sin q
1, i
) m
2
v
2, f
(sin q
2, f
)
v
2, f
(sin q
2, f
) = v
1, i
(sin q
1, i
) + v
2, i
(sin q
2, i
) − v
2, f
(sin q
2, f
)
v
2, f
(sin q
2, f
) = (2.00 m/s)(sin 0°) + 0 m/s − (1.73 m/s)(sin 30.0°) =−0.865 m/s
=
tan q
2, f
=−1.7
q
2, f
= tan
−1
(−1.7) = (−6.0 × 10
1
)°
v
2, f
= = 1.0 m/s
v
2, f
=
Conservation of kinetic energy (check)
1
2
m
1
v
1, i
2
+
1
2
m
2
v
2, i
2
=
1
2
m
i
v
1, f
2
+
1
2
m
2
v
2, f
2
1
2
(7.00 kg)(2.00 m/s)
2
+
1
2
(7.00 kg)(0 m/s)
2
=
1
2
(7.00 kg)(1.73 m/s)
2
+
1
2
(7.00 kg)(1.0 m/s)
2
14.0 J + 0 J = 10.5 J + 3.5 J
14.0 J = 14.0 J
1.0 m/s at (6.0 × 10
1
)° south of east
0.50 m/s
cos(−6.0 × 10
1
)°
− 0.865 m/s
0.50 m/s
v
2, f
(sin q
2, f
)
v
2, f
(cos q
2, f
)
190. m
1
= 2.0 kg
v
1, i
= 8.0 m/s
v
2, i
= 0 m/s
v
1, f
= 2.0 m/s
m
1
v
1, i
+ m
2
v
2, i
= m
1
v
1, f
+ m
2
v
2, f
1
2
m
1
v
1, i
2
+
1
2
m
2
v
2, i
2
=
1
2
m
1
v
1, f
2
+
1
2
m
2
v
2, f
2
m
2
=
1
2
m
1
v
1, i
2
+
1
2
v
2, i
2
=
1
2
m
1
v
1, f
2
+
1
2
v
2, f
2
v
1, i
2
(v
2, i
- v
2, f
) + (v
1, f
- v
1, i
)v
2, i
2
= v
1, f
2
(v
2, i
- v
2, f
) + (v
1, f
- v
1, i
)v
2, f
2
(v
1, i
2
v
2, i
+ v
1, f
v
2, i
2
- v
1, i
v
2, i
2
- v
1, f
2
v
2, i
+ v
2, f
(v
1, f
2
- v
1, i
2
) = v
2, f
2
(v
1, f
- v
1, i
)
Because v
2, i
= 0, the above equation simplifies to
v
1, f
2
− v
1, i
2
= v
2, f
(v
1, f
− v
1, i
)
v
2, f
= v
1, f
+ v
1, i
= 2.0 m/s + 8.0 m/s = 10.0 m/s
m
2
= = =
m
2
= 1.2 kg
−12 kg
•
m/s
−10.0 m/s
4.0 kg
•
m/s − 16 kg
•
m/s
−10.0 m/s
(2.0 kg)(2.0 m/s) − (2.0 m/s)(8.0 m/s)
0 m/s − 10.0 m/s
m
1
v
1, f
− m
1
v
1, i
v
2, i
− v
2, f
m
1
v
1, f
− m
1
v
1, i
v
2, i
− v
2, f
m
1
v
1, f
− m
1
v
1, i
v
2, i
− v
2, f
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–34
191. r = 3.81 m
v
t
= 124 m/s
a
c
=
v
r
t
2
=
(1
3
2
.
4
81
m
m
/s)
2
= 4.04 × 10
3
m/s
2
Givens Solutions
Circular Motion and Gravitation
192. v
t
= 75.0 m/s
a
c
= 22.0 m/s
2
r =
v
a
t
c
2
=
(7
2
5
2
.
.
0
0
m
m
/
/
s
s
)
2
2
= 256 m
193. r = 8.9 m
a
c
= (20.0) g
g = 9.81 m/s
2
v
t
=
ra
c
=
(8
.9
m
)(
20
.0
)(
9.
81
m
/s
2
)
= 42 m/s
194. m = 1250 kg
v
t
= 48.0 km/h
r = 35.0 m
F
c
= m
v
r
t
2
= (1250 kg)
F
c
= 6350 kg
•
m/s
2
= 6350 N
[(48.0 km/h)(1000 m/km)(1h/3600 s)]
2
35.0 m
195. F
c
= 8.00 × 10
2
N
r = 0.40 m
v
t
= 6.0 m/s
m =
F
v
t
c
2
r
= = 8.9 kg
(8.00 × 10
2
N)(0.40 m)
(6.0 m/s)
2
196. m = 7.55 × 10
13
kg
v
t
= 0.173 km/s
F
c
= 505 N
r =
m
F
v
c
t
2
= = 4.47 × 10
15
m
(7.55 × 10
13
kg)(0.173 × 10
3
m/s)
2
505 N
197. m = 2.05 × 10
8
kg
r = 7378 km
F
c
= 3.00 × 10
9
N
v
t
=
F
m
c
r
=
v
t
= 1.04 × 10
4
m/s = 10.4 km/s
(3.00 × 10
9
N)(7378 × 10
3
m)
2.05 × 10
8
kg
198. m
1
= 0.500 kg
m
2
= 2.50 × 10
12
kg
r = 10.0 km
G = 6.673 × 10
−11
N
•
m
2
kg
2
F
g
= G
m
r
1
m
2
2
=
6.673 × 10
−11
= 8.34 × 10
−7
N
(0.500 kg)(2.50 × 10
12
kg)
(10.0 × 10
3
m)
2
N
•
m
2
kg
2
199. F
g
= 1.636 × 10
22
N
m
1
= 1.90 × 10
27
kg
r = 1.071 × 10
6
km
G = 6.673 × 10
−11
N
•
m
2
kg
2
m
2
== =1.48 × 10
23
kg
(1.636 × 10
22
N)(1.071 × 10
9
m)
2
6.673 × 10
−11
(1.90 × 10
27
kg)
F
g
r
2
Gm
1
N
•
m
2
kg
2
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–35
200. m
1
= 1.00 kg
m
2
= 1.99 × 10
30
kg
F
g
= 274 N
G = 6.673 × 10
−11
N
•
m
2
kg
2
r =
G
m
F
1
g
m
2
=
= 6.96 × 10
8
m
6.673 × 10
−11
N
k
•
g
m
2
2
(1.00 kg)(1.99 × 10
30
kg)
274 N
201. m
1
= 1.00 kg
m
2
= 3.98 × 10
31
kg
F
g
= 2.19 × 10
−3
N
G = 6.673 × 10
−11
N
•
m
2
kg
2
r =
G
m
F
1
g
m
2
=
= 1.10 × 10
12
m
6.673 × 10
−11
N
k
•
g
m
2
2
(1.00 kg)(3.98 × 10
31
kg)
2.19 × 10
−3
N
202. m = 8.6 × 10
25
kg
r = 1.3 × 10
5
km
= 1.3 × 10
8
m
G = 6.673 × 10
−11
N
•
m
2
/kg
2
T = 2p
= 2p
=
T = 1.2 × 10
5
s
36
1
0
h
0s
= 34 h
1.2 × 10
5
m
(1.3× 10
8
m)
3
6.673 × 10
−11
(8.6 × 10
25
kg)
r
3
Gm
203. m = 8.6 × 10
25
kg
r = 1.3 × 10
5
km
= 1.3 × 10
8
m
G = 6.673 × 10
−11
N
•
m
2
/kg
2
v
t
=
G
r
m
=
v
t
= 6.6 × 10
3
m/s = 6.6 km/s
6.673 × 10
−11
N
k
•
g
m
2
2
(8.6 × 10
25
kg)
(1.3 × 10
8
m)
204. F
max
= 2.27 × 10
5
N
•
m
r = 0.660 m
d =
1
2
r
t
max
= F
max
d =
F
m
2
ax
r
t
max
= = 7.49 × 10
4
N
•
m
(2.27 × 10
5
N
•
m)(0.660 m)
2
205. t = 0.46 N
•
m
F = 0.53 N
q = 90°
d =
F(si
t
n q)
=
d = 0.87 m
0.46 N
•
m
(0.53 N)(sin 90°)
206. m = 6.42 × 10
23
kg
T = 30.3 h
G = 6.673 × 10
−11
N
•
m
2
/kg
2
r =
3
=
3
r =
3
1.29 ×
10
22
m
3
= 2.35 × 10
7
m = 2.35 × 10
4
km
6.673 × 10
−11
N
k
•
g
m
2
2
(6.42 × 10
23
kg)[(30.3 h)(3600 s/h)]
2
4p
2
GmT
2
4p
2
207. d = 1.60 m
t = 4.00 × 10
2
N
•
m
q = 80.0°
F =
d(si
t
n q)
=
F = 254 N
4.00 × 10
2
N • m
(1.60 m)(sin 80.0°)
208. r = 11 m
v
t
= 1.92 × 10
−2
m/s
a
c
=
v
r
t
2
=
(1.92 ×
1
1
1
0
m
−2
m/s)
2
= 3.4 × 10
−5
m/s
2
N
•
m
2
kg
2
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–36
209. v
t
= 0.35 m/s
a
c
= 0.29 m/s
2
r =
v
a
t
c
2
=
(0
0
.
.
3
2
5
9
m
m
/
/
s
s
)
2
2
= 0.42 m = 42 cm
210. a
c
= g = 9.81 m/s
2
r = 150 m
v
t
=
ra
c
=
(1
50
m
)(
9.
81
m
/s
2
)
= 38 m/s
211. r = 0.25 m
v
t
= 5.6 m/s
m = 0.20 kg
F
c
= m
v
r
t
2
= (0.20 kg)
(5
0
.6
.2
m
5m
/s)
2
= 25 N
212. m = 1250 kg
r = 35.0 m
θ
= 9.50°
g = 9.81 m/s
2
µ
k
= 0.500
F = F
f
+ mg(sin
θ
) =
µ
k
F
n
+ mg(sin
θ
) =
µ
k
mg(cos
θ
) + mg(sin
θ
)
F = (0.500)(1250 kg)(9.81 m/s
2
)(cos 9.50°) + (1250 kg)(9.81 m/s
2
)(sin 9.50°)
F = 6.05 × 10
3
N + 2.02 × 10
3
N
F =
Fc = F = 8.07 × 10
3
N
v
t
=
F
m
c
r
=
v
t
= 15.0 m/s = 54.0 km/h
(8.07 × 10
3
N)(35.0 m)
1250 kg
8.07 × 10
3
N
213. F
g
= 2.77 × 10
−3
N
r = 2.50 × 10
−2
m
m
1
= 157 kg
G = 6.673 × 10
−11
N
•
m
2
kg
2
m
2
== =165 kg
(2.77 × 10
−3
N)(2.50 × 10
−2
m)
2
6.673 × 10
−11
(157 kg)
F
g
r
2
Gm
1
214. m
1
= 2.04 × 10
4
kg
m
2
= 1.81 × 10
5
kg
r = 1.5 m
G = 6.673 × 10
−11
N
•
m
2
kg
2
F
g
= G
m
r
1
m
2
2
=
6.673 × 10
−11
= 0.11 N
(2.04 × 10
4
kg)(1.81 × 10
5
kg)
(1.5 m)
2
N
•
m
2
kg
2
215. r = 3.56 × 10
5
km
= 3.56 × 10
8
m
m = 1.03 × 10
26
kg
G = 6.673 × 10
−11
N
•
m
2
/kg
2
T = 2π
= 2π
T = 5.09 × 10
5
s
36
1
0
h
0s
= 141 h
(3.56 × 10
8
m)
3
6.673 × 10
−11
N
k
•
g
m
2
2
(1.03 × 10
26
kg)
r
3
Gm
216. r = 3.56 × 10
5
km
= 3.56 × 10
8
m
m = 1.03 × 10
26
kg
G = 6.673 × 10
−11
N
•
m
2
/kg
2
v
t
=
G
r
m
=
v
t
= 4.39 × 10
3
m/s = 4.39 km/s
6.673 × 10
−11
N
k
•
g
m
2
2
(1.03 × 10
26
kg)
(3.56 × 10
8
m)
N
•
m
2
kg
2
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–37
217. m = 1.0 × 10
26
kg
T = 365 days
G = 6.673 × 10
−11
N
•
m
2
/kg
2
r =
3
=
3
r = 5.5 × 10
9
m = 5.5 × 10
6
km
(6.673 × 10
−11
N
•
m
2
/kg
2
)(1.0 × 10
26
kg)[(365 days)(24 h/day)(3600 s/h)]
2
4p
2
GmT
2
4p
2
218. t = 1.4 N
•
m
d = 0.40 m
q = 60.0°
F =
d(si
t
n q)
=
F = 4.0 N
1.4 N
•
m
(0.40 m)(sin 60.0°)
219. F = 4.0 N
d = 0.40 m
t
max
is produced when q = 90°,or
t
max
= Fd = (4.0 N)(0.40 m) = 1.6 N
•
m
220. t = 8.25 × 10
3
N
•
m
F = 587 N
q = 65.0°
d =
F(si
t
n q)
=
(5
8
8
.2
7
5
N
×
)
1
(s
0
i
3
n
N
65
•
.0
m
°)
d = 15.5 m
221. r
gasoline
= 675 kg/m
3
V
s
= 1.00 m
3
g = 9.81 m/s
2
F
B
= F
g
r
ga
r
so
s
line
=
m
r
s
s
g
r
gasoline
= V
s
g r
gasoline
F
B
= (1.00 m
3
)(9.81 m/s
2
)(675 kg/m
3
) = 6.62 × 10
3
N
Fluid Mechanics
222. r
r
= 2.053 × 10
4
kg/m
3
V
r
= (10.0 cm)
3
g = 9.81 m/s
2
apparent weight = 192 N
F
B
= F
g
− apparent weight
F
B
= m
r
g − apparent weight = r
r
V
r
g − apparent weight
F
B
= (2.053 × 10
4
kg/m
3
)(10.0 cm)
3
(10
−2
m/cm)
3
(9.81 m/s
2
) − 192 N = 201 N − 192 N
F
B
= 9 N
223. m
h
= 1.47 × 10
6
kg
A
h
= 2.50 × 10
3
m
2
r
sw
= 1.025 × 10
3
kg/m
3
g = 9.81 m/s
2
F
B
= F
g
= m
h
g
F
B
= (1.47 × 10
6
kg)(9.81 m/s
2
) = 1.44 × 10
7
N
volume of hull submerged = V
sw
=
m
r
s
s
w
w
=
r
m
sw
h
h =
V
A
s
h
w
=
A
h
m
r
h
sw
h = = 0.574 m
1.47 × 10
6
kg
(2.50 × 10
3
m
2
)(1.025 × 10
3
kg/m
3
)
224. A = 1.54 m
2
P = 1.013 × 10
3
Pa
F = PA = (1.013 × 10
3
Pa)(1.54 m
2
) = 1.56 × 10
3
N
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–38
225. P = 1.50 × 10
6
Pa
F = 1.22 × 10
4
N
A =
P
F
=
1
1
.
.
5
2
0
2
×
×
1
1
0
0
6
4
P
N
a
= 8.13 × 10
−3
m
2
226. h = 760 mm
r = 13.6 × 10
3
kg/m
3
g = 9.81 m/s
2
P =
A
F
=
m
A
g
=
m
A
g
h
h
=
m
V
gh
= rgh
P = (13.6 × 10
3
kg/m
3
)(9.81 m/s
2
)(760 × 10
−3
m) = 1.0 × 10
5
Pa
227. V = 166 cm
3
apparent weight = 35.0 N
r
w
= 1.00 × 10
3
kg/m
3
g = 9.81 m/s
2
F
g
= F
B
+ apparent weight
r
osmium
Vg = r
w
Vg + apparent weight
r
osmium
= r
w
+
appare
V
nt
g
weight
r
osmium
= 1.00 × 10
3
kg/m
3
+
r
osmium
= 1.00 × 10
3
kg/m
3
+ 2.15 × 10
4
kg/m
3
r
osmium
= 2.25 × 10
4
kg/m
3
35.0 N
(166 cm
3
)(10
−6
m
3
/cm
3
)(9.81 m/s
2
)
228. V = 2.5 × 10
−3
m
3
apparent weight = 7.4 N
r
w
= 1.0 × 10
3
kg/m
3
g = 9.81 m/s
2
F
g
= F
B
+ apparent weight
r
ebony
V
g
= r
w
V
g
+ apparent weight
r
ebony
= r
w
+
appare
V
nt
g
weight
r
ebony
= 1.0 × 10
3
kg/m
3
+
= 1.0 × 10
3
kg/m
3
+ 3.0 × 10
2
kg/m
3
r
ebony
= 1.3 × 10
3
kg/m
3
7.4 N
(2.5 × 10
−3
m
3
)(9.81 m/s
2
)
229. m = 1.40 × 10
3
kg
h = 0.076 m
r
ice
= 917 kg/m
3
P
1
= P
2
A
F
1
1
=
A
F
2
2
m
A
1
g
=
m
A
ic
2
e
g
=
m
V
ic
i
e
c
h
e
g
= r
ice
hg
A
1
=
r
m
ice
h
= = 2.0 × 10
1
m
2
1.40 × 10
3
kg
(917 kg/m
3
)(0.076 m)
230. F
1
= 4.45 × 10
4
N
h
1
= 448 m
h
2
= 8.00 m
P
1
= P
2
A
F
1
1
=
A
F
2
2
A
F
1
1
h
h
1
1
=
F
1
V
h
1
=
A
F
2
2
h
h
2
2
=
F
2
V
h
2
F
2
=
F
h
1
h
2
1
=
F
2
= 2.49 × 10
6
N
(4.45 × 10
4
N)(448 m)
8.00 m
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–39
231. r
platinum
= 21.5 g/cm
3
r
w
= 1.00 g/cm
3
apparent weight = 40.2 N
g = 9.81 m/s
2
F
g
= F
B
+ apparent weight
mg = r
w
Vg + apparent weight = r
w
r
pla
m
tinum
g + apparent weight
mg
1 −
r
pla
r
t
w
inum
= apparent weight
m = =
m = =
m = 4.30 kg
40.2 N
(9.81 m/s
2
)(0.953)
40.2 N
(9.81 m/s
2
)(1 − 0.047)
40.2 N
(9.81 m/s
2
)
1 −
1
2
.
1
0
.
0
5
g
g
/
/
c
c
m
m
3
3
apparent weight
g
1 −
r
pla
r
t
w
inum
232. T
1
= 463 K
T
2
= 93 K
T
C,1
= (T − 273)°C = (463 − 273)°C =
T
C,2
= (T − 273)°C = (93 − 273)°C =−180 × 10
2
°C
1.90 × 10
2
°C
Heat
233. T
1
= 463 K
T
2
= 93 K
T
F,1
=
9
5
T
C,1
+ 32 =
9
5
(1.90 × 10
2
)°F + 32°F = 342°F + 32°F =
T
F,2
=
9
5
T
C,2
+ 32 =
9
5
(−1.80 × 10
2
)°F + 32°F =−324°F + 32°F =−292°F
374°F
234. T
F,i
=− 5 °F
T
F,f
=+ 37°F
T
C,i
=
5
9
(T
F, i
− 32)°C =
5
9
(−5 − 32)°C =
5
9
(− 37)°C =−21°C
T
C,f
=
5
9
(T
F, f
− 32)°C =
5
9
(37 − 32)°C =
5
9
(5)°C = 3°C
∆T = (T
C,f
+ 273 K) − (T
C,i
+ 273 K) = T
C,f
− T
C,i
∆T = [3 − (−21)] K = 24 K
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–40
235. h = 9.5 m
g = 9.81 m/s
2
∆U
acorn
= (0.85)∆U
k/m =
12
1
0
.0
0
°
J
C
/kg
∆PE +∆KE +∆U = 0
The change in kinetic energy from before the acorn is dropped to after it has landed
is zero, as is PE
f
.
∆PE +∆KE +∆U = PE
f
− PE
i
+ 0 +∆U =−PE
i
+∆U = 0
∆U = PE
i
= mgh
∆U
acorn
= (0.85) ∆U = (0.85)mgh
∆T =
∆U
k
acorn
=
(0.85
k
)mgh
=
(0
(
.
k
8
/
5
m
)g
)
h
∆T = = 6.6 × 10
−2
°C
(0.85)(9.81 m/s
2
)(9.5 m)
12
1
0
.
0
0°
J
C
/kg
236. v
f
= 0 m/s
v
i
= 13.4 m/s
∆U = 5836 J
∆PE +∆KE +∆U = 0
The bicyclist remains on the bicycle, which does not change elevation, so ∆PE = 0 J.
∆KE = KE
f
− KE
i
= 0 −
1
2
mv
i
2
=−∆U
m =
2
v
∆
i
2
U
=
(
(
1
2
3
)(
.4
58
m
36
/s)
J)
2
= 65.0 kg
237. v
i
= 20.5 m/s
v
f
= 0 m/s
m = 61.4 kg
∆PE +∆E +∆U = 0
The height of the skater does not change, so ∆PE = 0 J.
∆KE = KE
f
− KE
i
= 0 −
1
2
mv
i
2
∆U =−∆KF =−(−
1
2
mv
i
2
) =
1
2
(61.4 kg)(20.5 m/s)
2
= 1.29 × 10
4
J
238. m
t
= 0.225 kg
c
p,t
= 2.2 × 10
3
J/kg • °C
Q =−3.9 × 10
4
J
c
p,t
=
m
t
Q
∆T
t
∆T
t
=
m
Q
t
c
p,t
= = −79°C
−3.9 × 10
4
J
(0.225 kg)(2.2 × 10
3
J/kg • °C)
239. c
p,b
= 121 J/kg • °C
Q = 25 J
∆T
b
= 5.0°C
c
p,b
=
m
b
Q
∆T
b
m
b
=
c
p,b
Q
∆T
b
= = 4.1 × 10
−2
kg
25 J
(121 J/kg •°C)(5.0°C)
240. m
a
= 0.250 kg
m
w
= 1.00 kg
∆T
w
= 1.00° C
∆T
a
=−17.5° C
c
p,w
= 4186 J/kg • °C
−c
p,a
m
a
∆T
a
= c
p,w
m
w
∆T
w
c
pa
= − = −
c
p,a
= 957 J/kg • °C
(4186 J/kg • °C)(1.00 kg)(1.00°C)
(0.25 kg)(−17.5° C)
c
p,w
m
w
∆T
w
m
a
∆T
a
241. T
F
= 2192°F
T
C
=
5
9
(T
F
− 32)°C =
5
9
(2192 − 32)°C =
5
9
(2.160 × 10
3
)°C
T
C
= 1.200 × 10
3
°C
242. T = 2.70 K
T
C
= (T − 273)°C = (2.70 − 273)°C =−270°C
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–41
243. T = 42°C
T = (T + 273)K = (42 + 273) K = 315 K
244. ∆KE = 2.15 × 10
4
J
∆U
air
= 33%∆KE
∆PE = 0 J
∆PE +∆KE +∆U = 0
∆PE +∆KE −∆U
sticks
−∆U
air
= 0
∆U
sticks
=∆KE −∆U
air
=∆KE − 0.33∆KE = 0.67∆KE
∆U
sticks
= 0.667(2.15 × 10
4
J) = 1.4 × 10
4
J
245. h = 561.7 m
∆U = 105 J
g = 9.81 m/s
2
∆PE =∆KE +∆U = 0
When the stone lands, its kinetic energy is transferred to the internal energy of the
stone and the ground. Therefore, overall, ∆KE = 0 J
∆PE = PE
f
− PE
e
= 0 − mgh =−∆U
m =
∆
g
U
h
==1.91 × 10
−2
kg = 19.1 g
105 J
(9.81 m/s
2
)(561.7 m)
246. m = 2.5 kg
v
i
= 5.7 m/s
3.3 × 10
5
J melts 1.0 kg
of ice
∆U = KE
i
=
1
2
mv
i
2
=
1
2
(2.5 kg)(5.7 m/s)
2
= 41 J
ice melted =
(4
3
1
.3
J)
×
(1
1
.
0
0
5
k
J
g)
= 1.2 × 10
−4
kg
247. m
i
= 3.0 kg
m
w
= 5.0 kg
∆T
w
= 2.25° C
∆T
i
=−29.6° C
c
p,w
= 4186 J/kg • °C
−c
p,i
m
i
∆T
i
= c
p,w
m
w
∆T
w
c
p,i
=− = −
c
p,i
= 530 J/kg • °C
(4186 J/kg • °C)(5.0 kg)(2.25°C)
(3.0 kg)(−29.6°C)
c
p,w
m
w
∆T
w
m
i
∆T
i
248. Q = 45 × 10
6
J
∆T
a
= 55° C
c
p,a
= 1.0 × 10
3
J/kg • °C
c
p,a
=
m
a
Q
∆T
a
m
a
=
c
p,a
Q
∆T
a
=
a
= 820 kg
45 × 10
6
J
(1.0 × 10
3
J/kg • °C)(55°C)
249. c
p,t
= 140 J/kg • °C
m
t
= 0.23 kg
Q =−3.0 × 10
4
J
c
p,t
=
m
t
Q
∆T
t
∆T
t
=
m
Q
t
c
p,t
= = −930°C
−3.0 × 10
4
J
(0.23 kg)(140 J/kg • °C)
250. P = 2.07 × 10
7
Pa
∆V = 0.227 m
3
W = P ∆V = (2.07 × 10
7
Pa)(0.227 m
3
) = 4.70 × 10
6
J
Thermodynamics
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–42
251. W = 3.29 × 10
6
J
∆V = 2190 m
3
P =
∆
W
V
=
3.
2
2
1
9
9
×
0
1
m
0
3
6
J
= 1.50 × 10
3
Pa = 1.50 kPa
252. W = 472.5 J
P = 25.0 kPa = 2.50 × 10
4
Pa
∆V =
W
P
=
2.50
47
×
2
1
.5
0
4
J
Pa
= 1.89 × 10
−2
m
3
253. ∆U = 873 J
∆V = 0, so W = 0 J
∆U = Q − W
Q =∆U + W = 873 J + 0 J = 873 J
254. U
i
= 39 J
U
f
= 163 J
Q = 114 J
∆U = U
f
− U
i
= Q − W
W = Q −∆U = Q − (U
f
− U
i
) = Q − U
f
+ U
i
W = 114 J − 163 J + 39 J =−10 J
255. Q = 867 J
W = 623 J
∆U = Q − W = 867 J − 623 J = 244 J
256. eff = 0.29
Q
h
= 693 J
W
net
= eff Q
h
= (0.29)(693 J) = 2.0 × 10
2
J
257. eff = 0.19
W
net
= 998 J
Q
h
=
W
ef
n
f
et
=
9
0
9
.1
8
9
J
= 5.3 × 10
3
J
258. Q
h
= 571 J
Q
c
= 463 J
eff = 1 −
Q
Q
h
c
= 1 −
4
5
6
7
3
1
J
J
= 1 − 0.811 = 0.189
259. W = 1.3 J
∆V = 5.4 × 10
−4
m
3
P =
∆
W
V
=
5.4 ×
1
1
.3
0
−
J
4
m
3
= 2.4 × 10
3
Pa = 2.4 kPa
260. W = 393 J
P = 655 kPa = 6.55 × 10
5
Pa
∆V =
W
P
=
6.55
3
×
93
10
J
5
Pa
= 6.00 × 10
−4
m
3
261. U
i
= 8093 J
U
f
= 2.092 × 10
4
J
Q = 6932 J
∆U = U
f
− U
i
= Q − W
W = Q −∆U = Q − (U
f
− U
i
) = Q − U
f
+ U
i
W = 6932 J − 2.092 × 10
4
J + 8093 J =−5895 J
262. W = 192 kJ
∆U = 786 kJ
∆U = Q − W
Q =∆U + W = 786 kJ + 192 kJ = 978 kJ
263. Q = 632 kJ
W = 102 kJ
∆U = Q − W = 632 kJ − 102 kJ = 5.30 × 10
2
kJ = 5.30 × 10
5
J
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–43
264. eff = 0.35
Q
h
= 7.37 × 10
8
J
W
net
= eff Q
h
= (0.35)(7.37 × 10
8
J) = 2.6 × 10
8
J
265. eff = 0.11
W
net
= 1150 J
Q
h
=
W
ef
n
f
et
=
1
0
1
.
5
1
0
1
J
= 1.0 × 10
4
J
266. W
net
= 128 J
Q
h
= 581 J
eff =
W
Q
n
h
et
=
1
5
2
8
8
1
J
J
= 0.220
267. k = 420 N/m
x = 4.3 × 10
−2
m
F
elastic
=−kx =−(420 N/m)(4.3 × 10
−2
m) =−18 N
Vibrations and Waves
268. F
g
= –669 N
x = –6.5 × 10
−2
m
F
net
= 0 = F
elastic
+ F
g
=−kx + F
g
F
g
= kx
k =
F
x
g
=
–6.5
–6
×
6
1
9
0
N
−2
m
= 1.0 × 10
4
N/m
269. F
elastic
= 52 N
k = 490 N/m
F
elastic
=−kx
x = −
F
el
k
astic
= −
49
5
0
2
N
N
/m
= − 0.11 m = −11 cm
270. L = 1.14 m
T = 3.55 s
T = 2p
L
g
T
2
=
4p
g
2
L
g =
4p
T
2
2
L
=
(4p
(
2
3
)
.5
(1
5
.1
s)
4
2
m)
= 3.57 m/s
2
271. f = 2.5 Hz
g = 9.81 m/s
2
T = 2p
L
g
=
1
f
f
1
2
=
4p
g
2
L
L =
4p
g
2
f
2
=
(4p
9
2
.8
)(
1
2
m
.5
/
s
s
−
2
1
)
2
= 4.0 × 10
−2
m
272. L = 6.200 m
g = 9.819 m/s
2
T = 2p
L
g
= 2p
9.
6
8
.
1
2
9
00
m
m
/
s
2
= 4.993 s
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–44
273. L = 6.200 m
g = 9.819 m/s
2
f =
T
1
=
4.9
1
93 s
= 0.2003 Hz
274. k = 364 N/m
m = 24 kg
T = 2p
m
k
= 2p
36
2
4
4
N
k
g
/m
= 1.6 s
275. F = 32 N
T = 0.42 s
g = 9.81 m/s
2
F = mg
m =
F
g
=
9.8
3
1
2
m
N
/s
2
= 3.3 kg
T = 2p
m
k
T
2
=
4p
k
2
m
k =
4p
T
2
2
m
=
4
g
p
T
2
2
F
= = 730 N/m
4p
2
(32 N)
(9.81 m/s
2
)(0.42 s)
2
276. T = 0.079 s
k = 63 N/m
T = 2p
m
k
T
2
=
4p
k
2
m
m =
4
kT
p
2
2
=
(63 N/m
4
)
p
(
2
0.079 s)
2
= 1.0 × 10
−2
kg
277. f = 2.8 × 10
5
Hz
l = 0.51 cm = 5.1 × 10
−3
m
v = fl = (2.8 × 10
5
Hz)(5.1 × 10
−3
m) = 1.4 × 10
3
m/s
278. f = 20.0 Hz
v = 331 m/s
v = fl
l =
v
f
=
3
2
3
0
1
.0
m
H
/
z
s
= 16.6 m
279. l = 1.1 m
v = 2.42 × 10
4
m/s
v = fl
f =
l
v
=
2.42
1
×
.1
10
m
4
m/s
= 2.2 × 10
4
Hz
280. k = 65 N/m
x = –1.5 × 10
−1
m
F
elastic
=−kx =−(65 N/m)(–1.5 × 10
−1
m) = 9.8 N
281. F
g
= 620 N
x = 7.2 × 10
−2
m
F
net
= 0 = F
elastic
+ F
g
=−kx + F
g
F
g
= kx
k =
F
x
g
=
7.2
6
×
20
10
N
−2
m
= 8.6 × 10
3
N/m
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–45
282. m = 3.0 kg
g = 9.81 m/s
2
k = 36 N/m
F
net
= 0 = F
elastic
+ F
g
=−kx −mg
mg =−kx
x = −
m
k
g
= −
(3.0 k
3
g)
6
(
N
9.8
/m
1 m/s
2
)
= –0.82 m =−82 cm
283. L = 2.500 m
g = 9.780 m/s
2
T = 2p
L
g
= 2p
9.
2
7
.
8
5
0
00
m
m
/
s
2
= 3.177 s
284. f = 0.50 Hz
g = 9.81 m/s
2
T = 2p
L
g
=
1
f
f
1
2
=
4p
g
2
L
L =
4p
g
2
f
2
=
(4p
9
2
.
)
8
(
1
0.
m
50
/s
s
2
−1
)
2
= 0.99 m = 99 cm
285. k = 2.03 × 10
3
N/m
f = 0.79 Hz
T = 2p
m
k
=
1
f
f
1
2
=
4p
k
2
m
m =
4p
k
2
f
2
=
(
2
4
.
p
03
2
)
×
(0
1
.
0
7
3
9
N
H
/
z
m
)
2
= 82 kg
286. f = 87 N
T = 0.64 s
g = 9.81 m/s
2
k = m
2
T
p
2
=
g
f
2
T
p
2
=
9.8
8
1
7
m
N
/s
2
0.
2
6
p
4s
2
= 850 N/m
287. m = 8.2 kg
k = 221 N/m
T = 2p
m
k
= 2p
22
8
1
.
2
N
k
/
g
m
= 1.2 s
288. l = 10.6 m
v = 331 m/s
v = fl
f =
l
v
=
3
1
3
0
1
.6
m
m
/s
= 31.2 Hz
289. l = 2.3 × 10
4
m
f = 0.065 Hz
v = fl = (0.065 Hz)(2.3 × 10
4
m) = 1.5 × 10
3
m/s
I
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–46
290. P = 5.88 × 10
−5
W
Intensity = 3.9 × 10
−6
W/m
2
Intensity =
4p
P
r
2
r =
(4
p
)(
In
P
t
en
si
ty
)
=
r = 1.1 m
5.88 × 10
−5
W
(4p) (3.9 × 10
−6
W/m
2
)
Givens Solutions
Sound
291. P = 3.5 W
r = 0.50 m
Intensity =
4p
P
r
2
=
(4p)
3
(
.
0
5
.5
W
0m)
2
= 1.1 W/m
2
292. Intensity = 4.5 × 10
−4
W/m
2
r = 1.5 m
Intensity =
4p
P
r
2
P = 4pr
2
Intensity = (4p) (1.5 m)
2
(4.5 × 10
−4
W/m
2
)
P = 1.3 × 10
−2
W
293. n = 1
v = 499 m/s
L = 0.850 m
f
n
=
2
nv
L
f
1
=
(
(
1
2
)
)
(
(
4
0
9
.8
9
5
m
m
/s
)
)
= 294 Hz
294. n = 1
f
n
= f
1
= 392 Hz
v = 329 m/s
L = n
2
v
f
= (1) = 0.420 Hz
(329 m/s)
2(392 s
−1
)
295. n = 7
f
1
= 466.2 Hz
L = 1.53 m
f
n
=
4
nv
L
v =
4
n
Lf
n
= = 408 m/s
(4)(1.53 m)(466.2 Hz)
7
296. n = 1
f
1
= 125 Hz
L = 1.32 m
f
n
=
2
nv
L
v =
2L
n
f
n
= = 330 m/s
(2)(1.32 m)(125 Hz)
1
297. P = 1.57 × 10
−3
W
Intensity = 5.20 × 10
−3
W/m
2
Intensity =
4p
P
r
2
r =
(4
p
)(
In
P
t
en
si
ty
)
=
r = 0.155 m
1.57 × 10
−3
W
(4p)(5.20 × 10
−3
W/m
2
)
298. Intensity = 9.3 × 10
−8
W/m
2
r = 0.21 m
Intensity =
4p
P
r
2
P = 4pr
2
Intensity = (4p)(0.21 m)
2
(9.3 × 10
−8
W/m
2
)
P = 5.2 × 10
−8
W
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–47
299. n = 1
f
1
= 392.0 Hz
v = 331 m/s
f
n
=
4
nv
L
L =
4
n
f
v
n
=
(
(
4
1
)
)
(
(
3
3
9
3
2
1
.0
m
H
/s
z
)
)
= 0.211 m = 21.1 cm
300. n = 1
f
1
= 370.0 Hz
v = 331 m/s
f
n
=
2
nv
L
L =
2
n
f
v
n
=
(
(
2
1
)
)
(
(
3
3
7
3
0
1
.0
m
H
/s
z
)
)
= 0.447 m = 44.7 cm
301. f = 7.6270 × 10
8
Hz
l = 3.9296 × 10
−1
m
c = fl = (7.6270 × 10
8
s
−1
)(3.9296 × 10
−1
m) =
The radio wave travels through Earth’s atmosphere.
2.9971 × 10
8
m/s
Light and Reflection
302. l = 3.2 × 10
−9
m
f =
l
c
=
3
3
.0
.2
0
×
×
1
1
0
0
−
8
9
m
m
/s
= 9.4 × 10
16
Hz
303. f = 9.5 × 10
14
Hz
l =
c
f
=
3
9
.
.
0
5
0
×
×
1
1
0
0
1
8
4
m
s
−
/
1
s
= 3.2 × 10
−7
m = 320 nm
304. f = 17 cm
q = 23 cm
p
1
=
1
f
−
1
q
=
17
1
cm
−
23
1
cm
=
(
2
1
3
7
c
c
m
m)
−
(2
1
3
7
c
c
m
m
)
=
(17 cm
6
)
c
(
m
23 cm)
p = 65 cm
305. f = 17 cm
q = 23 cm
h = 2.7 cm
h′= −
q
p
h
=−
(23 cm
62
)(
c
2
m
.7 cm)
=−0.96 cm
306. f = 9.50 cm
q = 15.5 cm
p
1
=
1
f
−
1
q
=
9.5
1
cm
−
15.5
1
cm
= 0.105 cm
−1
− 0.0645 cm
−1
= 0.0405 cm
−1
p = 24.7 cm
307. h = 3.0 cm
h′=−
q
p
h
=−
(15.5 c
2
m
5
)
c
(
m
3.0 cm)
=−1.9 cm
308. h = 1.75 m
M = 0.11
q =−42 cm =−0.42 m
M =
h
h
′
=−
p
q
h′=Mh = (0.11)(1.75 m) = 0.19 m
309. M = 0.11
q =−42 cm =−0.42 m
p =−
M
q
=−
0.
0
4
.
2
11
m
= 3.8 m
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–48
310. f =−12 cm
q =−9.0 cm
p
1
=
1
f
−
1
q
=
−12
1
cm
−
−9.0
1
cm
=
0
1
.0
c
8
m
3
+
0
1
.1
c
1
m
1
=
0
1
.0
c
2
m
8
p = 36 cm
311. f =−12 cm
q =−9.0 cm
M =−
p
q
=−
9
3
.
6
0
c
c
m
m
= 0.25
312. p = 35 cm
q = 42 cm
1
f
=
p
1
+
1
q
=
R
2
=
35
1
cm
+
42
1
cm
1
f
=
0
1
.0
c
2
m
9
+
0
1
.0
c
2
m
4
=
0
1
.0
c
5
m
3
f = 19 cm
313. p = 35 cm
q = 42 cm
R
2
=
1
f
R = 2f = (2)(19 cm) = 38 cm
314. f = 60.0 cm
p = 35.0 cm
1
q
=
1
f
−
p
1
=
60.0
1
cm
−
35.0
1
cm
=
0
1
.0
c
1
m
67
−
0
1
.0
c
2
m
86
=
−0
1
.0
cm
119
q =−84.0 cm
315. q =−84.0 cm
p = 35.0 cm
M =−
p
q
=−
−
3
8
5
4
.0
.0
c
c
m
m
= 2.40
316. q =−5.2 cm
p = 17 cm
1
f
=
p
1
+
q
1
=
17
1
cm
+
−5.2
1
cm
=
0
1
.0
c
5
m
9
−
1
0.
c
1
m
9
=
−
1
0
c
.
m
13
f =−7.7 cm
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–49
317. q =−5.2 cm
p = 17 cm
h = 3.2 cm
h′=−
q
p
h
=−
(−5.2 c
1
m
7
)
c
(
m
3.2 cm)
= 0.98 cm
318. l = 5.291 770 × 10
−11
m
f =
l
c
= = 5.67 × 10
18
Hz
3.00 × 10
8
m/s
5.291 770 × 10
−11
m
319. f = 2.85 × 10
9
Hz
l =
c
f
=
3
2
.
.
0
8
0
5
×
×
1
1
0
0
8
9
m
s
−
/
1
s
= 0.105 m = 10.5 cm
320. f
1
= 1800 MHz = 1.8 × 10
9
Hz
f
2
= 2000 MHz = 2.0 × 10
9
Hz
l
1
=
f
c
1
=
3
1
.0
.8
0
×
×
1
1
0
0
9
8
s
m
−1
/s
= 0.17 m =
l
2
=
f
c
2
=
3
2
.0
.0
0
×
×
1
1
0
0
9
8
s
m
−1
/s
= 0.15 m = 15 cm
17 cm
321. f = 32.0 cm
You want to appear to be shaking hands with yourself, so the image must appear to
be where your hand is. So
p = q
1
f
=
p
1
+
1
q
=
p
2
p = 2f = (2)(32.0 cm) =
q = p = 64.0 cm
64.0 cm
322. p = 5.0 cm
A car’s beam has rays that are parallel, so q =∞.
1
q
=
∞
1
= 0
1
f
=
p
1
+
1
q
=
p
1
+ 0 =
p
1
f = p = 5.0 cm
R
2
=
p
1
+
1
q
=
1
f
R = 2 f = (2)(5.0 cm) = 1.0 × 10
1
cm
323. p = 19 cm
q = 14 cm
1
f
=
p
1
+
1
q
=
19
1
cm
+
14
1
cm
1
f
=
0
1
.0
c
5
m
3
+
0
1
.0
c
7
m
1
=
1
0.
c
1
m
2
f = 8.3 cm
324. f =−27 cm
p = 43 cm
1
q
=
1
f
−
p
1
=
−27
1
cm
−
43
1
cm
=
−
1
0.
c
0
m
37
−
0
1
.0
c
2
m
3
=
−
1
0.
c
0
m
60
q =−17 cm
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–50
325. q =−17 cm
p = 43 cm
M =−
p
q
= −
−
4
1
3
7
c
c
m
m
= 0.40
326. f =−8.2 cm
p = 18 cm
1
q
=
1
f
−
p
1
=
−8.2
1
cm
−
18
1
cm
=
−
1
0.
c
1
m
22
−
0
1
.0
c
5
m
6
=
−
1
0
c
.
m
18
q =−5.6 cm
327. f =−39 cm
p = 16 cm
1
q
=
1
f
−
p
1
=
−39
1
cm
−
16
1
cm
=
−
1
0.
c
0
m
26
−
0
1
.0
c
6
m
2
=
−
1
0.
c
0
m
88
q =−11 cm
328. h = 6.0 cm
M =
h
h
′
=−
p
q
h′=−
q
p
h
= −
(−11 c
1
m
6
)
c
(
m
6.0 cm)
= 4.1 cm
329. f = 1.17306 × 10
11
Hz
l = 2.5556 × 10
−3
m
c = fl = (1.17306 × 10
11
s
−1
)(2.5556 × 10
−3
m) = 2.9979 × 10
8
m/s
330. f = 2.5 × 10
10
Hz
l =
c
f
=
3
2
.
.
0
5
0
×
×
1
1
0
0
1
8
0
m
s
−
/
1
s
= 1.2 × 10
−2
m = 1.2 cm
331. p = 3.00 cm = 3.00 × 10
2
cm
f = 30.0 cm
1
q
=
1
f
−
p
1
=
30.0
1
cm
−
3.00 ×
1
10
2
cm
1
q
=
0
1
.0
c
3
m
33
−
0.
1
00
c
3
m
33
=
0
1
.0
c
3
m
00
q = 33.3 cm
332. f =−6.3 cm
q =−5.1 cm
p
1
=
1
f
−
1
q
=
−6.3
1
cm
−
−5.1
1
cm
=
0
1
.1
c
5
m
9
−
0
1
.1
c
9
m
6
=
0
1
.0
c
3
m
7
p = 27 cm
333. p = 27 cm
q =−5.1 cm
M =
−
p
q
=
−(−
2
5
7
.1
cm
cm)
= 0.19
334. q
r
= 35°
n
r
= 1.553
n
i
= 1.000
q
i
= sin
−1
n
r
(s
n
in
i
q
r
)
= sin
−1
(1.553
1
)
.0
(s
0
i
0
n 35°)
= 63°
Refraction
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–51
335. q
i
= 59.2°
n
r
= 1.61
n
i
= 1.00
q
r
= sin
−1
n
i
(s
n
in
r
q
i
)
= sin
−1
(1.00)(
1
s
.
i
6
n
1
59.2°)
= 32.2°
336. c = 3.00 × 10
8
m/s
v = 1.97 × 10
8
m/s
n =
v
c
=
3
1
.
.
0
9
0
7
×
×
1
1
0
0
8
8
m
m
/
/
s
s
= 1.52
337. f =−13.0 cm
M = 5.00
M =−
p
q
q =−Mp =−(5.00)p
1
f
=
p
1
+
1
q
=
p
1
+
−(5.
1
00)p
=
−5
−
.0
(5
0
.0
+
0
1
)p
.00
=
−(
−
5
4
.0
.0
0
0
)p
=
(5
4
.0
.0
0
0
)p
M =
h
h
′
=−
p
q
p =
(4
5
.
.
0
0
0
0
)f
=
(4.00)(
5
−
.0
1
0
3.0 cm)
=−10.4 cm
338. h = 18 cm
h′=−9.0 cm
f = 6.0 cm
M =
h
h
′
=
−
1
9
8
.0
c
c
m
m
=−0.50
339. h = 18 cm
h′=−9.0 cm
f = 6.0 cm
M =−
p
q
q =−Mp =−(−0.50)p = (0.50)p
1
f
=
p
1
+
1
q
=
p
1
+
(0.5
1
0)p
=
(0
0
.5
.5
0
0
)p
+
(0.5
1
0)p
=
(0
1
.5
.5
0
0
)p
=
3
p
.0
p = (3.0)f = (3.0)(6.0 cm) = 18 cm
340. M =−0.50
p = 18 cm
q =−Mp = (0.50)(18 cm) = 9.0 cm
341. q
c
= 37.8°
n
r
= 1.00
sin q
c
=
n
n
r
i
n
i
=
sin
n
r
q
c
=
sin
1.
3
0
7
0
.8°
= 1.63
342. n
i
- = 1.766
n
r
= 1.000
sin q
c
=
n
n
r
i
q
c
= sin
−1
n
n
r
i
= sin
−1
1
1
.
.
0
7
0
6
0
6
= 34.49°
343. n
i
= 1.576
n
r
= 1.000
sin q
c
=
n
n
r
i
q
c
= sin
−1
n
n
r
i
= sin
−1
1
1
.
.
0
5
0
7
0
6
= 39.38°
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–52
344. q
i
= 35.2°
n
i
= 1.00
n
r,1
= 1.91
n
r,2
= 1.66
q
r,1
= sin
−1
n
i
(s
n
i
r
n
,1
q
i
)
= sin
−1
(1.00)(
1
s
.
i
9
n
1
35.2°)
=
q
r,2
= sin
−1
n
i
(s
n
i
r
n
,2
q
i
)
= sin
−1
(1.00)(
1
s
.
i
6
n
6
35.2°)
= 20.3°
17.6°
345. q
r
= 33°
n
r
= 1.555
n
i
= 1.000
q
i
= sin
−1
n
r
(s
n
in
i
q
r
)
= sin
−1
(1.555
1
)
.0
(s
0
i
0
n 33°)
= 58°
346. q
c
= 39.18°
n
r
= 1.000
sin q
c
=
n
n
r
i
n
i
=
sin
n
r
q
c
=
sin
1.
3
0
9
0
.
0
18
= 1.583
347. p = 44 cm
q =−14 cm
h = 15 cm
1
f
=
p
1
+
1
q
=
44
1
cm
+
−14
1
cm
=
0
1
.0
c
2
m
3
+
0
1
.0
c
7
m
1
=
−
1
0
c
.0
m
48
f =−21 cm
348. p = 44 cm
q =−14 cm
h = 15 cm
M =
h
h
′
=−
p
q
h′=−
q
p
h
= −
(−14 c
4
m
4
)
c
(
m
15 cm)
= 4.8 cm
349. p = 4 m
f = 4 m
1
f
=
p
1
+
1
q
,but f = p, so
1
q
= 0. That means q = •
350. p = 4 m
f = 4 m
M =−
p
q
=−
4
•
m
=
The rays are parallel, and the light can be seen from very far away.
•
351. n
i
= 1.670
q
c
= 62.85°
sin q
c
=
n
n
r
i
n
r
= n
i
(sin q
c
) = (1.670)(sin 62.85°) = 1.486
352. c = 3.00 × 10
8
m/s
v = 2.07 × 10
8
m/s
n =
v
c
=
3
2
.
.
0
0
0
7
×
×
1
1
0
0
8
8
m
m
/
/
s
s
= 1.45
353. c = 3.00 × 10
8
m/s
v = 1.95 × 10
8
m/s
n =
v
c
=
3
1
.
.
0
9
0
5
×
×
1
1
0
0
8
8
m
m
/
/
s
s
= 1.54
354. p = 0.5 m
f = 0.5 m
1
f
=
p
1
+
1
q
p = f, so
1
q
= 0, and q = •
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–53
355. f = 3.6 cm
q = 15.2 cm
p
1
=
1
f
−
1
q
=
3.6
1
cm
−
15.2
1
cm
=
1
0.
c
2
m
8
−
0
1
.0
c
6
m
6
=
1
0.
c
2
m
1
p = 4.8 cm
356. q =−12 cm
f =−44 cm
p
1
=
1
f
−
1
q
=
−44
1
cm
−
−12
1
cm
=
−
1
0
c
.0
m
23
−
−
1
0.
c
0
m
83
=
0
1
.0
c
6
m
0
p = 17 cm
357. q
c,1
= 35.3°
q
c,2
= 33.1°
n
r
= 1.00
sin q
c
=
n
n
r
i
n
i,1
=
sin
n
q
r
c,1
=
sin
1.
3
0
5
0
.3°
=
n
i,2
=
sin
n
q
r
c,2
=
sin
1.
3
0
3
0
.1°
= 1.83
1.73
358. n
i
= 1.64
q
c
= 69.9°
sin q
c
=
n
n
r
i
n
r
= n
i
(sin q
c
) = (1.64)(sin 69.9°) = 1.54
359. l = 5.875 × 10
–7
m
m = 2
q = 0.130°
d =
s
m
in
l
q
= = 5.18 × 10
–4
m
d = 0.518 mm
2(5.875 × 10
–7
m)
sin (0.130°)
Interference and Diffraction
360. d = 8.04 × 10
–6
m
m = 3
q = 13.1 °
l =
d(s
m
in q)
= = 6.07 × 10
–7
m
l = 607 nm
(8.04 × 10
–6
m) sin (13.1°)
3
361. d = 2.20 × 10
–4
m
l= 5.27 × 10
–7
m
m = 1
q = sin
–1
(ml/d)
q = sin
–1
[(1)(5.27 × 10
–7
m) ÷ (2.20 × 10
–4
m)] = 0.137°
362. l= 5.461 × 10
–7
m
m = 1
q = 75.76°
d =
s
m
in
l
q
= = 5.634 × 10
–7
m
d = 5.634 × 10
–5
cm
# lines/cm = (5.634 × 10
–5
cm)
–1
= 1.775 × 10
4
lines/cm
(1)(5.461 × 10
–7
m)
sin (75.76°)
363. 3600 lines/cm
m = 3
q = 76.54°
l =
d(s
m
in q)
= = 9.0 × 10
−7
= 9.0 × 10
2
nm
(360 000 m)
–1
sin (76.54°)
3
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–54
364. 1950 lines/cm
l = 4.973 × 10
–7
m
m = 1
m = 1: q
1
= sin
–1
(ml/d)
q
1
= sin
–1
[(1)(4.973 × 10
–7
m) ÷ (195 000 lines/m)
–1
]
q
1
= 5.56°
365. 1950 lines/cm
l = 4.973 × 10
–7
m
m = 2
m = 1: q
1
= sin
–1
(ml/d)
m= 2: q
2
= sin
–1
[(2)(4.973 × 10
–7
m) ÷ (195 000 lines/m)
–1
]
q
2
= 11.2°
367. l = 430.8 nm
d = 0.163 mm
m = 1
q = sin
−1
= sin
−1
q = sin
−1
0.00396 =
0.227°
1+
1
2
(430.8 × 10
−9
nm)
0.163 × 10
−3
m
m+
1
2
l
d
366. d = 3.92 × 10
–6
m
m = 2
q = 13.1 °
l =
d(s
m
in q)
= = 4.44 × 10
–7
m
l = 444 nm
(3.92 × 10
–6
m) sin (13.1°)
2
368. l = 656.3 nm
m = 3
q = 0.548°
d ==
d = 2.40 ×
−4
m = 0.240 mm
3+
1
2
(656.3 × 10
−9
m)
sin 0.548°
m+
1
2
l
sin q
369. l = 4.471 × 10
–7
m
m = 1
q = 40.25°
d =
s
m
in
l
q
= = 6.920 × 10
–7
m
d = 6.920 × 10
–7
cm
# lines/cm = (6.920 × 10
–7
cm)
–1
=
1.445 × 10
4
lines/cm
(1)(4.471 × 10
–7
m)
sin (40.25°)
370. 9550 lines/cm
m = 2
q = 54.58°
l =
d(s
m
in q)
==
4.27 × 10
−7
m = 427 nm
(955 000 m)
–1
sin (54.58°)
2
371. q
1
=−5.3 µC =−5.3 × 10
−6
C
q
2
=+5.3 µC = 5.3 × 10
−6
C
r = 4.2 cm = 4.2 × 10
−2
m
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
F
electric
=
k
C
r
q
2
1
q
2
F
electric
=
F
electric
= 140 N attractive
(8.99 × 10
9
N
•
m
2
/C
2
)(5.3 × 10
−6
C)
2
(4.2 × 10
−2
m)
2
Electric Forces and Fields
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–55
372. q
1
=−8.0 × 10
−9
C
q
2
=+8.0 × 10
−9
C
r = 2.0 × 10
−2
m
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
F
electric
=
k
C
r
q
2
1
q
2
F
electric
=
F
electric
= 1.4 × 10
−3
N
(8.99 × 10
9
N
•
m
2
/C
2
)(−8.0 × 10
−9
C)(8.0 × 10
−9
C)
(2.0 × 10
−2
m)
2
373. r = 6.5 × 10
−11
m
F
electric
= 9.92 × 10
−4
N
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
F
electric
=
k
C
r
q
2
1
q
2
=
k
C
r
2
q
2
q =
F
el
e
k
c
t
C
ri
c
r
2
=
q = 2.2 × 10
−17
C
(9.92 × 10
−4
N)(6.5 × 10
−11
m)
2
8.99 × 10
9
N
•
m
2
/C
2
374. q
1
=−1.30 × 10
−5
C
q
2
=−1.60 × 10
−5
C
F
electric
= 12.5 N
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
F
electric
=
k
C
r
q
2
1
q
2
r =
k
F
C
el
q
ec
1
t
q
r
i
2
c
=
r = 0.387 m = 38.7 cm
(8.99 × 10
9
N
•
m
2
/C
2
)(−1.30 × 10
−5
C)(−1.60 × 10
−5
C)
12.5 N
375. q
1
= q
2
= q
3
= 4.00 × 10
−9
C
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
r
2,1
= r
2,3
= 4.00 m
F
12
=
k
C
r
q
2
1
q
2
= (8.99 × 10
9
N
•
m
2
/C
2
)
F
12
= 5.99 × 10
−9
N to the right, F
12
= 5.99 × 10
−9
N
F
23
= k
C
q
r
2
q
2
3
= (8.99 × 10
9
N
•
m
2
/C
2
)
F
12
= 5.99 × 10
−9
N to the left, F
23
=−5.99 × 10
−9
N
F
net
= F
12
+ F
23
= 5.99 × 10
−9
N − 5.99 × 10
−9
N = 0.00 N
(4.00 × 10
−9
C)
2
(4.00 m)
2
(4.00 × 10
−9
C)
2
(4.00 m)
2
376. q
p
= 1.60 × 10
−19
C
r
4,1
= r
2,1
= 1.52 × 10
−9
m
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
q
p
= q
1
= q
2
= q
3
= q
4
r
3,2
=
(1
.5
2
×
1
0
−
9
m
)
2
+
(
1.
52
×
1
0
−
9
m
)
2
= 2.15 × 10
−9
m
F
2,1
=
k
r
C
2
q
,1
p
2
2
= = 9.96 × 10
−11
N
F
3,1
=
k
r
C
3
q
,1
p
2
2
= = 4.98 × 10
−11
N
F
4,1
=
k
r
C
4
q
,1
2
2
p
= = 9.96 × 10
−11
N
j = tan
−1
1
1
.
.
5
5
2
2
×
×
1
1
0
0
−
−
9
9
m
m
= 45°
F
2,1
: F
x
= 0 N
F
y
= 9.96 × 10
−11
N
F
3,1
: F
x
= F
3,1
cos 45°=(4.98 × 10
−11
N)(cos 45°) = 3.52 × 10
−11
N
F
y
= F
3,1
sin 45°=(4.98 × 10
−11
N)(sin 45°) = 3.52 × 10
−11
N
F
4,1
: F
x
= 9.96 × 10
−11
N
F
y
= 0 N
(8.99 × 10
9
N
•
m
2
/C
2
)(1.60 × 10
−19
C)
2
(1.52 × 10
−9
m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(1.60 × 10
−19
C)
2
(2.15 × 10
−9
m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(1.60 × 10
−19
C)
2
(1.52 × 10
−9
m)
2
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–56
F
x,tot
= 0 N + 3.52 × 10
−11
+ 9.96 × 10
−11
= 1.35 × 10
−10
N
F
y,tot
= 9.96 × 10
−10
N + 3.52 × 10
−11
N + 0 N = 1.35 × 10
−10
N
F
tot
=
(F
x,tot
)
2
+ (F
y
,tot
)
2
=
(1.35 ×
10
−10
N)
2
+ (
1.35 ×
10
−10
N
)
2
F
tot
=
j = tan
−1
1
1
.
.
3
3
5
5
×
×
1
1
0
0
−
−
1
1
0
0
N
N
= 45.0°
1.91 × 10
−10
N
377. q
1
= q
2
= q
3
= 2.0 × 10
−9
C
r
1,2
= 1.0 m
r
1,3
=
(1
.0
m
)
2
+
(
2.
0
m
)
2
= 2.24 m
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
F
12
=
k
C
r
1
q
2
1
2
q
2
==3.6 × 10
−8
N
Components of F
12
: F
12,x
= 3.6 × 10
−8
N
F
12,y
= 0 N
F
13
=
k
C
r
1
q
3
1
2
q
3
==7.2 × 10
−8
N
j
13
= tan
−1
2
1
.
.
0
0
m
m
= 63°
Components of F
13
:
F
13,x
= F
13
cos q = (7.2 × 10
−9
N) cos (63.4°) = 3.2 × 10
−9
N
F
13,y
= F
13
sin q = (7.2 × 10
−9
N) sin (63.4°) = 6.4 × 10
−9
N
F
x,tot
= F
12,x
+ F
13,x
= 7.2 × 10
−8
N + 3.2 × 10
−9
N = 3.9 × 10
−8
N
F
y,tot
= F
12,y
+ F
13,y
= 0 N + 6.4 × 10
−9
N = 6.4 × 10
−9
N
F
tot
=
(F
x,tot
)
2
+ (F
y
,tot
)
2
=
(3.9 ×
10
−8
N
)
2
+ (6
.4 × 10
−9
N)
2
F
tot
=
j = tan
−1
F
F
x
y
.
.t
t
o
o
t
t
= tan
−1
6
3
.
.
4
9
×
×
1
1
0
0
−
−
9
8
N
N
= 9.3°
4.0 × 10
−8
N
(8.99 × 10
9
N
•
m
2
/C
2
)(2.0 × 10
−9
C)
2
(2.24 m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(2.0 × 10
−9
C)
2
(1.0 m)
2
378. q
1
= 7.2 nC
q
2
= 6.7 nC
q
3
=−3.0 nC
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
r
1,2
= 3.2 × 10
−1
m = 0.32 m
The charge, q
3
, must be between the charges to achieve electrostatic equilibrium.
F
1,3
+ F
1,2
=
k
C
x
q
2
1
q
3
−
(x −
k
C
0.
q
3
2
2
q
3
m)
2
= 0
(q
1
− q
2
)x
2
− (0.64 m)q
1
x + (0.32 m)
2
q
1
x = 0
x =
x = 16 cm
(0.64 m)(7.2 nC) ±
(0
.6
4
m
)
2
(
7.
2
n
C
)
2
−
4
(7
.2
n
C
−
6
.7
n
C
)(
0.
32
m
)
2
(7
.2
n
C
)
2(7.2 nC − 6.7 nC)
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–57
379. q
1
= 6.0 mC
q
2
=−12.0 mC
q
3
= 6.0 mC
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
r
1,0
= 5.0 × 10
−2
m
F
2,3
=−F
1,2
=
−k
r
C
1,
q
2
1
2
q
2
=
F
2,3
= 260 N
−(8.99 × 10
9
N
•
m
2
/C
2
)(6.0 × 10
−6
C)(−12.0 × 10
−6
C)
(5.0 × 10
−2
m)
2
380. E
x
= 9.0 N/C
q =−6.0 C
E
x
=
F
ele
q
ctric
F
electric
= E
x
q = (9.0 N/C)(−6.0 C)
F
electric
=−54 N in the −x direction
381. E = 4.0 × 10
3
N/C
F
electric
= 6.43 × 10
−9
N
E =
F
ele
q
ctric
q = =
4
6
.
.
0
43
×
×
10
1
3
0
−
N
9
/
N
C
= 1.6 × 10
−12
C
F
electric
E
382. q
1
= 1.50 × 10
−5
C
q
2
= 5.00 × 10
−6
C
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
r
1
= 1.00 m
r
2
= 0.500 m
E
1
= E
y,1
=
k
r
C
1
q
2
1
= = 1.35 × 10
5
N/C
E
2
= E
y,2
=
k
r
C
2
q
2
2
= = 1.80 × 10
5
N/C
E
y,tot
= E
tot
= 1.35 × 10
5
N/C + 1.80 × 10
5
N/C =
The electric field points along the y-axis.
3.15 × 10
5
N/C
(8.99 × 10
9
N
•
m
2
/C
2
)(5.00 × 10
−6
C)
(0.500 m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(1.50 × 10
−5
C)
(1.00 m)
2
383. q
1
= 9.99 × 10
−5
C
q
2
= 3.33 × 10
−5
C
F
electric
= 87.3 N
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
F
electric
=
k
C
r
q
2
1
q
2
r =
k
F
C
el
q
ec
1
t
q
r
i
2
c
=
r = 0.585 m = 58.5 cm
(8.99 × 10
9
N
•
m
2
/C
2
)(9.99 × 10
−5
C)(3.33 × 10
−5
C)
1
87.3 N
384. r = 9.30 × 10
−11
m
F
electric
= 2.66 × 10
−8
N
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
F
electric
=
k
C
r
q
2
1
q
2
=
k
C
r
2
q
2
q =
F
el
e
k
c
t
C
ri
c
r
2
=
q = 1.60 × 10
−19
C
(2.66 × 10
−8
N)(9.30 × 10
−11
m)
2
8.99 × 10
9
N
•
m
2
/C
2
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–58
385. q
1
=−2.34 × 10
−8
C
q
2
= 4.65 × 10
−9
C
q
3
= 2.99 × 10
−10
C
r
1,2
= 0.500 m
r
1,3
= 1.00 m
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
F
1,2
=
k
C
r
1
q
,2
1
2
q
2
=
F
1,2
= F
y
=−3.91 × 10
−6
N
F
1,3
=
k
C
r
1
q
,3
1
2
q
3
=
F
1,3
= F
y
=−6.29 × 10
−8
N
F
y,tot
=−3.91 × 10
−6
N +−6.29 × 10
−8
N = 3.97 × 10
−6
N
There are no x-components of the electrical force, so the magnitude of the electrical
force is
(F
y,t
ot
)
2
.
F
tot
= 3.97 × 10
−6
N upward
(8.99 × 10
9
N
•
m
2
/C
2
)(−2.34 × 10
−8
C)(2.99 × 10
−10
C)
(1.00 m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(−2.34 × 10
−8
C)(4.65 × 10
−9
C)
(0.500 m)
2
386. q
1
=−9.00 × 10
−9
C
q
2
=−8.00 × 10
−9
C
q
3
= 7.00 × 10
−9
C
r
1,2
= 2.00 m
r
1,3
= 3.00 m
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
F
1,2
=
k
C
r
1
q
,2
1
2
q
2
= = 1.62 × 10
−7
N
F
1,3
=
k
C
r
1
q
,3
1
2
q
3
= = −6.29 × 10
−8
N
F
1,2
: F
x
= 4.05 × 10
−8
N
F
y
= 0 N
F
1,3
: F
x
= 0 N
F
y
=−6.29 × 10
−8
N
F
tot
=
(1
.6
2
×
1
0
−
7
N
)
2
+
(
−
6.
29
×
1
0
−
8
N
)
2
=
F
tot
is negative because the larger, y-component of the force is negative.
j = tan
−1
−
1
6
.6
.2
2
9
×
×
1
1
0
0
−
−
7
8
N
N
=−21.2°
1.74 × 10
−7
N
(8.99 × 10
9
N
•
m
2
/C
2
)(−9.00 × 10
−9
C)(−7.00 × 10
−9
C)
(3.00 m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(−9.00 × 10
−9
C)(−8.00 × 10
−9
C)
(2.00 m)
2
387. q
1
=−2.5 nC
q
2
=−7.5 nC
q
3
= 5.0 nC
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
r
1,2
= 20.0 cm
The charge, q
3
, must be between the charges to achieve electrostatic equilibrium.
F
1,3
+ F
1,2
=
k
C
x
q
2
1
q
3
−
(x −
k
2
C
0
q
.
2
0
q
c
3
m)
2
= 0
(q
1
− q
2
)x
2
− (40.0 cm)q
1
x + (20.0 cm)
2
q
1
x = 0
x =
x = 7.3 cm
(40.0 cm)(−2.5 nC) ±
(4
0.
0
cm
)
2
(−
2.
5
n
C
)
2
−
4
(−
2.
5
n
C
+
7
.5
n
C
)(
20
.0
c
m
)
2
(−
2.
5
n
C
)
2(−2.5 nC + 7.5 nC)
388. q
1
=−2.3 C
q
3
=−4.6 C
r
1,2
= r
3,1
= 2.0 m
r
3,2
= 4.0 m
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
F
3,1
+ F
3,2
=
−k
r
C
3,
q
1
3
2
q
1
−
k
C
r
q
3,
3
2
q
2
= 0
q
2
=
−q
r
1
3
r
,
3
1
,2
2
2
=
−(−2.
(
3
2.
C
0
)
m
(4
)
.
2
0m)
2
= 9.2 C
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–59
389. E
y
= 1500 N/C
q = 5.0 × 10
−9
C
E
y
=
F
ele
q
ctric
F
electric
= E
y
q = (1500 N/C)(5.0 × 10
−9
C)
F
electric
= 7.5 × 10
−6
N in the +y direction
390. E = 1663 N/C
F
electric
= 8.4 × 10
−9
N
E =
F
ele
q
ctric
q = =
8.4
1
2
66
×
3
1
N
0
−
/C
9
N
= 5.06 × 10
−12
C
F
electric
E
391. q
q
= 3.00 × 10
−6
C
q
2
= 3.00 × 10
−6
C
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
r
1
= 0.250 m
r
2
=
(2
.0
0
m
)
2
+
(
2.
00
m
)
2
= 2.02 m
E
1
= E
y
= E
y
=
k
r
C
1
q
2
1
=
E
1
= E
y,1
= 4.32 × 10
5
N/C
E
2
=
k
r
C
2
q
2
2
= = 6.61 × 10
3
N/C
j = tan
−1
x
y
= tan
−1
0
2
.2
.0
5
0
0
m
m
= 7.12°
E
x,2
= E
2
cos 7.12°=(6.61 × 10
3
N/C)(cos 7.12°) = 6.56 × 10
3
N/C
E
y,2
= E
2
sin 7.12°=(6.61 × 10
3
N/C)(sin 7.12°) = 8.19 × 10
3
N/C
E
x,tot
= 0 N/C + 6.56 × 10
3
N/C = 6.56 × 10
3
N/C
E
y,tot
= 4.32 × 10
5
N/C + 8.19 × 10
3
N/C = 4.40 × 10
5
N/C
E
tot
=
(E
x,
to
t
2
+
(
E
y,t
ot
)
2
E
tot
=
(6
.5
6
×
1
0
3
N
/C
)
2
+
(
4.
40
×
1
0
5
N
/C
)
2
E
tot
=
tan j =
E
E
x
y,
,
t
t
o
o
t
t
=
4
6
.
.
4
5
0
6
×
×
1
1
0
0
5
3
N
N
/
/
C
C
j = 89.1°
4.40 × 10
5
N/C
(8.99 × 10
9
N
•
m
2
/C
2
)(3.00 × 10
−6
C)
(2.02 m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(3.00 × 10
−6
C)
(0.250 m)
2
392. q
1
=−1.6 × 10
−19
C
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
q
2
=−1.60 × 10
−19
C
q
3
= 1.60 × 10
−19
C
r
1
= 3.00 × 10
−10
m
r
2
= 2.00 × 10
−10
m
F
x,tot
=
k
C
r
2
q
1
+
k
r
C
2
q
2
2
+
k
C
x
2
q
3
= 0
q
1
= q
2
=−q
3
k
C
q
1
r
1
1
2
+
r
1
2
2
−
x
1
2
= 0
k
C
q
1
r
1
1
2
+
r
1
2
2
=
k
C
x
2
q
1
x
2
= =
x = 1.66 × 10
−10
m
1
(3.00 × 1
1
0
−10
m)
2
+
(2.00 × 1
1
0
−10
m)
1
r
1
1
2
+
r
1
2
2
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–60
393. q
1
=−7.0 C
x
1
= 0
q
2
= 49 C
x
2
= 18 m
x
3
= 25 m
To remain in equilibrium, the force on q
2
by q
1
(F
21
, which is in the negative direc-
tion) must equal the force on q
2
by q
3
(F
23
, which must be in the positive direction).
−
k
C
r
1
q
2
2
2
q
1
=
k
C
r
2
q
3
2
2
q
3
−
r
q
12
2
2
=
r
q
23
3
2
q
3
=−q
2
r
r
2
1
3
2
2
2
=−(49 C)
(
(
2
1
5
8
m
m
−
−
1
0
8
m
m
)
)
2
2
=−7.4 C
394. r = 8.3 × 10
−10
m
F
electric
= 3.34 × 10
−10
N
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
F
electric
=
k
C
r
q
2
1
q
2
=
k
C
r
2
q
2
q =
F
el
e
k
c
t
C
ri
c
r
2
=
q = 1.6 × 10
−19
C
(3.34 × 10
−10
N)(8.3 × 10
−10
N)
2
8.99 × 10
9
N
•
m
2
/C
2
395. r = 6.4 × 10
−8
m
F
electric
= 5.62 × 10
−14
N
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
F
electric
=
k
C
r
q
2
1
q
2
=
k
C
r
2
q
2
q =
F
el
e
k
c
t
C
ri
c
r
2
=
q = 1.6 × 10
−19
C
(5.62 × 10
−14
N)(6.4 × 10
−8
m)
2
8.99 × 10
9
N
•
m
2
C
2
396. q
e
=−1.60 × 10
−19
C
r
2,3
= r
4,3
= 3.02 × 10
−5
m
r
1,3
=
2(
3.
02
×
1
0
−
5
m
)
2
= 4.27 × 10
−5
m
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
q
e
= q
1
= q
2
= q
3
= q
4
F
3,2
= F
x
=
k
r
C
3
q
,2
2
2
e
= = 2.52 × 10
−19
N
F
3,4
= F
y
=
k
r
C
3
q
,4
e
2
2
= = 2.52 × 10
−19
N
F
3,1
=
k
r
C
3,
q
1
e
2
2
= = 1.26 × 10
−19
N
j = tan
−1
3
3
.
.
0
0
2
2
×
×
1
1
0
0
−
−
5
5
m
m
= 45°
F
3,1
: F
x
= F
3,1
cos 45°=(1.26 × 10
−19
N) cos 45°=8.91 × 10
−20
N
F
y
= F
3,1
sin 45°=(1.26 × 10
−19
N) sin 45°=8.91 × 10
−20
N
F
x,tot
= 8.91 × 10
−20
N + 2.52 × 10
−19
N + 0 N = 3.41 × 10
−19
N
F
y,tot
= 8.91 × 10
−20
N + 0 N + 2.52 × 10
−19
N = 3.41 × 10
−19
N
F
tot
=
(F
x,
to
t
)
2
+
(
F
y,t
ot
)
2
=
(3
.4
1
×
1
0
−
19
N
)
2
(
3.
41
×
1
0
−
19
N
)
2
F
tot
=
j = tan
−1
F
F
x
y
,
,
t
t
o
o
t
t
= tan
−1
3
3
.
.
4
4
1
1
×
×
1
1
0
0
−
−
1
1
9
9
N
N
= 45°
4.82 × 10
−19
N
(8.99 × 10
9
N
•
m
2
/C
2
)(−1.60 × 10
−19
C)
2
(4.27 × 10
−5
m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(−1.60 × 10
−19
C)
2
(3.02 × 10
−5
m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(−1.60 × 10
−19
C)
2
(3.02 × 10
−5
m)
2
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–61
397. q
1
= 5.5 nC
q
2
= 11 nC
q
3
=−22 nC
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
r
1,2
= 88 cm
The charge, q
3
, must be between the charges to achieve electrostatic equilibrium.
F
1,3
+ F
1,2
=
k
C
x
q
2
1
q
3
−
(x −
k
C
8
q
8
2
q
cm
3
)
2
= 0
(q
1
− q
2
)x
2
− (176 cm)q
1
x + (88 cm)
2
q
1
x = 0
x =
x = 36 cm
(176 cm)(5.5 nC) ±
(1
76
c
m
)
2
(5
.5
n
C
)
2
−
4
(5
.5
n
C
−
1
1
n
C
)(
88
c
m
)
2
(5
.5
n
C
)
2(5.5 nC − 11 nC)
398. q
1
= 72 C
q
3
=−8.0 C
r
1,2
= 15 mm = 1.5 × 10
−2
m
r
3,1
=−9.0 mm =−9.0 × 10
−3
m
r
3,2
= 2.4 × 10
−2
m
F
3,1
+ F
3,2
=
− k
r
C
3,
q
1
2
3
q
1
−
k
C
r
3
q
,2
3
2
q
2
= 0
q
2
=
−q
r
1
3
r
,1
3
2
,2
2
= = −512 C
−(72 C)(2.4 × 10
−2
m)
2
(−9.0 × 10
−3
m)
2
399. q = 1.45 × 10
−8
C
E = 105 N/C
d = 290 m
PE
electric
=−qEd =−(1.45 × 10
−8
C)(−105 N/C)(290 m)
PE
electric
= 4.4 × 10
−4
J
Electrical Energy and Current
400. PE
electric
=−1.39 × 10
11
J
E = 3.4 × 10
5
N/C
d = 7300 m
q =
−PE
E
e
d
lectric
=
q = 56 C
−(−1.39 × 10
11
J)
(3.4 × 10
5
N/C)(7300 m)
401. R = 6.4 × 10
6
m
C
sphere
=
k
R
c
=
8.99
6
×
.4
1
×
0
9
1
N
0
6
•m
m
2
/C
2
= 7.1 × 10
−4
F
402. C = 5.0 × 10
−13
F
∆V = 1.5 V
Q = C∆V = (5 × 10
−13
F)(1.5 V) = 7.5 × 10
−13
C
403. ∆Q = 76 C
∆t = 19 s
I =
∆
∆
Q
t
=
7
1
6
9
C
s
= 4.0 A
404. ∆Q = 98 C
I = 1.4 A
∆t =
∆
I
Q
=
1
9
.
8
4
C
A
= 70 s
405. I = 0.75 A
∆V = 120 V
R =
∆
I
V
=
0
1
.
2
7
0
5
V
A
= 1.6 × 10
2
Ω
406. ∆V = 120 V
R = 12.2 Ω
I =
∆
R
V
=
1
1
2
2
.
0
2
V
Ω
= 9.84 A
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–62
407. ∆V = 720 V
R = 0.30 Ω
P =
(∆V
R
)
2
=
(7
0
2
.3
0
0
V
Ω
)
2
= 1.7 × 10
6
W
408. ∆V = 120 V
P = 1750 W
R =
(∆V
P
)
2
=
(
1
1
7
2
5
0
0
V
W
)
2
= 8.23 Ω
409. q = 64 nC = 64 × 10
9
C
d = 0.95 m
∆PE
electric
= − 3.88 × 10
−5
J
E = −
∆PE
q
e
d
lectric
= −
E = 6.4 × 10
2
N/C
−3.88 × 10
−5
5 J
(64 × 10
9
C)(0.95)
410. q = − 14 nC = − 14 × 10
−9
C
E = 156 N/C
∆PE
electric
= 2.1 × 10
−6
J
d =
∆P
−
E
q
el
E
ectric
=
d = 0.96 m = 96 cm
2.1 × 10
−6
J
−(−14 × 10
−9
C)(156 N/C)
411. C = 5.0 × 10
−5
F
Q = 6.0 × 10
−4
C
∆V =
Q
C
=
6
5
.
.
0
0
×
×
1
1
0
0
−
−
4
5
C
F
= 12 V
412. Q = 3 × 10
−2
C
∆V = 30 kV
C =
∆
Q
V
=
3
3
0
×
×
1
1
0
0
−2
3
C
V
= 1 × 10
−6
F = 1 µF
413. A = 6.4 × 10
−3
m
2
C = 4.55 × 10
−9
F
d =
e
C
0
A
=
d = 1.2 × 10
−5
m
(8.85 × 10
−12
C
2
/N•m
2
)(6.4 × 10
−3
m
2
)
4.55 × 10
−9
F
414. C = 1.4 × 10
−5
F
∆V = 1.5 × 10
4
V
Q = C∆V = (1.4 × 10
−5
F)(1.5 10
4
V) = 0.21 C
415. ∆t = 15 s
I = 9.3 A
∆Q = I∆t = (9.3 A) (15 s) = 1.4 × 10
2
C
416. ∆Q = 1.14 × 10
−4
C
∆t = 0.36 s
I =
∆
∆
Q
t
=
1.14
0
×
.3
1
6
0
s
−4
C
= 0.32 mA
417. ∆Q = 56 C
I = 7.8 A
∆t =
∆
I
Q
=
7
5
.
6
8
C
A
= 7.2 s
418. ∆t = 2.0 min = 120 s
I = 3.0 A
∆Q = I∆t = (3.0 A) (120 s) = 3.6 × 10
2
C
419. I = 0.75 A
R = 6.4 Ω
∆V = IR = (0.75 A) (6.4 Ω) = 4.8 V
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–63
420. ∆V = 650 V
R = 1.0 × 10
2
Ω
I =
∆
R
V
=
1.0
6
×
50
10
V
2
Ω
= 6.5 A
421. I = 4.66 A
R = 25.0 Ω
∆V = IR = (4.66 A) (25.0 Ω) = 116 V
422. I = 0.545 A
∆V = 120 V
R =
∆
I
V
=
0
1
.5
2
4
0
5
V
A
= 220 Ω
423. ∆V = 2.5 × 10
4
V
I = 20.0 A
P = I∆V = (20.0 A) (2.5 × 10
4
V) = 5.0 × 10
5
W
424. P = 230 W
R = 91 Ω
I
2
=
R
P
I =
R
P
=
2
9
3
1
0
Ω
W
= 1.59 A
425. I = 8.0 × 10
6
A
P = 6.0 × 10
13
W
∆V =
P
I
=
6
8
.0
.0
×
×
1
1
0
0
1
6
3
A
W
= 7.5 × 10
6
V
426. P = 350 W
R = 75 Ω
I
2
=
R
P
I =
R
P
=
3
7
5
5
0
Ω
W
= 2.2 A
427. 25 speakers
R
each speaker
= 12.0 Ω
R
eq
=ΣR
each speaker
All speakers have equal resistance.
R
eq
= (25)(12.0 Ω) = 3.00 × 10
2
Ω
Circuits and Circuit Elements
428. 57 lights
R
each light
= 2.0 Ω
R
eq
=ΣR
each light
All lights have equal resistance.
R
eq
= (57)(2.0 Ω) = 114 Ω
429. R
1
= 39 Ω
R
2
= 82 Ω
R
3
= 12 Ω
R
4
= 22 Ω
∆V = 3.0 V
R
1
eq
=
R
1
1
+
R
1
2
+
R
1
3
+
R
1
4
=
39
1
Ω
+
82
1
Ω
+
12
1
Ω
+
22
1
Ω
R
1
eq
=
0
1
.0
Ω
26
+
0
1
.0
Ω
12
+
0
1
.0
Ω
83
+
0
1
.0
Ω
45
=
0
1
.1
Ω
7
R
eq
= 6.0 Ω
R
1
eq
=
R
1
1
+
R
1
2
+
R
1
3
+
R
1
4
=
33
1
Ω
+
39
1
Ω
+
47
1
Ω
+
68
1
Ω
R
1
eq
=
0
1
.0
Ω
30
+
0
1
.0
Ω
26
+
0
1
.0
Ω
21
+
0
1
.0
Ω
15
R
eq
= 11 Ω
430. R
1
= 33 Ω
R
2
= 39 Ω
R
3
= 47 Ω
R
4
= 68 Ω
V = 1.5 V
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–64
431. ∆V = 12 V
R
1
= 16 Ω
I = 0.42 A
R
2
=
∆
I
V
− R
1
=
0
1
.4
2
2
V
A
− 16 Ω=29 Ω−16 Ω= 13 Ω
432. ∆V = 3.0 V
R
1
= 24Ω
I = 0.062 A
R
2
=
∆
I
V
− R
1
=
0
3
.0
.0
62
V
A
− 24 Ω=48 Ω−24 Ω= 24 Ω
433. ∆V = 3.0 V
R
1
= 3.3 Ω
I = 1.41 A
∆V = IR
eq
I =
R
∆
e
V
q
=
∆
R
V
1
+
∆
R
V
2
∆
R
V
2
=
I −
∆
R
V
1
R
2
= = =
[1.41 A
3.0
−
V
0.91 A]
= 6.0 Ω
3.0 V
1.41 A −
3
3
.
.
3
0
Ω
V
∆V
I −
∆
R
V
1
434. ∆V = 12 V
R
1
= 56 Ω
I = 3.21 A
∆V = IR
eq
I =
R
∆
e
V
q
=
∆
R
V
1
+
∆
R
V
2
∆
R
V
2
=
I −
∆
R
V
1
R
2
= = = = 4.0 Ω
12 V
[3.21 A − 0.21 A]
12 V
3.21 A −
5
1
6
2
Ω
V
∆V
I −
∆
R
V
1
435. R
1
= 56 Ω
R
2
= 82 Ω
R
3
= 24 Ω
∆V = 9.0 V
R
eq
=ΣR = R
1
+ R
2
+ R
3
= 56Ω+82Ω+24Ω=162Ω
I =
R
∆
e
V
q
=
1
9
6
.0
2
V
Ω
= 56 mA
436. R
1
= 96 Ω
R
2
= 48 Ω
R
3
= 29 Ω
∆V = 115 V
R
eq
=ΣR = R
1
+ R
2
+ R
3
= 96 Ω+48 Ω+29 Ω=173 Ω
I =
R
∆
e
V
q
=
1
1
7
1
3
5
Ω
V
= 665 mA
437. ∆V = 120 V
R
1
= 75 Ω
R
2
= 91 Ω
I
1
=
R
V
1
I
2
=
R
V
2
I
1
=
1
7
2
5
0
Ω
V
= I
2
=
1
9
2
1
0
Ω
V
= 1.3 A1.6 A
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–65
438. ∆V = 120 V
R
1
= 82 Ω
R
2
= 24 Ω
I
1
=
R
V
1
I
2
=
R
V
2
I
1
=
1
8
2
2
0
Ω
V
= I
2
=
1
2
2
4
0
Ω
V
= 5.0 A1.5 A
439. R
1
= 1.5 Ω
R
2
= 6.0 Ω
R
3
= 5.0 Ω
R
4
= 4.0 Ω
R
5
= 2.0 Ω
R
6
= 5.0 Ω
R
7
= 3.0 Ω
Parallel:
Group (a):
R
e
1
q.a
=
R
1
2
+
R
1
3
=
6.0
1
Ω
+
5.0
1
Ω
=
5.0
30
+
Ω
6.0
R
eq,a
=
3
1
0
1.
Ω
0
= 2.7 Ω
Group (b):
R
e
1
q.a
=
R
1
5
+
R
1
6
=
2.0
1
Ω
+
5.0
1
Ω
=
5.0
10
+
Ω
2.0
R
eq,a
=
1
7
0
.0
Ω
= 1.4 Ω
Series:
R
eq
= R
1
+ R
eq,a
+ R
4
+ R
eq,b
+ R
7
= 1.5 Ω+2.7 Ω+4.0 Ω+1.4 Ω+3.0 Ω
R
eq
= 12.6 Ω
440. ∆V
tot
= 12.0 V
R
eq
= 12.6 Ω
I
tot
=
∆
R
V
e
t
q
ot
=
1
1
2
2
.
.
6
0
Ω
V
= 0.952 A
441. I
tot
= 0.952 A
R
2
= 6.0 Ω
R
3
= 5.0 Ω
R
e
1
q.a
=
R
1
2
+
R
1
3
=
6.0
1
Ω
+
5.0
1
Ω
=
5.0
30
+
Ω
6.0
R
eq,a
= 2.7 Ω
∆V
2
=∆V
a
= I
tot
R
eq,a
= (0.952 A)(2.7 Ω) = 2.6 V
442. ∆V
2
= 2.6 V
R
2
= 6.0 Ω
I
6
=
∆
R
V
2
2
=
6
2
.
.
0
6
Ω
V
= 0.43 A
443. R
1
= 3.0 Ω
R
2
= 5.0 Ω
R
3
= 5.0 Ω
R
4
= 5.0 Ω
R
5
= 5.0 Ω
R
6
= 5.0 Ω
R
7
= 5.0 Ω
R
8
= 3.0 Ω
Parallel:
R
e
1
q.a
=
R
1
2
+
R
1
3
+
R
1
4
=
5.0
1
Ω
+
5.0
1
Ω
+
5.0
1
Ω
= 3(0.20 Ω)
R
eq,a
= 1.7 Ω=R
eq,b
Series:
R
eq
= R
1
+ R
eq,a
+ R
8
+ R
eq,b
= 3.0 Ω+1.7 Ω+3.0 Ω+1.7 Ω
R
eq
= 9.4 Ω
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–66
444. ∆V
tot
= 15.0 V
R
eq
= 9.4 Ω
I
tot
=
∆
R
V
e
t
q
ot
=
1
9
5
.4
.0
Ω
V
= 1.6 A
445. I
tot
= 1.6 A
I
1
= I
tot
= 1.6 A
446. R
1
= 3.0 Ω
R
2
= 2.0 Ω
R
3
= 3.0 Ω
R
4
= 4.0 Ω
R
5
= 8.0 Ω
R
6
= 5.0 Ω
R
7
= 2.0 Ω
R
8
= 8.0 Ω
R
9
= 4.0 Ω
Parallel:
R
e
1
q.a
=
R
1
1
+
R
1
2
=
3.0
1
Ω
+
2.0
1
Ω
=
2.
6
0
.0
+
Ω
3.0
R
eq,a
=
6.
5
0
.0
Ω
= 1.2 Ω
R
e
1
q.b
=
R
1
4
+
R
1
5
=
4.0
1
Ω
+
8.0
1
Ω
=
8.0
32
+
Ω
4.0
R
eq,b
=
3
1
2
2.
Ω
0
= 2.7 Ω=R
eq,c
Series:
R
eq
= R
eq,a
+ R
3
+ R
eq,b
+ R
6
+ R
7
+ R
eq,c
R
eq
= 1.2 Ω+3.0 Ω+2.7 Ω+5.0 Ω+2.0 Ω + 2.7 Ω= 16.6 Ω
447. ∆V
tot
= 24.0 V
R
eq
= 16.6 Ω
I
tot
=
∆
R
V
e
t
q
ot
=
1
2
6
4
.
.
6
0
Ω
V
= 1.45 A
448. I
tot
= 1.45 A
R
4
= R
9
= 4.0 Ω
R
5
= R
8
= 8.0 Ω
I
tot
= I
4
+ I
5
I
5
= I
tot
− I
4
∆V
4
=∆V
5
I
4
R
4
= I
5
R
5
I
4
R
4
= (I
tot
− I
4
)R
5
I
4
(R
4
+ R
5
) = I
tot
R
5
I
4
= I
tot
R
4
R
+
5
R
5
= (1.45 A)
4.0 Ω
8.0
+
Ω
8.0 Ω
= (1.45 A)
1
8
2
.0
.0
= 0.97 A
449. q = 1.60 × 10
−19
C
B = 0.8 T
v = 3.0 × 10
7
m/s
F
magnetic
= qvB = (1.60 × 10
−19
C)(3.0 × 10
7
m/s)(0.8 T) = 4 × 10
−12
N
Magnetism
450. q = 1.60 × 10
−19
C
v = 3.9 × 10
6
m/s
F
magnetic
= 1.9 × 10
−22
N
B =
F
ma
q
g
v
netic
== 3.0 × 10
−10
T
1.9 × 10
−22
N
(1.60 × 10
−19
C)(3.9 × 10
6
m/s)
451. q = 1.60 × 10
−19
C
B = 5.0 × 10
−5
T
F
magnetic
= 6.1 × 10
−17
N
v =
F
m
q
ag
B
netic
== 7.6 × 10
6
m/s
6.1 × 10
−17
N
(1.60 × 10
−19
C)(5.0 × 10
−5
T)
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–67
452. I = 14 A
l
= 2 m
B = 3.6 × 10
−4
T
F
magnetic
= BI
l
= (3.6 × 10
−4
T)(14 A)(2 m) = 1 × 10
−2
N
453.
l
= 1.0 m
F
magnetic
= 9.1 × 10
−5
N
B = 1.3 × 10
−4
T
I == = 0.70 A
9.1 × 10
−5
N
(1.3 × 10
−4
T)(1.0 m)
F
magnetic
B
l
454. B = 4.6 × 10
−4
T
F
magnetic
= 2.9 × 10
−3
N
T = 10.0 A
l
=
F
ma
B
g
I
netic
==0.63 m
2.9 × 10
−3
N
(4.6 × 10
−4
T)(10.0 A)
455.
l
= 12 m
I = 12 A
F
magnetic
= 7.3 × 10
−2
N
B ==
(
7
1
.
2
3
A
×
)
1
(
0
1
−
2
2
m
N
)
= 5.1 × 10
−4
T
F
magnetic
I
l
456. q = 1.60 × 10
−19
C
v = 7.8 × 10
6
m/s
F
magnetic
= 3.7 × 10
−13
N
B =
F
ma
q
g
v
netic
== 0.30 T
3.7 × 10
−13
N
(1.60 × 10
−19
C)(7.8 × 10
6
m/s)
457. q = 1.60 × 10
−19
C
v = 2.2 × 10
6
m/s
B = 1.1 × 10
−2
T
F
magnetic
= qvB = (1.60 × 10
−19
C)(2.2 × 10
6
m/s)(1.1 × 10
−2
T) = 3.9 × 10
−15
N
458. B = 1 × 10
−8
T
q = 1.60 × 10
−19
C
F
magnetic
= 3.2 × 10
−22
N
v =
F
m
q
ag
B
netic
== 2 × 10
5
m/s
3.2 × 10
−22
N
(1.60 × 10
−19
C)(1 × 10
−8
T)
459.
l
= 10 m
m = 75 kg
B = 4.8 × 10
−4
T
g = 9.81 m/s
2
mg = BI
l
I == = 1.5 × 10
5
A
(75 kg)(9.81 m/s
2
)
(4.8 × 10
−4
T)(10 m)
mg
B
l
460. I = 1.5 × 10
3
A
l
= 15 km = 1.4 × 10
4
m
q = 45°
B = 2.3 × 10
−5
T
F
magnetic
= Bcos qI
l
= (2.3 × 10
−5
T)cos 45°(1.5 × 10
3
A)(1.5 × 10
4
m)
F
magnetic
= 3.7 × 10
2
N
461. N = 540 turns
A = 0.016 m
2
q
i
= 0°
q
f
= 90.0°
∆t = 0.05 s
emf = 3.0 V
B =
−N
em
A∆
f
c
∆
o
t
sq
=
B =
B = 1.7 × 10
−2
T
(3.0 V)(0.05 s)
−(540)(0.016 m
2
)[cos 90.0° − cos 0°]
emf ∆t
−NA[cosq
f
− cosq
i
]
Electromagnetic Induction
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–68
462. N = 550 turns
A = 5.0 × 10
−5
m
2
∆B = 2.5 × 10
−4
T
∆t = 2.1 × 10
−5
s
q = 0°
emf =
−NA∆
∆
B
t
cos q
emf
=
emf
= 0.33 V
−(550)(5.0 × 10
−5
m
2
)(2.5 × 10
−4
T)(cos 0°)
2.1 × 10
−5
s
463. N = 246 turns
A = 0.40 m
2
q = 0°
B
i
= 0.237 T
B
f
= 0.320 T
∆t = 0.9 s
emf = 9.1 V
∆t =
−NA∆
em
B
f
cos q
=
−NA[B
f
e
−
m
B
f
i
]cosq
∆t =
∆t = 0.90 s
−(246)(0.40 m
2
)[0.320 T − 0.237 T](cos 0°)
9.1 V
464. emf = 9.5 V
q
i
= 0.0°
q
f
= 90.0°
B = 1.25 × 10
−2
T
∆t = 25 ms
A = 250 cm
2
N =
−A∆
em
(B
f
c
∆
o
t
s q)
=
N =
N = 7.6 × 10
2
turns
(9.5 V)(25 × 10
−3
s)
−(250 cm
2
)(1.25 × 10
−2
T)(cos 90.0°−cos 0.0°)
emf ∆t
−AB(cos q
f
− cos q
i
)
465. ∆V
rms
= 320 V
R = 100 Ω
∆V
max
=
∆
0.
V
7
r
0
m
7
s
=
3
0
2
.7
0
0
V
7
= 450 V
466. ∆V
rms
= 320 V
R = 100 Ω
I
rms
=
∆V
R
rms
=
1
3
0
2
0
0
Ω
V
= 3 A
467. I
rms
= 1.3 A
I
max
=
0
I
.
r
7
m
0
s
7
=
0
1
.
.
7
3
0
A
7
= 1.8 A
468. ∆V
2
= 6.9 × 10
3
V
N
1
= 1400 turns
N
2
= 140 turns
∆V
1
=∆V
2
N
N
1
2
= (6.9 × 10
3
V)
1
1
4
4
0
0
0
= 6.9 × 10
4
V
469. ∆V
1
= 5600 V
N
1
= 140 turns
N
2
= 840 turns
∆V
2
=∆V
1
N
N
2
1
= (5600 V)
8
1
4
4
0
0
= 3.4 × 10
4
V
470. ∆V
1
= 1800 V
∆V
2
= 3600 V
N
1
= 58 turns
N
2
= N
1
∆
∆
V
V
2
1
= (58 turns)
1
3
8
6
0
0
0
0
V
V
= 29 turns
471. ∆V
1
= 4900 V
∆V
2
= 4.9 × 10
4
V
N
2
= 480 turns
N
1
= N
2
∆
∆
V
V
1
2
= (480)
4.9
49
×
0
1
0
0
V
4
V
= 48 turns
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–69
472. N = 320 turns
q
i
= 0.0°
q
f
= 90.0°
B = 0.046 T
∆t = 0.25 s
emf = 4.0 V
A =
−N
e
∆
m
(B
f
c
∆
o
t
s q)
=
A =
A = 6.8 × 10
−2
m
2
(4.0 V)(0.25 s)
−(320)(0.046 T)(cos 90.0°−cos 0.0°)
emf ∆t
−NB(cos q
f
− cos q
i
)
473. N = 180 turns
A = 5.0 × 10
−5
m
2
∆B = 5.2 × 10
−4
T
q = 0°
∆t = 1.9 × 10
−5
s
R = 1.0 × 10
2
Ω
emf =
−NA∆
∆
B
t
cos q
emf
=
emf
= 0.25 V
I =
em
R
f
=
1.0
0.
×
25
10
V
2
Ω
= 2.5 × 10
−3
A = 25 mA
−(180)(5.0 × 10
−5
m
2
)(5.2 × 10
−4
T)(cos 0°)
1.9 × 10
−5
s
474. I
max
= 1.2 A
∆V
max
= 211 V
∆V
rms
= 0.707 V
max
= 0.707(211 V) = 149 V
475. I
max
= 1.2 A
∆V
max
= 211 V
I
rms
= 0.707 I
max
= 0.707(1.2 A) = 0.85 A
476. V
max
= 170 V
∆V
rms
= 0.707 V
max
= 0.707(170 V) = 120 V
477. ∆V
1
= 240 V
∆V
2
= 5.0 V
N
N
1
2
=
∆
∆
V
V
1
2
=
2
5
4
.0
0
V
V
= 48:1
478. λ=527 nm = 5.27 × 10
−7
m
E = hf =
h
λ
c
= = 3.77 × 10
−19
J
(6.63 × 10
−34
J
•
s)(3.00 × 10
8
m/s)
5.27 × 10
−7
m
Atomic Physics
479. m
e
= 9.109 × 10
−31
kg
v = 2.19 × 10
6
m/s
λ=
m
h
v
= = 3.32 × 10
−10
m
6.63 × 10
−34
J
•
s
(9.109 × 10
−31
kg)(2.19 × 10
6
m/s)
480. E = 20.7 eV
f =
E
h
==5.00 × 10
15
Hz
(20.7 eV)(1.60 × 10
−19
J/eV)
6.63 × 10
−34
J
•
s
481. E = 12.4 MeV
E = 1.24 × 10
7
eV
λ=
h
E
c
= = 1.00 × 10
−13
m
(6.63 × 10
−34
J
•
s)(3.00 × 10
8
m/s)
(1.24 × 10
7
eV)(1.60 × 10
−19
J/eV)
482. λ=240 nm = 2.4 × 10
−7
m
hf
t
= 2.3 eV
KE
max
=
h
λ
c
− hf
t
KE
max
= − 2.3 eV
KE
max
= 5.2 eV − 2.3 eV = 2.9 eV
(6.63 × 10
−34
J
•
s)(3.00 × 10
8
m/s)
2.4 × 10
−7
m)(1.60 × 10
−19
J/eV)
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–70
483. hf
t
= 4.1 eV
λ=
h
E
c
= = 3.0 × 10
−7
m = 300 nm
(6.63 × 10
−34
J
•
s)(3.00 × 10
8
m/s)
(4.1 eV)(1.60 × 10
−19
eV)
484. l = 2.64 × 10
−14
m
m
p
= 1.67 × 10
−27
kg
v =
m
h
l
==1.50 × 10
7
m/s
6.63 × 10
−34
J
•
s
(1.67 × 10
−27
kg)(2.64 × 10
−14
m)
485. v = 28 m/s
λ=8.97 × 10
−37
m
m =
λ
h
v
==26 kg
6.63 × 10
−34
J
•
s
(8.97 × 10
−37
m)(28 m/s)
486. λ=430.8 nm
λ = 4.308 × 10
−7
m
E = hf =
h
λ
c
= = 4.62 × 10
−19
J
(6.63 × 10
−34
J
•
s)(3.00 × 10
8
m/s)
4.308 × 10
−7
m
487. E = 1.78 eV
f =
E
h
= = 4.30 × 10
14
Hz
(1.78 eV)(1.60 × 10
−19
J/eV)
6.63 × 10
−34
J
•
s
488. E = 3.1 × 10
−6
eV
λ=
h
E
c
= = 0.40 m
(6.63 × 10
−34
J
•
s)(3.00 × 10
8
m/s)
(3.1 × 10
−6
eV)(1.60 × 10
−19
J/eV)
489. f = 6.5 × 10
14
Hz
KE
max
= 0.20 eV
f
t
=
hf − K
h
E
max
f
t
=
f
t
= 6.0 × 10
14
Hz
[(6.63 × 10
−34
J
•
s)(6.5 × 10
14
Hz) − (0.20 eV)(1.60 × 10
−19
J/eV)]
6.63 × 10
−34
J
•
s
KE
max
=
h
λ
c
− hf
t
KE
max
= − 2.16 eV
KE
max
= 2.40 eV − 2.16 eV = 0.24 eV
(6.63 × 10
−34
J
•
s)(3.00 × 10
8
m/s)
(5.19 × 10
−7
m)(1.60 × 10
−19
J/eV)
490. λ=519 nm = 5.19 × 10
−7
m
hf
t
= 2.16 eV
491. v = 5.6 × 10
−6
m/s
λ=2.96 × 10
−8
m
m =
λ
h
v
==4.0 × 10
−21
kg
6.63 × 10
−34
J
•
s
(2.96 × 10
−8
m)(5.6 × 10
−6
m/s)
492. f
t
= 1.36 × 10
15
Hz
hf
t
= = 5.64 eV
(6.63 × 10
−34
J
•
s)(1.36 × 10
15
Hz)
1.60 × 10
−19
J/eV
493. m = 7.6 × 10
7
kg
v = 35 m/s
λ=
m
h
v
= = 2.5 × 10
−43
m
6.63 × 10
−34
J
•
s
(7.6 × 10
7
kg)(35 m/s)
494. hf
t
= 5.0 eV
λ=
h
E
c
= = 2.5 × 10
−7
m = 250 nm
(6.63 × 10
−34
J
•
s)(3.00 × 10
8
m/s)
(5.0 eV)(1.60 × 10
−19
eV)
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–71
495. f = 9.89 × 10
14
Hz
KE
max
= 0.90 eV
f
t
=
hf − K
h
E
max
f
t
=
f
t
= 7.72 × 10
14
Hz
(6.63 × 10
−34
J
•
s)(9.89 × 10
14
Hz) − (0.90 eV)(1.60 × 10
−19
J/eV)
6.63 × 10
−34
J
•
s
496. m
n
= 1.675 × 10
−27
kg
λ=5.6 × 10
−14
m
v =
m
h
λ
==7.1 × 10
6
m/s
6.63 × 10
−34
J
•
s
(1.675 × 10
−27
kg)(5.6 × 10
−14
m)
497. Z = 19
A = 39
atomic mass of K-39
= 38.963 708 u
atomic mass of H = 1.007 825 u
m
n
= 1.008 665 u
N = A − Z = 39 − 19 = 20
∆m = Z (atomic mass of H) + Nm
n
− atomic mass of K-39
∆m = 19(1.007 825) + 20 (1.008 665 u)–38.963 708 u
∆m = 19.148 675 u + 20.173 300 u − 38.963 708 u
∆m = 0.358 267 u
E
bind
= (0.358 267 u)(931.50 MeV/u) = 333.73 MeV
Subatomic Physics
498. For
107
47
Ag:
Z = 47
A = 107
atomic mass of Ag-107
= 106.905 091 u
atomic mass of H
= 1.007 825 u
m
n
= 1.008 665 u
For
63
29
Cu:
Z = 29
A = 63
atomic mass of Cu-63
= 62.929 599 u
N = A − Z = 107 − 47 = 60
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of Ag-107
∆m = 47(1.007 825 u) + 60(1.008 665 u) − 106.905 091 u
∆m = 47.367 775 u + 60.519 900 u − 106.905 091 u
∆m = 0.982 584 u
E
bind
= (0.982 584 u)(931.50 MeV/u) = 915.28 MeV
N = A − Z = 63 − 29 = 34
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of Cu-63
∆m = 29(1.007 825 u) + 34(1.008 665 u) − 62.929 599 u
∆m = 29.226 925 u + 34.294 610 u − 62.929 599 u
∆m = 0.591 936 u
E
bind
= (0.591 936 u)(931.50 MeV/u) = 551.39 MeV
The difference in binding energy is 915.28 MeV − 551.39 MeV = 363.89 MeV
499. A = 58
Z = 28
atomic mass of Ni-58
= 57.935 345 u
atomic mass of H
= 1.007 825 u
m
n
= 1.008 665 u
N = A − Z = 58 − 28 = 30
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of Ni-58
∆m = 28(1.007 825 u) + 30(1.008 665 u) − 57.935 345 u
∆m = 28.219 100 u + 30.259 950 u − 57.935 345 u
∆m = 0.543 705 u
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–72
500.
212
84
Po → ? +
4
2
He
A = 212 − 4 = 208
Z = 84 − 2 = 82
? =
208
82
Pb
501.
16
7
N → ? +
0
−1
e + v
A = 16 − 0 = 16
Z = 7 − (−1) = 8
? =
16
8
O
502.
147
62
Sm →
143
60
Nd + ? + v
A = 147 − 143 = 4
Z = 62 − 60 = 2
? =
4
2
He
503. m
i
= 3.29 × 10
−3
g
m
f
= 8.22 × 10
−4
g
∆t = 30.0 s
m
m
i
f
=
8
3
.
.
2
2
2
9
×
×
1
1
0
0
−
−
4
3
g
g
=
1
4
If
1
4
of the sample remains after 30.0 s, then
1
2
of the sample must have remained after
15.0 s, so T
1/2
= .15.0 s
504. T
1/2
= 21.6 h
N = 6.5 × 10
6
λ=
0
T
.6
1
9
/2
3
=
(21.6 h
0
)
.
(
6
3
9
6
3
00 s/h)
= 8.90 × 10
−6
s
−1
activity = N λ= = 1.5 × 10
−9
Ci
(8.9 × 10
−6
s
−1
)(6.5 × 10
6
)
3.7 × 10
10
s
−1
/Ci
505. T
1/2
= 10.64 h
For the sample to reach
1
2
its original strength, it takes 10.64 h. For the sample to
reach
1
4
its original strength, it takes 2(10.64 h) = 21.28 h. For the sample to reach
8
1
its
original strength, it takes 3(10.64 h) = 31.92 h
506. Z = 50
A = 120
atomic mass of Sn-120
= 119.902 197
atomic mass of H = 1.007 825 u
m
n
= 1.008 665 u
N = A − Z = 120 − 50 = 70
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of Sn-120
∆m = 50(1.007 825 u) + 70(1.008 665 u) − 119.902 197 u
∆m = 50.391 25 u + 70.606 55 u − 119.902 197 u
∆m = 1.095 60 u
E
bind
= (1.095 60 u)(931.50 MeV/u) = 1020.6 MeV
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section One—Student Edition Solutions V Apx I–73
N = A − Z = 12 − 6 = 6
∆m = Z (atomic mass of H) + Nm
n
− atomic mass of C-12
∆m = 6(1.007 825 u) + 6(1.008 665u) − 12.000 000 u
∆m = 6.046 95 u + 6.051 99 u − 12.000 000 u
∆m = 0.098 94 u
E
bind
= (0.098 94 u)(931.50 MeV/u) = 92.163 MeV
N = A − Z = 16 − 8 = 8
∆m = Z (atomic mass of H) + Nm
n
− atomic mass of O-16
∆m = 8(1.007 825 u) + 8(1.008 665u) − 15.994 915 u
∆m = 8.0626 u + 8.06932 u − 15.994 915 u
∆m = 0.1370 u
E
bind
= (0.1370 u)(931.50 MeV/u) = 127.62 MeV
The difference in binding energy is
127.62 MeV − 92.163 MeV = 35.46 MeV
507. For
12
6
C:
Z = 6
A = 12
atomic mass of C-12
= 12.000 000 u
atomic mass of H
= 1.007 825 u
m
n
= 1.008 665 u
For
16
8
O:
Z = 8
A = 16
atomic mass of O-16
= 15.994 915
508. A = 64
Z = 30
atomic mass of Zn-64
= 63.929 144 u
atomic mass of H
= 1.007 825 u
m
n
= 1.008 665 u
N = A − Z = 64 − 30 = 34
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of Zn-64
∆m = 30(1.007 825 u) + 34(1.008 665 u) − 63.929 144 u
∆m = 30.234 750 u + 34.294 610 u − 63.929 144 u
∆m = 0.600 216 u
509. ? →
131
54
Xe +
0
−1
e + v
A = 131 + 0 = 131
Z = 54 + (−1) = 53
? =
131
53
I
510.
160
74
W →
156
72
Hf + ?
A = 160 − 156 = 4
Z = 74 − 72 = 2
? =
4
2
He
511. ? →
107
52
Te +
4
2
He
A = 107 + 4 = 111
Z = 52 + 2 = 54
? =
111
54
Xe
512. m
i
= 4.14 × 10
−4
g
m
f
= 2.07 × 10
−4
g
∆t = 1.25 days
m
m
i
f
=
2
4
.
.
0
1
7
4
×
×
1
1
0
0
−
−
4
4
g
g
=
1
2
If
1
2
of the sample remains after 1.25 days, then T
1/2
= 1.25 days
I
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualV Apx I–74
513. T
1/2
= 462 days
For the sample to reach
1
2
its original strength, it takes 462 days. For the sample to
reach
1
4
its original strength, it takes 2(462 days) = 924 days
514. T
1/2
= 2.7 y
N = 3.2 × 10
9
λ=
0
T
.6
1
9
/2
3
==8.1 × 10
−9
s
−1
0.693
(2.7 y)(3.156 × 10
7
s/y)
solutions
Problem Workbook
Solutions
II
Section
Holt Physics
II
The Science of Physics
Problem Workbook Solutions
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. distance = 4.35 light years
distance = 4.35 light years ×
9.4
1
6
l
1
ig
×
ht
1
y
0
e
1
a
5
r
m
= 4.12 × 10
16
m
a. distance = 4.12 × 10
16
m ×
1
10
M
6
m
m
=
b. distance = 4.12 × 10
16
m ×
10
1
−
p
12
m
m
= 4.12 × 10
28
pm
4.12 × 10
10
Mm
Additional Practice A
Givens Solutions
2. energy = 1.2 × 10
44
J
a. energy = 1.2 × 10
44
J ×
1
1
0
k
3
J
J
=
b. energy = 1.2 × 10
44
J ×
1
1
0
−
n
9
J
J
= 1.2 × 10
53
nJ
1.2 × 10
41
kJ
6. m = 1.90 × 10
5
kg
m = 1.90 × 10
5
kg ×
1.78 ×
1
1
e
0
V
−36
kg
= 1.07 × 10
41
eV
a. m = 1.07 × 10
41
eV ×
1
10
M
6
e
e
V
V
=
b. m = 1.07 × 10
41
eV ×
1
1
0
1
T
2
e
e
V
V
= 1.07 × 10
29
Te V
1.07 × 10
35
MeV
4. distance = 152 100 000 km
a. distance = 152 100 000 km ×
1
1
00
k
0
m
m
×
10
1
−
y
2
m
4
m
=
b. distance = 152 100 000 km ×
1
1
00
k
0
m
m
×
1
1
0
2
Y
4
m
m
= 1.521 × 10
−13
Ym
1.521 × 10
35
ym
5. energy = 2.1 × 10
15
W•h
a. energy = 2.1 × 10
15
W•h ×
1
1
J
W
/s
×
36
1
0
h
0s
=
b. energy = 7.6 × 10
18
J ×
1
1
0
G
9
J
J
= 7.6 × 10
9
GJ
7.6 × 10
18
J
3. m = 1.0 × 10
−16
g
a. m = 1.0 × 10
−16
g ×
1
1
0
1
P
5
g
g
=
b. m = 1.0 × 10
−16
g ×
10
1
−
1
fg
5
g
=
c. m = 1.0 × 10
−16
g ×
10
1
−
a
1
g
8
g
= 1.0 × 10
2
ag
0.10 fg
1.0 × 10
−31
Pg
Section Two — Problem Workbook Solutions II Ch. 1–1
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
7. m = (200)(2 × 10
30
kg) =
4 × 10
32
kg
a. m = 4 × 10
32
kg ×× =
b. m = 4 × 10
32
kg ×
1
1
0
k
3
g
g
×
1
1
0
1
E
8
g
g
= 4 × 10
17
Eg
4 × 10
38
mg
10
3
mg
1 g
10
3
g
1kg
Givens Solutions
8. area = 166 241 700 km
2
depth = 3940 m
V = volume = area × depth
V = (166 241 700 km
2
)(3940 m) ×
1
1
00
k
0
m
m
2
V = 6.55 × 10
17
m
3
a. V = 6.55 × 10
17
m
3
×
10
1
6
m
cm
3
3
=
b. V = 6.55 × 10
17
m
3
×
10
1
9
m
m
3
m
3
= 6.55 × 10
26
mm
3
6.55 × 10
23
cm
3
Holt Physics Solution ManualII Ch. 1–2
Section Two — Problem Workbook Solutions II Ch. 2–1
Motion In One
Dimension
Problem Workbook Solutions
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. ∆x = 443 m
v
avg
= 0.60 m/s
∆t =
v
∆
a
v
x
g
=
0
4
.6
4
0
3
m
m
/s
= 740 s = 12 min, 20 s
Additional Practice A
Givens Solutions
2. v
avg
= 72 km/h
∆x = 1.5 km
∆t =
v
∆
a
v
x
g
==
75 s
1.5 km
72
k
h
m
36
1
0
h
0s
3. ∆x = 5.50 × 10
2
m
v
avg
= 1.00 × 10
2
km/h
v
avg
= 85.0 km/h
a. ∆t =
v
∆
av
x
g
==
b. ∆x =∆v
avg
∆t
∆x = (85.0 km/h)
36
1
0
h
0s
1
1
0
k
3
m
m
(19.8 s) = 468 m
19.8 s
5.50 × 10
2
m
1.00 × 10
2
k
h
m
36
1
0
h
0s
1
1
00
k
0
m
m
4. ∆x
1
= 1.5 km
v
1
= 85 km/h
∆x
1
= 0.80 km
v
2
= 67 km/h
a. ∆t
tot
=∆t
1
+∆t
2
=
∆
v
x
1
1
+
∆
v
x
2
2
∆t
tot
=+=64 s + 43 s =
b. v
avg
== = =77 km/h
2.3 km
(107 s)
36
1
0
h
0s
1.5 km + 0.80 km
(64 s + 43 s)
3
1
60
h
0
∆x
1
+∆x
2
∆t
1
+∆t
2
107 s
0.80 km
67
k
h
m
36
1
0
h
0s
1.5 km
85
k
h
m
36
1
0
h
0s
5. r = 7.1 × 10
4
km
∆t = 9 h, 50 min
∆x =2
π
r
v
avg
== =
v
avg
=
4.5 × 10
8
m
(590 min)
1
6
m
0
i
s
n
4.5 × 10
8
m
(540 min + 50 min)
1
6
m
0
i
s
n
2
π
(7.1 × 10
7
m)
(9 h)
60
1
m
h
in
+ 50 min
1
6
m
0
i
s
n
∆x
∆t
v
avg
=
Thus the average speed = 1.3 × 10
4
m/s.
On the other hand, the average velocity for this point is zero, because the point’s dis-
placement is zero.
1.3 × 10
4
m/s
Holt Physics Solution ManualII Ch. 2–2
Givens Solutions
6. ∆x = –1.73 km
∆t = 25 s
7. v
avg,1
= 18.0 km/h
∆t
1
= 2.50 s
∆t
2
= 12.0 s
a. ∆x
1
= v
avg,1
∆t
1
= (18.0 km/h)
36
1
0
h
0s
1
1
0
k
3
m
m
(2.50s) = 12.5 m
∆x
2
= –∆x
1
= –12.5 m
v
avg,2
=
∆
∆
x
t
2
2
=
–
1
1
2
2
.
.
0
5
s
m
=
b. v
avg,tot
=
∆
∆
x
t
1
1
+
+
∆
∆
x
t
2
2
=
12.
2
5
.5
m
0
+
s +
(−
1
1
2
2
.0
.5
s
m)
==
c. total distance traveled =∆x
1
– ∆x
2
= 12.5 m – (–12.5 m) = 25.0 m
total time of travel =∆t
1
+∆t
2
= 2.50 s + 12.0 s = 14.5 s
average speed =
to
t
t
o
a
t
l
a
d
l
i
t
s
i
t
m
an
e
ce
=
2
1
5
4
.
.
0
5
m
s
= 1.72 m/s
0.0 m/s
0.0 m
14.5 s
–1.04 m/s
8. ∆x = 2.00 × 10
2
km
∆t = 5 h, 40 min, 37 s
v
avg
= (1.05)v
avg
∆x =
1
2
∆x
a. v
avg
=
∆
∆
x
t
==
2.0
2
0
0
×
43
1
7
0
5
s
m
v
avg
=
b.
∆t == =
9.73 × 10
3
s
2.00 ×
2
10
5
m
(1.05)
9.79
m
s
∆x
v
avg
9.79 m/s = 35.2 km/h
2.00 × 10
5
m
5 h
360
h
0s
+
40 min
m
60
in
s
+ 37 s
v
avg
==
–1.73
2
×
5
1
s
0
3
m
= –69 m/s = –250 km/h
∆x
∆t
∆t = (9.73 × 10
3
s)
36
1
0
h
0s
= 2.70 h
(0.70 h)
60
1
m
h
in
= 42 min
∆t = 2 h, 42 min
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section Two — Problem Workbook Solutions II Ch. 2–3
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. v
i
= 0 km/h = 0 m/s
a
avg
= 1.8 m/s
2
∆t = 1.00 min
v
f
= a
avg
∆t + v
i
= (1.80 m/s
2
)(1.00 min)
1
6
m
0
i
s
n
+ 0 m/s =
v
f
= 108 m/s = (108 m/s)
36
1
0
h
0s
1
1
0
k
3
m
m
= 389 km/h
108 m/s
Additional Practice B
Givens Solutions
2. ∆t = 2.0 min
a
avg
= 0.19 m/s
2
v
i
= 0 m/s
v
f
= a
avg
∆t + v
i
= (0.19 m/s
2
) (2.0 min)
1
6
m
0
i
s
n
+ 0 m/s = 23 m/s
3. ∆t = 45.0 s
a
avg
= 2.29 m/s
2
v
i
= 0 m/s
v
f
= a
avg
∆t + v
i
= (2.29 m/s
2
)(45.0 s) + 0 m/s = 103 m/s
5. ∆x = (15 hops)
1
1
0
h
.0
o
m
p
= 1.50 × 10
2
m
∆t = 60.0 s
∆t
stop
= 0.25 s
v
f
= 0 m/s
v
i
= v
avg
=+2.50 m/s
a. v
avg
=
∆
∆
x
t
=
1.50
60
×
.0
10
s
2
m
=
b. a
avg
=
v
∆
f
t
−
sto
v
p
i
=
0m/s
0
−
.2
2
5
.5
s
0m/s
=
−
0
2
.2
.5
5
0
m
m
/
/
s
s
= −1.0 × 10
1
m/s
2
+2.50 m/s
6. ∆x = 1.00 × 10
2
m, backward
=−1.00 × 10
2
m
∆t = 13.6 s
∆t = 2.00 s
v
i
= 0 m/s
v
f
= v
avg
v
avg
=
∆
∆
x
t
=
−1.00
13
×
.6
1
s
0
2
m
=−7.35 m/s
a
avg
=
v
f
∆
−
t
v
i
= = 3.68 m/s
2
−7.35 m/s − 0 m/s
2.00 s
7. ∆x = 150 m
v
i
= 0 m/s
v
f
= 6.0 m/s
v
avg
= 3.0 m/s
a. ∆t =
v
∆
av
x
g
=
3
1
.
5
0
0
m
m
/s
=
b. a
avg
=
v
f
∆
−
t
v
i
=
6.0
5
m
.0
/s
×
−
1
0
0
1
m/s
= 0.12 m/s
2
5.0 × 10
1
s
4. ∆x = 29 752 m
∆t = 2.00 h
v
i
= 3.00 m/s
v
f
= 4.13 m/s
∆t = 30.0 s
a. v
avg
=
∆
∆
x
t
==
b. a
avg
=
∆
∆
v
t
==
1.
3
1
0
3
.0
m
s
/s
= 3.77 × 10
−2
m/s
2
4.13 m/s − 3.00 m/s
30.0 s
4.13 m/s
29 752 m
(2.00 h)
36
1
0
h
0s
Holt Physics Solution ManualII Ch. 2–4
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
8. v
i
=+245 km/h
a
avg
=−3.0 m/s
2
v
f
= v
i
−(0.200) v
i
Givens Solutions
9. ∆x = 3.00 km
∆t = 217.347 s
a
avg
=−1.72 m/s
2
v
f
= 0 m/s
v
i
= v
avg
=
∆
∆
x
t
==13.8 m/s
t
stop
=
v
f
a
a
−
vg
v
i
=
==8.02 s
−13.8 m/s
−1.72 m/s
2
0 m/s − 13.8 m/s
−1.72 m/s
2
3.00 × 10
3
m
217.347 s
10. ∆x =+5.00 × 10
2
m
∆t = 35.76 s
v
i
= 0 m/s
∆t = 4.00 s
v
max
= v
avg
+ (0.100) v
avg
v
f
= v
max
= (1.100)v
avg
= (1.100)
∆
∆
x
t
= (1.100)
5.0
3
0
5
×
.7
1
6
0
s
2
m
=+15.4 m/s
a
avg
=
∆
∆
t
v
=
v
f
∆
−
t
v
i
==+3.85 m/s
2
15.4 m/s − 0 m/s
4.00 s
1. ∆x = 115 m
v
i
= 4.20 m/s
v
f
= 5.00 m/s
∆t =
v
i
2∆
+
x
v
f
=
4.20
(
m
2)
/
(
s
1
+
15
5.
m
00
)
m/s
=
(2
9
)
.
(
2
1
0
1
m
5
/
m
s
)
= 25.0 s
Additional Practice C
2. ∆x = 180.0 km
v
i
= 3.00 km/s
v
f
= 0 km/s
∆t =
v
i
2∆
+
x
v
f
==
3
3
.
6
0
0
0
.0
km
km
/s
= 1.2 × 10
2
s
(2)(180.0 km)
3.00 km/s + 0 km/s
3. v
i
= 0 km/h
v
f
= 1.09 × 10
3
km/h
∆x = 20.0 km
∆x = 5.00 km
v
i
= 1.09 × 10
3
km/h
v
f
= 0 km/h
a. ∆t =
v
i
2
+
∆x
v
f
=
∆t ==
b. ∆t =
v
i
2
+
∆x
v
f
=
∆t ==33.0 s
10.0 × 10
3
m
(1.09 × 10
3
km/h)
36
1
0
h
0s
1
1
00
k
0
m
m
(2)(5.00 × 10
3
m)
(1.09 × 10
3
km/h + 0 km/h)
36
1
0
h
0s
1
1
00
k
0
m
m
132 s
40.0 × 10
3
m
(1.09 × 10
3
km/h)
36
1
0
h
0s
1
1
00
k
0
m
m
(2)(20.0 × 10
3
m)
(1.09 × 10
3
km/h + 0 km/h)
36
1
0
h
0s
1
1
00
k
0
m
m
v
i
=
245
k
h
m
36
1
0
h
0s
1
1
0
k
3
m
m
=+68.1 m/s
v
f
= (1.000 − 0.200) v
i
= (0.800)(68.1 m/s) =+54.5 m/s
∆t =
v
f
a
a
−
vg
v
i
=
54.5 m
−3
/s
.0
−
m
6
/
8
s
.
2
1m/s
= = 4.5 s
−13.6 m/s
− 3.0 m/s
2
Section Two — Problem Workbook Solutions II Ch. 2–5
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
4. v
i
= v
avg
= 518 km/h
v
f
= (0.600) v
avg
∆t = 2.00 min
v
avg
=
518
k
h
m
60
1
m
h
in
1
1
0
k
3
m
m
= 8.63 × 10
3
m/min
∆x =
1
2
(v
i
+ v
f
)∆t =
1
2
[v
avg
+ (0.600) v
avg
]∆t =
1
2
(1.600)(8.63 × 10
3
m/min)(2.00 min)
∆x = 13.8 × 10
3
m = 13.8 km
Givens Solutions
5. ∆t = 30.0 s
v
i
= 30.0 km/h
v
f
= 42.0 km/h
∆x =
1
2
(v
i
+ v
f
)∆t =
1
2
(30.0 km/h + 42.0 km/h)
36
1
0
h
0s
(30.0 s)
∆x =
1
2
72.0
k
h
m
36
1
0
h
0s
(30.0 s)
∆x = 3.00 × 10
−1
km = 3.00 × 10
2
m
1. v
i
= 186 km/h
v
f
= 0 km/h = 0 m/s
a =−1.5 m/s
2
∆t =
v
f
−
a
v
i
==
−
−
5
1
1
.5
.7
m
m
/s
/
2
s
= 34 s
0 m/s − (186 km/h)
36
1
0
h
0s
1
1
0
k
3
m
m
−1.5 m/s
2
Additional Practice D
6. v
f
= 96 km/h
v
i
= 0 km/h
∆t = 3.07 s
∆x =
1
2
(v
i
+ v
f
)∆t =
1
2
(0 km/h + 96 km/h)
36
1
0
h
0s
1
1
0
k
3
m
m
(3.07 s)
∆x =
1
2
96 × 10
3
m
h
(8.53 +×10
−4
h) = 41 m
7. ∆x = 290.0 m
∆t = 10.0 s
v
f
= 0 km/h = 0 m/s
v
i
=
2
∆
∆
t
x
− v
f
=
(2)(
1
2
0
9
.
0
0
.0
s
m)
− 0 m/s =
(Speed was in excess of 209 km/h.)
58.0 m/s = 209 km/h
8. ∆x = 5.7 × 10
3
km
∆t = 86 h
v
f
= v
i
+ (0.10) v
i
v
f
+ v
i
=
2
∆
∆
t
x
v
i
(1.00 + 0.10) + v
i
=
2
∆
∆
t
x
v
i
=
(2)
(
(
2
5
.
.
1
7
0
×
)(
1
8
0
6
3
h
k
)
m)
= 63 km/h
9. v
i
= 2.60 m/s
v
f
= 2.20 m/s
∆t = 9.00 min
∆x =
1
2
(v
i
+ v
f
)∆t =
1
2
(2.60 m/s + 2.20 m/s)(9.00 min)
m
60
in
s
=
1
2
(4.80 m/s)(5.40 × 10
2
s)
∆x = 1.30 × 10
3
m = 1.30 km
2. v
i
=−15.0 m/s
v
f
= 0 m/s
a =+2.5 m/s
2
v
i
= 0 m/s
v
f
=+15.0 m/s
a =+2.5 m/s
For stopping:
∆t
1
=
v
f
a
− v
i
=
0 m/s
2
−
.5
(−
m
1
/
5
s
.
2
0 m/s)
=
1
2
5
.5
.0
m
m
/s
/
2
s
= 6.0 s
For moving forward:
∆t
2
=
v
f
a
− v
i
==
1
2
5
.5
.0
m
m
/s
/
2
s
= 6.0 s
∆t
tot
=∆t
1
+∆t
2
= 6.0 s + 6.0 s = 12.0 s
15.0 m/s − 0.0 m/s
2.5 m/s
2
Holt Physics Solution ManualII Ch. 2–6
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
3. v
i
= 24.0 km/h
v
f
= 8.0 km/h
a =−0.20 m/s
2
∆t =
v
f
−
a
v
i
∆t =
∆t =
= 22 s
−16.0
k
h
m
36
1
0
h
0s
1
1
0
k
3
m
m
−0.20 m/s
2
(8.0 km/h − 24.0 km/h)
36
1
0
h
0 s
1
1
0
k
3
m
m
−0.20 m/s
2
4. v
1
= 65.0 km/h
v
i,2
= 0 km/h
a
2
= 4.00 × 10
−2
m/s
2
∆x = 2072 m
For cage 1:
∆x = v
1
∆t
1
∆t
1
=
∆
v
1
x
==
For cage 2:
∆x = v
i,2
∆t
2
+
1
2
a
2
∆t
2
2
Because v
i,2
= 0 km/h,
∆t
2
=
2
a
∆
2
x
=
4.
0
(2
0
)
×
(
2
1
0
0
7
−
2
2
m
m
)
/s
2
=
Cage 1 reaches the bottom of the shaft in nearly a third of the time required for cage 2.
322 s
115 s
2072 m
(65.0 km/h)
36
1
0
h
0 s
1
1
0
k
3
m
m
5. ∆x = 2.00 × 10
2
m
v = 105.4 km/h
v
i,car
= 0 m/s
a. ∆t ==
=
b. ∆x = v
i,car
∆t +
1
2
a
car
∆t
2
a
car
=
2
∆
∆
t
2
x
=
(2)(2
(
.
6
0
.
0
83
×
s
1
)
0
2
2
m)
= 8.57 m/s
2
6.83 s
2.00 × 10
2
m
105.4
k
h
m
36
1
0
h
0 s
1
1
0
k
3
m
m
∆x
v
Givens Solutions
7. v
i
= 3.17 × 10
2
km/h
v
f
= 2.00 × 10
2
km/h
∆t = 8.0 s
a =
v
f
∆
−
t
v
i
=
a ==
∆x = v
i
∆t +
1
2
a∆t
2
= (3.17 × 10
2
km/h)
36
1
0
h
0s
1
1
0
k
3
m
m
(8.0 s) +
1
2
(−4.1 m/s
2
)(8.0 s)
2
∆x = (7.0 × 10
2
m) + (−130 m) =+570 m
−4.1 m/s
2
(−117 km/h)
36
1
0
h
0 s
1
1
0
k
3
m
m
8.0 s
(2.00 × 10
2
km/h − 3.17 × 10
2
km/h)
36
1
0
h
0 s
1
1
0
k
3
m
m
8.0 s
6. v
i
= 6.0 m/s
a = 1.4 m/s
2
∆t = 3.0 s
∆x = v
i
∆t +
1
2
a∆t
2
= (6.0 m/s)(3.0 s) +
1
2
(1.4 m/s
2
)(3.0 s)
2
= 18 m + 6.3 m = 24 m
Section Two — Problem Workbook Solutions II Ch. 2–7
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
10. v
i
= 24.0 m/s
a =−0.850 m/s
2
∆t = 28.0 s
v
f
= v
i
+ a∆t = 24.0 m/s + (− 0.850 m/s
2
)(28.0 s) = 24.0 m/s − 23.8 m/s =+0.2 m/s
Givens Solutions
11. a =+2.67 m/s
2
∆t = 15.0 s
∆x =+6.00 × 10
2
m
v
i
∆t =∆x −
1
2
a∆t
2
v
i
=
∆
∆
x
t
−
1
2
a∆t =
6.00
15
×
.0
10
s
2
m
−
1
2
(2.67 m/s
2
)(15.0 s) = 40.0 m/s − 20.0 m/s =+20.0 m/s
12. a = 7.20 m/s
2
∆t = 25.0 s
v
f
= 3.00 × 10
2
ms
v
i
= v
f
− a∆t
v
i
=(3.00 × 10
2
m/s) − (7.20 m/s
2
)(25.0 s) = (3.00 × 10
2
m/s) −(1.80 × 10
2
m/s)
v
i
= 1.20 × 10
2
m/s
13. v
i
= 0 m/s
∆x = 1.00 × 10
2
m
∆t = 12.11 s
∆x = v
i
∆t +
1
2
a∆t
2
Because v
i
= 0 m/s,
a =
2
∆
∆
t
2
x
=
(2)(
(
1
1
.0
2
0
.1
×
1
1
s)
0
2
2
m)
= 1.36 m/s
2
8. v
i
= 0 m/s
v
f
= 3.06 m/s
a = 0.800 m/s
2
∆t
2
= 5.00 s
∆t
1
=
v
f
a
− v
i
=
3.0
0
6
.
m
80
/
0
s
m
−
/
0
s
2
m/s
= 3.82
∆x
1
= v
i
∆t
1
+
1
2
a∆t
1
2
= (0 m/s) (3.82 s) +
1
2
(0.800 m/s
2
) (3.82 s)
2
= 5.84 m
∆x
2
= v
f
∆t
2
= (3.06 m/s)(5.00 s) = 15.3 m
∆x
tot
=∆x
1
+∆x
2
= 5.84 m + 15.3 m = 21.1 m
9. v
f
= 3.50 × 10
2
km/h
v
i
= 0 km/h = 0 m/s
a = 4.00 m/s
2
∆t =
(v
f
a
− v
i
)
==
∆x = v
i
∆t +
1
2
a∆t
2
= (0 m/s)(24.3 s) +
1
2
(4.00 m/s
2
)(24.3 s)
2
∆x = 1.18 × 10
3
m = 1.18 km
24.3 s
(3.50 × 10
2
km/h − 0 km/h)
36
1
0
h
0 s
1
1
0
k
3
m
m
(4.00 m/s
2
)
14. v
i
= 3.00 m/s
∆x = 1.00 × 10
2
m
∆t = 12.11 s
a =
2(∆x
∆
−
t
2
v
i
∆t)
=
a =
a =
(
(
2
1
)
2
(
.
6
1
4
1
m
s)
2
)
= 0.87 m/s
2
(2)(1.00 × 10
2
m − 36.3 m)
(12.11 s)
2
(2)[1.00 × 10
2
m − (3.00 m/s)(12.11 s)]
(12.11 s)
2
15. v
f
= 30.0 m/s
v
i
= 18.0 m/s
∆t = 8.0 s
a =
v
f
∆
−
t
v
i
==
12
8
.0
.0
m
s
/s
= 1.5 m/s
2
30.0 m/s − 18.0 m/s
8.0 s
Holt Physics Solution ManualII Ch. 2–8
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. v
i
= 0 km/h
v
f
= 965 km/h
a = 4.0 m/s
2
∆x =
v
f
2
2
−
a
v
i
2
=
∆x =
7.19
8
×
.0
1
m
0
4
/
m
s
2
2
/s
2
= 9.0 × 10
3
m = 9.0 km
(965 km/h)
2
− (0 km/h)
2
36
1
0
h
0 s
2
1
1
0
k
3
m
m
2
(2)(4.0 m/s
2
)
2. v
i
= (0.20) v
max
v
max
= 2.30 × 10
3
km/h
v
f
= 0 km/h
a =−5.80 m/s
2
∆x =
v
f
2
2
−
a
v
i
2
=
∆x =
−1.6
−
3
11
×
.6
1
m
0
4
/
m
s
2
2
/s
2
= 1.41 × 10
3
m = 1.41 km
(0 km/h)
2
− (0.20)
2
(2.30 × 10
3
km/h)
2
36
1
0
h
0 s
2
1
1
0
k
3
m
m
2
(2)(−5.80 m/s
2
)
3. v
f
= 9.70 × 10
2
km/h
v
i
= (0.500)v
f
a = 4.8 m/s
2
∆x =
v
f
2
2
−
a
v
i
2
=
∆x =
∆x =
∆x = = 5.7 × 10
3
m = 5.7 km
5.45 × 10
4
m
2
/s
2
9.6 m/s
2
(7.06 ×10
5
km
2
/h
2
)
36
1
0
h
0 s
2
1
1
0
k
3
m
m
2
(2)(4.8 m/s
2
)
(9.41 ×10
5
km
2
/h)
2
−2.35 × 10
5
km
2
/h
2
)
36
1
0
h
0 s
2
1
1
0
k
3
m
m
2
(2)(4.8 m/s
2
)
(9.70 ×10
2
km/h)
2
−(0.50)
2
(9.70 × 10
2
km/h)
2
36
1
0
h
0 s
2
1
1
0
k
3
m
m
2
(2)(4.8 m/s
2
)
Additional Practice E
Givens Solutions
4. v
i
= 8.0 m/s
∆x = 40.0 m
a = 2.00 m/s
2
v
f
=
2a
∆
x
+
v
i
2
=
(2
)(
2.
0
m
/s
2
)
(4
0.
m
)
+
(
8.
0
m
/s
)
2
=
1.
60
×
1
0
2
m
2
/
s
2
+
6
4
m
2
/
s
2
v
f
=
22
4
m
2
/
s
2
=±15 m/s = 15 m/s
5. ∆x =+9.60 km
a =−2.0 m/s
2
v
f
= 0 m/s
v
i
= v
f
2
−
2
a∆
x
= (0
m
/s
)
2
−
(
2)
(−
2.
0
m
/s
2
)
(9
.6
0
×
1
0
3
m
)
v
i
=
3.
84
×
1
0
4
m
2
/
s
2
=±196 m/s = +196 m/s
7. ∆x = 44.8 km
∆t = 60.0 min
a =−2.0 m/s
2
∆x = 20.0 m
v
i
= 12.4 m/s
a. v
avg
=
∆
∆
x
t
==
b. v
f
=
2a
∆
x
+
v
i
2
=
(2
)(
−
2.
0
m
/s
2
)
(2
0.
0
m
)
+
(
12
.4
m
/s
)
2
v
f
=
(−
80
.0
m
2/
s
2
)
+
1
54
m
2/
s
2
=
74
m
2
/
s
2
=±8.6 m/s = 8.6 m/s
12.4 m/s
44.8 × 10
3
m
(60.0 min)(60 s/min)
6. a =+0.35 m/s
2
v
i
= 0 m/s
∆x = 64 m
v
f
=
2a
∆
x
+
v
i
2
=
(2
)(
0.
35
m
/s
2
)
(6
4
m
)
+
(
0
m
/s
)
2
v
f
=
45
m
2
s
2
=±6.7 m/s = +6.7 m/s
Section Two — Problem Workbook Solutions II Ch. 2–9
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
3. ∆y =−443 m + 221 m
=−222 m
a =−9.81 m/s
2
v
i
= 0 m/s
v
f
=
2a
∆
y
−
v
i
2
=
(2
)(
−
9.
81
m
/s
2
)
(−
22
2
m
)
−
(
0
m
/s
)
2
=
43
60
m
2
/
s
2
v
f
=±66.0 m/s =−66.0 m/s
Givens Solutions
4. ∆y =+64 m
a =−9.81 m/s
2
∆t = 3.0 s
∆y = v
i
∆t +
1
2
a∆t
2
v
i
= = =
64 m
3.
+
0
4
s
4m
v
i
=
1
3
0
.
8
0
m
s
= 36 m/s initial speed of arrow = 36 m/s
3.0 s
∆t
5. ∆y =−111 m
∆t = 3.80 s
a =−9.81 m/s
2
∆y = v
i
∆t +
1
2
a∆t
2
v
i
== =
v
i
=
−
3
4
.
0
8
.
0
2
s
m
= −10.6 m/s
−111 m + 70.8 m
3.80 s
3.80 s
∆t
9. ∆x = 4.0 × 10
2
m
∆t = 11.55
v
i
= 0 km/h
v
f
= 2.50 × 10
2
km/h
1. ∆y =−343 m
a =−9.81 m/s
2
v
i
= 0 m/s
v
f
=
2a
∆
y
+
v
i
2
=
(2
)(
−
9.
81
m
/s
2
)
(−
34
3
m
)
+
(
0
m
/s
)
2
=
67
30
m
2
/
s
2
v
f
=±82.0 m/s =−82.0 m/s
Additional Practice F
2. ∆y =+4.88 m
v
i
=+9.98 m/s
a =−9.81 m/s
2
v
f
=
2a
∆
y
+
v
i
2
=
(2
)(
−
9.
81
m
/s
2
)
(4
.8
8
m
)
+
(
9.
98
m
/s
)
2
=
−
95
.7
m
2
/
s
2
+
9
9.
6
m
2
/
s
2
v
f
=
3.
90
m
2
/
s
2
=±1.97 m/s =±1.97 m/s
a =
v
f
2
2∆
−
x
v
i
2
=
a =
4.8
8
2
.0
×
×
1
1
0
0
3
2
m
m
2
/s
2
= 6.0 m/s
2
(2.50 × 10
2
km/h)
2
− (0 km/h)
2
36
1
0
h
0s
2
1
1
0
k
3
m
m
2
(2)(4.0 × 10
2
m)
8. ∆x = 2.00 × 10
2
m
a = 1.20 m/s
2
v
f
= 25.0 m/s
v
i
=
v
f
2
−
2
a∆
x
=
(2
5.
0
m
/s
)
2
−
(
2)
(1
.2
0
m
/s
2
)
(2
.0
0
×
1
0
2
m
)
v
i
=
62
5
m
2
/
s
2
−
4
.8
0
×
1
0
2
m
2
/
s
2
v
i
=
14
5
m
2
/
s
2
=±12.0 m/s = 12.0 m/s
10. v
i
= 25.0 km/h
v
f
= 0 km/h
∆x = 16.0 m
a =
v
f
2
2∆
−
x
v
i
2
=
a ==−1.51 m/s
2
−4.82 m
2
/s
2
32.0 m
(0 km/h)
2
− (25.0 km/h)
2
36
1
0
h
0 s
2
1
1
0
k
3
m
m
2
(2)(16.0 m)
64 m −
1
2
(−9.81 m/s
2
)(3.0 s)
2
∆y −
1
2
a∆t
2
−111 m −
1
2
(−9.81 m/s
2
)(3.80 s)
2
∆y −
1
2
a∆t
2
Holt Physics Solution ManualII Ch. 2–10
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
9. ∆y
max
=+21 cm
a =−9.81 m/s
2
v
f
= 0 m/s
∆y =+7.0 cm
v
i
=
v
f
2
−
2
a
∆
y
m
ax
=
(0
m
/s
)
2
−
(2
)(
−9
.8
1
m
/s
2
)
(2
.
1
×
1
0
−
1
m
)
=
4.
1
m
2
/
s
2
v
i
=+2.0 m/s
For the flea to jump +7.0 cm =+7.0 × 10
−2
m =∆y,
∆y =
v
i
∆t +
1
2
a∆t
2
or
1
2
a∆t
2
+ v
i
∆t −∆y = 0
Solving for ∆t by means of the quadratic equation,
∆t =
∆t =
∆t ==
∆t =
= 0.37 s or 0.04 s
To choose the correct value for ∆t, insert ∆t, a, and v
i
into the equation for v
f
.
v
f
= a∆t + v
i
= (−9.81 m/s
2
)(0.37 s) + 2.0 m/s
v
f
= (−3.6 m/s) + 2.0 m/s =−1.6 m/s
v
f
= a∆t + v
i
= (−9.81 m/s
2
)(0.04 s) + 2.0 m/s
v
f
= (−0.4 m/s) + 2.0 m/s =+1.6 m/s
Because v
f
is still directed upward, the shorter time interval is correct. Therefore,
∆t = 0.04 s
2.0 m/s ± 1.6 m/s
9.81 m/s
2
2.0 m/s ±
2.
6
m
2
/
s
2
9.81 m/s
2
−2.0 m/s ±
4.
0
m
2
/
s
2
−
1
.4
m
2
/
s
2
−9.81 m/s
2
−2.0 m/s ±
(2
.0
m
/s
)
2
−
(
2)
(−
9.
81
m
/s
2
)
(−
7.
0
×
1
0
−
2
m
)
−9.81 m/s
2
−v
i
±
(v
i
)
2
−
4
2
a
(−
∆
y
)
2
2
a
6. ∆y =−228 m
a =−9.81 m/s
2
v
i
= 0 m/s
When v
i
= 0 m/s,
∆t =
2
a
∆
y
=
=
In the presence of air resistance, the sandwich would require more time to fall be-
cause the downward acceleration would be reduced.
6.82 s
(2)(−228 m)
−9.81 m/s
2
Givens Solutions
7. v
i
= 12.0 m/s, upward =
+12.0 m/s
v
f
= 3.0 m/s, upward =
+3.0 m/s
a =−9.81 m/s
2
y
i
= 1.50 m
∆y =
v
f
2
2
−
a
v
i
2
==
∆y ==6.88 m
height of nest from ground = h
∆y = h − y
i
h =∆y + y
i
= 6.88 m + 1.50 m = 8.38 m
−135 m
2
/s
2
−19.6 m/s
2
9.0 m
3
/s
2
− 144 m
2
/s
2
(2)(−9.81 m/s
2
)
(3.0 m/s)
2
− (12.0 m/s)
2
(2)(−9.81 m/s
2
)
8. ∆y =+43 m
a =−9.81 m/s
2
v
f
= 0 m/s
Because it takes as long for the ice cream to fall from the top of the flagpole to the
ground as it does for the ice cream to travel up to the top of the flagpole, the free-fall
case will be calculated.
Thus, v
i
= 0 m/s, ∆y =−43 m, and ∆y =
1
2
a∆t
2
.
∆t =
2
a
∆
y
=
= 3.0 s
(2)(−43 m)
−9.81 m/s
2
Section Two — Problem Workbook Solutions II Ch. 3–1
Two-Dimensional
Motion and Vectors
Problem Workbook Solutions
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. ∆t
x
= 7.95 s
∆y = 161 m
d = 226 m
d
2
=∆x
2
+∆y
2
∆x =
d
2
−
∆
y
2
=
(2
26
m
)
2
−
(
16
1
m
)
2
=
5.
11
×
1
0
4
m
2
−
2
.5
9
×
1
0
4
m
2
∆x =
2.
52
×
1
0
4
m
2
= 159 m
∆x =
v =
∆
∆
t
x
x
=
1
7
5
.9
9
5
m
s
= 20.0 m/s
159 m
Additional Practice A
Givens Solutions
2. d
1
= 5.0 km
θ
1
= 11.5°
d
2
= 1.0 km
q
2
=−90.0°
∆x
tot
= d
1
(cos q
1
) + d
2
(cos q
2
) = (5.0 km)(cos 11.5°) + (1.0 km)[cos(−90.0°)]
∆x
tot
= 4.9 km
∆y
tot
= d
1
(sin q
1
) + d
2
(sin q
2
) = (5.0 km)(sin 11.5°) + (1.0 km)[sin(−90.0
°
)]
= 1.0 km − 1.0 km
∆y
tot
= 0.0 km
d =
(∆
x
t
ot
)
2
+
(
∆
y
t
ot
)
2
=
(4
.9
k
m
)
2
+
(
0.
0
km
)
2
d =
q = tan
−1
∆
∆
x
y
t
t
o
o
t
t
= tan
−1
0
4
.
.
0
9
k
k
m
m
= 0.0
°
, or due east
4.9 km
3. ∆x = 5 jumps
1 jump = 8.0 m
d = 68 m
d
2
=∆x
2
+∆y
2
∆y =
d
2
−
∆
x
2
=
(6
8
m
)
2
−
[
(5
)(
8.
0
m
)]
2
=
4.
6
×
1
0
3
m
2
−
1
.6
×
1
0
3
m
2
∆y =
3.
0
×
1
0
3
m
= 55 m
number of jumps northward =
8.0
5
m
5
/
m
jump
= 6.9 jumps =
q = tan
−1
∆
∆
x
y
= tan
−1
(5)
5
(
5
8.
m
0m)
= 36° west of north
7 jumps
4. ∆x = 25.2 km
∆y = 21.3 km
d =
∆
x
2
+
∆
y
2
=
(2
5.
2
km
)
2
+
(
21
.3
k
m
)
2
d =
63
5
km
2
+
4
54
k
m
2
=
10
89
k
m
2
d =
q = tan
−1
∆
∆
x
y
= tan
−1
2
2
1
5
.
.
3
2
k
k
m
m
q = 42.6° south of east
33.00 km
Holt Physics Solution ManualII Ch. 3–2
Givens Solutions
5. ∆y =−483 m
∆x = 225 m
q = tan
−1
∆
∆
x
y
= tan
−1
2
−
2
4
5
8
m
3
=−65.0°=
d =
∆
x
2
+
∆
y
2
=
(2
25
m
)
2
+
(
−
48
3
m
)
2
d =
5.
06
×
1
0
4
m
2
+
2
.3
3
×
1
0
5
m
2
=
2.
84
×
1
0
5
m
2
d = 533 m
65.0° below the waters surface
6. v = 15.0 m/s
∆t
x
= 8.0 s
d = 180.0 m
d
2
=∆x
2
+∆y
2
= (v∆t
x
)
2
+ (v∆t
y
)
2
d
2
= v
2
(∆t
x
2
+∆t
y
2
)
∆t
y
=
d
v
2
−
∆
t
x
2
=
1
1
5
8
.
0
0
.
0
m
m
/
s
2
−
(
8.
0
s)
2
=
14
4
s
2
−
6
4
s
2
=
8.
0
×
1
0
1
s
2
∆t
y
= 8.9 s
7. v = 8.00 km/h
∆t
x
= 15.0 min
∆t
y
= 22.0 min
d =
∆
x
2
+
∆
y
2
=
(v
∆
t
x
)
2
+
(
v∆
t
y
)
2
= v
∆
t
x
2
+
∆
t
y
2
d = (8.00 km/h)
60
1
m
h
in
(1
5.
0
m
in
)
2
+
(
22
.0
m
in
)
2
d = (8.00 km/h)
60
1
m
h
in
22
5
m
in
2
+
4
84
m
in
2
d =
8
6
.
0
00
m
k
i
m
n
70
9
m
in
2
=
q = tan
−1
∆
∆
x
y
= tan
−1
v
v
∆
∆
t
t
x
y
= tan
−1
∆
∆
t
t
x
y
= tan
−1
2
1
2
5
.
.
0
0
m
m
i
i
n
n
q = 55.7° north of east
3.55 km
1. d = (5)(33.0 cm)
∆y = 88.0 cm
q = sin
−1
∆
d
y
= sin
−1
(5)
8
(
8
3
.
3
0
.0
cm
cm)
=
∆x = d(cos q) = (5)(33.0 cm)(cos 32.2°) = 1.40 × 10
2
cm to the west
32.2° north of west
2. q = 60.0°
d = 10.0 m
∆x = d(cos q) = (10.0 m)(cos 60.0°) =
∆y = d(sin q) = (10.0 m)(sin 60.0°) = 8.66 m
5.00 m
3. d = 10.3 m
∆y =−6.10 m
Finding the angle between d and the x-axis yields,
q
1
= sin
−1
∆
d
y
= sin
−1
−
1
6
0
.
.
1
3
0
m
m
=−36.3°
The angle between d and the negative y-axis is therefore,
q =−90.0 − (−36.3°) =−53.7°
q =
d
2
+∆x
2
+∆
y
2
∆x =
d
2
−
∆
y
2
=
(1
0.
3
m
)
2
−
(
−
6.
10
m
)
2
=
10
6
m
2
−
3
7.
2
m
2
=
69
m
2
∆x =±8.3 m
53.7° on either side of the negative y-axis
Additional Practice B
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section Two — Problem Workbook Solutions II Ch. 3–3
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
4. d = (8)(4.5 m)
q = 35°
∆x = d(cos q) = (8)(4.5 m)(cos 35°) =
∆y = d(sin q) = (8)(4.5 m)(sin 35°) = 21 m
29 m
5. v = 347 km/h
q = 15.0°
v
x
= v(cos q) = (347 km/h)(cos 15.0°) =
v
y
= v(sin q) = (347 km/h)(sin 15.0°) = 89.8 km/h
335 km/h
6. v = 372 km/h
∆t = 8.7 s
q = 60.0°
d = v∆t = (372 km/h)
36
1
0
h
0s
(10
3
m/km)(8.7 s) = 9.0 × 10
2
m
∆x = d(cos q) = (9.0 × 10
2
m)(cos 60.0°) =
∆y = d(sin q) = (9.0 × 10
2
m)(sin 60.0°) = 780 m north
450 m east
Additional Practice C
7. d = 14 890 km
q = 25.0°
∆t = 18.5 h
v
avg
=
∆
d
t
=
1.48
1
9
8
×
.4
1
5
0
h
4
km
=
v
x
= v
avg
(cos q) = (805 km/h)(cos 25.0°) =
v
y
= v
avg
(sin q) = (805 km/h)(sin 25.0°) = 340 km/h south
730 km/h east
805 km/h
8. v
i
= 6.0 × 10
2
km/h
v
f
= 2.3 × 10
3
km/h
∆t = 120 s
q = 35° with respect to
horizontal
a =
∆
∆
v
t
=
v
f
∆
−
t
v
i
a =
a =
a = 3.9 m/s
2
a
x
= a(cos q) = (3.9 m/s
2
)(cos 35°) =
a
y
= a(sin q) = (3.9 m/s
2
)(sin 35°) = 2.2 m/s
2
vertically
3.2 m/s
2
horizontally
(1.7 × 10
3
km/h)
36
1
0
h
0s
(10
3
m/km)
1.2 × 10
2
s
(2.3 × 10
3
km/h − 6.0 × 10
2
km/h)
36
1
0
h
0s
(10
3
m/km)
1.2 × 10
2
s
1. ∆x
1
= 250.0 m
d
2
= 125.0 m
q
2
= 120.0°
∆x
2
= d
2
(cos q
2
) = (125.0 m)(cos 120.0°) =−62.50 m
∆y
2
= d
2
(sin q
2
) = (125.0 m)(sin 120.0°) = 108.3 m
∆x
tot
=∆x
1
+∆x
2
= 250.0 m − 62.50 m = 187.5 m
∆y
tot
=∆y
1
+∆y
2
= 0 m + 108.3 m = 108.3 m
d =
(∆
x
t
ot
)
2
+
(
∆
y
t
ot
)
2
=
(1
87
.5
m
)
2
+
(
10
8.
3
m
)
2
d =
3.
51
6
×
1
0
4
m
2
+
1
.1
73
×
1
0
4
m
2
=
4.
68
9
×
1
0
4
m
2
d =
q = tan
−1
∆
∆
x
y
t
t
o
o
t
t
= tan
−1
1
1
0
8
8
7
.
.
3
5
m
m
= 30.01° north of east
216.5 m
Holt Physics Solution ManualII Ch. 3–4
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. v = 3.53 × 10
3
km/h
∆t
1
= 20.0 s
∆t
2
= 10.0 s
q
1
= 15.0°
q
2
= 35.0°
∆x
1
= v∆t
1
(cos q
1
)
∆x
1
= (3.53 × 10
3
km/h)
36
1
0
h
0s
(10
3
m/km)(20.0 s)(cos 15.0°) = 1.89 × 10
4
m
∆y
1
= v∆t
1
(sin q
1
)
∆y
1
= (3.53 × 10
3
km/h)
36
1
0
h
0s
(10
3
m/km)(20.0 s)(sin 15.0°) = 5.08 × 10
3
m
∆x
2
= v∆t
2
(cos q
2
)
∆x
2
= (3.53 × 10
3
km/h)
36
1
0
h
0s
(10
3
m/km)(10.0 s)(cos 35.0°) = 8.03 × 10
3
m
∆y
2
= v∆t
2
(sin q
2
)
∆y
2
= (3.53 × 10
3
km/h)
36
1
0
h
0s
(10
3
m/km)(10.0 s)(sin 35.0°) = 5.62 × 10
3
m
∆y
tot
=∆y
1
+∆y
2
= 5.08 × 10
3
m + 5.62 × 10
3
m =
∆x
tot
=∆x
1
+∆x
2
= 1.89 × 10
4
m + 8.03 × 10
3
m =
d =
(∆
x
t
ot
)
2
+
(
∆
y
t
ot
)
2
=
(2
.6
9
×
1
0
4
m
)
2
+
(
1.
07
×
1
0
4
m
)
2
d =
7.
24
×
1
0
8
m
2
+
1
.1
1
×
1
0
8
m
2
=
8.
35
×
1
0
8
m
d =
q = tan
−1
∆
∆
x
y
t
t
o
o
t
t
= tan
−1
1
2
.
.
0
6
7
9
×
×
1
1
0
0
4
4
m
m
q = 21.7° above the horizontal
2.89 × 10
4
m
2.69 × 10
4
m
1.07 × 10
4
m
Givens Solutions
3. ∆x
1
+∆x
2
= 2.00 × 10
2
m
∆y
1
+∆y
2
= 0
q
1
= 30.0°
q
2
=−45.0°
v = 11.6 km/h
∆y
1
= d
1
(sin q
1
) =−∆y
2
=−d
2
(sin q
2
)
d
1
=−d
2
s
s
i
i
n
n
q
q
2
1
=−d
2
si
s
n
i
(
n
−
3
4
0
5
.
.
0
0
°
°)
= 1.41d
2
∆x
1
= d
1
(cos q
1
) = (1.41d
2
)(cos 30.0°) = 1.22d
2
∆x
2
= d
2
(cos q
2
) = d
2
[cos(−45.0°)] = 0.707d
2
∆x
1
+∆x
2
= d
2
(1.22 + 0.707) = 1.93d
2
= 2.00 × 10
2
m
d
2
=
d
1
= (1.41)d
2
= (1.41)(104 m) =
v = 11.6 km/h = (11.6 km/h)
36
1
0
h
0s
(10
3
m/km) = 3.22 m/s
∆t
1
=
d
v
1
=
3
1
.2
4
2
7
m
m
/s
= 45.7 s
∆t
2
=
d
v
2
=
3
1
.2
0
2
4
m
m
/s
= 32.3 s
∆t
tot
=∆t
1
+∆t
2
= 45.7 s + 32.3 s = 78.0 s
147 m
104 m
Section Two — Problem Workbook Solutions II Ch. 3–5
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
5. v = 57.2 km/h
∆t
1
= 2.50 h
∆t
2
= 1.50 h
θ
2
= 30.0°
d
1
= v∆t
1
= (57.2 km/h)(2.50 h) = 143 km
d
2
= v∆t
2
= (57.2 km/h)(1.50 h) = 85.8 km
∆
tot
= d
1
+ d
2
(cos q
2
) = 143 km + (85.8 km)(cos 30.0°) = 143 km + 74.3 km = 217 km
∆y
tot
= d
2
(sin q
2
) = (85.8 km)(sin 30.0°) = 42.9 km
d =
(∆
x
t
ot
)
2
+
(
∆
y
t
ot
)
2
=
(2
17
k
m
)
2
+
(
42
.9
k
m
)
d =
4.
71
×
1
0
4
k
m
2
+
1
.8
4
×
1
0
3
k
m
2
=
4.
89
×
1
0
4
k
m
2
d =
q = tan
−1
∆
∆
x
y
t
t
o
o
t
t
= tan
−1
4
2
2
1
.
7
9
k
k
m
m
= 11.2° north of east
221 km
1. v
x
= 9.37 m/s
∆y =−2.00 m
a
y
=−g =−9.81 m/s
2
∆t =
2
a
∆
y
y
=
∆
v
x
x
∆x = v
x
2
a
∆
y
y
= (9.37 m/s)
(
(
2
−
)
9
(
.
−
8
2
1
.0
m
0
/
m
s
2
)
)
= 5.98 m
The river is 5.98 m wide.
4. v = 925 km/h
∆t
1
= 1.50 h
∆t
2
= 2.00 h
q
2
= 135°
d
1
= v∆t
1
= (925 km/h)(10
3
m/km)(1.50 h) = 1.39 × 10
6
m
d
2
= v∆t
2
= (925 km/h)(10
3
m/km)(2.00 h) = 1.85 × 10
6
m
∆x
1
= d
1
= 1.39 × 10
6
m
∆y
1
= 0 m
∆x
2
= d
2
(cos q
2
) = (1.85 × 10
6
m)(cos 135°) =−1.31 × 10
6
m
∆y
2
= d
2
(sin q
2
) = (1.85 × 10
6
m)(sin 135°) = 1.31 × 10
6
m
∆x
tot
=∆x
1
+ ∆x
2
= 1.39 × 10
6
m + (− 1.31 × 10
6
m) = 0.08 × 10
6
m
∆y
tot
=∆y
1
+ ∆y
2
= 0 m + 1.31 × 10
6
m = 1.31 × 10
6
m
d =
(∆
x
t
ot
)
2
+
(
∆
y
t
ot
)
2
=
(0
.0
8
×
1
0
6
m
)
2
+
(
1.
31
×
1
0
6
m
)
2
d =
6
×
1
0
9
m
2
+
1
.7
2
×
1
0
1
2
m
2
=
1.
73
×
1
0
1
2
m
2
d =
q = tan
−1
∆
∆
x
y
t
t
o
o
t
t
= tan
−1
1
0
.
.
3
0
1
8
×
×
1
1
0
0
6
6
m
m
= 86.5° = 90.0°−3.5°
q = 3.5° east of north
1.32 × 10
6
m = 1.32 × 10
3
km
Givens Solutions
Additional Practice D
2. ∆x = 7.32 km
∆y =−8848 m
a
y
=−g =−9.81 m/s
2
∆t =
2
a
∆
y
y
=
∆
v
x
x
v
x
=
2
a
∆
y
y
∆x =
(
(
2
−
)
9
(−
.8
8
1
8
m
48
/s
m
2
)
)
(7.32 × 10
3
m) =
No. The arrow must have a horizontal speed of 172 m/s, which is much greater than
100 m/s.
172 m/s
Holt Physics Solution ManualII Ch. 3–6
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
4. v
x
= 372 km/h
∆x = 40.0 m
a
y
=−g =−9.81 m/s
2
∆t =
∆
v
x
x
∆y =
1
2
a
y
(∆t)
2
=
a
y
2
(
v
∆
x
x
2
)
2
=
∆y =−0.735 m
The ramp is 0.735 m above the ground.
(−9.81 m/s
2
)(40.0 m)
2
(2)
(372 km/h)
36
1
0
h
0s
1
1
0
k
3
m
m
2
5. ∆x = 25 m
v
x
= 15 m/s
a
y
=−g =−9.81 m/s
2
h = 25 m
∆t =
∆
v
x
x
∆y =
1
2
a
y
(∆t)
2
=
a
y
2
(
v
∆
x
x
2
)
2
=
∆y = h − h′=−14 m
h′=h −∆y = 25 m − (−14 m)
= 39 m
(−9.81 m/s
2
)(25 m)
2
(2)(15 m/s)
2
6.
l
= 420 m
∆y =
∆x =
l
a
y
=−g =−9.81 m/s
2
−
l
2
7. ∆y =−2.45 m
v = 12.0 m/s
a
y
=−g =−9.81 m/s
2
v
y
2
= 2a
y
∆y
v
2
= v
x
2
+ v
y
2
= v
x
2
+ 2a
y
∆y
v
x
=
v
2
− 2a
y
∆y
=
(12.0 m
/s)
2
− (
2)(−9.8
1 m/s
2
)(−2.45
m)
v
x
=
14
4
m
2
/
s
2
−
4
8.
1
m
2
/
s
2
=
96
m
2
/
s
2
v
x
= 9.8 m/s
3. ∆x = 471 m
v
i
= 80.0 m/s
a
y
=−g =−9.81 m/s
2
∆t =
∆
v
x
x
∆y =
1
2
a
y
(∆t)
2
=
a
y
2
(
v
∆
x
x
2
)
2
==−1.70 × 10
2
m
The cliff is 1.70 × 10
2
m high.
(−9.81 m/s
2
)(471 m)
2
(2)(80.0 m/s)
2
Givens Solutions
∆t =
2
a
∆
y
y
=
∆
v
x
x
v
x
=
2
a
∆
y
y
∆x =
(
(
−
2
9
)(
.8
−
1
2
1
m
0
/
m
s
2
)
)
(420 m) = 64 m/s
Section Two — Problem Workbook Solutions II Ch. 3–7
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
1. ∆x = 201.24 m
q = 35.0°
a
y
=−g =−9.81 m/s
2
∆y = v
i
(sin q)∆t +
1
2
a
y
(∆t)
2
= v
i
(sin q) +
1
2
a
y
∆t = 0
∆x = v
i
(cos q)∆t
∆t =
v
i
(c
∆
o
x
s q)
v
i
(sin q) = −
1
2
a
y
v
i
(c
∆
o
x
sq)
v
i
=
2(sin
−a
q
y
)(
∆
c
x
os q
)
=
v
i
= 45.8 m/s
−(−9.81 m/s
2
)(201.24 m)
(2)(sin 35.0°)(cos 35.0°)
2. ∆x = 9.50 × 10
2
m
q = 45.0°
a
y
=−g =−9.81 m/s
2
Using the derivation shown in problem 1,
v
i
=
2(sin
−a
q
y
)(
∆
c
x
os q
)
=
v
i
= 96.5 m/s
At the top of the arrow’s flight:
v = v
x
= v
i
(cos q ) = (96.5 m/s)(cos 45.0°) = 68.2 m/s
−(−9.81 m/s
2
)(9.50 × 10
2
m)
(2)(sin 45.0°)(cos 45.0°)
3. ∆x = 27.5 m
q = 50.0°
a
y
=−g =−9.81 m/s
2
Using the derivation shown in problem 1,
v
i
=
2(sin
−a
q
y
)(
∆
c
x
os q
)
=
v
i
= 16.6 m/s
−(−9.81 m/s
2
)(27.5 m)
(2)(sin 50.0°)(cos 50.0°)
8. ∆y =−1.95 m
v
x
= 3.0 m/s
a
y
=−g =−9.81 m/s
2
v
y
2
= 2a
y
∆y
v =
v
x
2
+
v
y
2
=
v
x
2
+ 2
a
y
∆y
v =
(3.0 m
/s)
2
+ (
2)(−9.8
1 m/s
2
)(−1.95
m)
v =
9.
0
m
2
/
s
2
+
3
8.
3
m
2
/
s
2
=
47
.3
m
2
/
s
2
=
q = tan
−1
v
v
x
y
= tan
−1
= tan
−1
q = 64° below the horizontal
(2)(−9
.81 m/
s
2
)(−1
.95 m)
3.0 m/s
2a
y
∆y
v
x
6.88 m/s
Additional Practice E
4. ∆x = 44.0 m
q = 45.0°
a
y
=−g =−9.81 m/s
2
Using the derivation shown in problem 1,
a. v
i
=
2(sin
−a
q
y
)(
∆
c
x
os q
)
=
v
i
= 20.8 m/s
−(−9.81 m/s
2
)(44.0 m)
(2)(sin 45.0°)(cos 45.0°)
Holt Physics Solution ManualII Ch. 3–8
b. At maximum height, v
y, f
= 0 m/s
v
y, f
2
= v
y, i
2
+ 2a
y
∆y
max
= 0
y
max
==
−v
i
2
(
2
s
a
in
y
q)
2
= = 11.0 m
c. y
max
=
−
2
v
a
y,
y
i
2
=
(2
−
)
(
(
2
−
0
9
.
.
8
81
m
m
/s
/
)
s
2
2
)
= 22.1 m
The brick’s maximum height is 22.1 m.
The brick’s maximum height is 11.0 m.
−(20.8 m/s)
2
(sin 45.0°)
2
(2)(−9.81 m/s
2
)
−v
y
,i
2
2a
y
Givens Solutions
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
5. ∆x = 76.5 m
q = 12.0°
a
y
=−g =−9.81 m/s
2
At maximum height, v
y, f
= 0 m/s.
v
y, f
2
= v
y, i
2
+ 2a
y
∆y
max
= 0
y
max
=
−
2
v
a
y,
y
i
2
=
−v
i
2
(
2
s
a
in
y
q)
2
Using the derivation for v
i
2
from problem 1,
∆y
max
=
2(sin
−a
q
y
)(
∆
c
x
os q)
−(s
2
in
a
y
q)
2
=
∆
4
x
(c
(s
o
i
s
n
q
q
)
)
=
∆x(t
4
an q)
∆y
max
=
(76.5 m)(
4
tan 12.0°)
= 4.07 m
6. v
runner
= 5.82 m/s
v
i,ball
= 2v
runner
In x-direction,
v
i,ball
(cos q) = 2v
runner
(cos q) = v
runner
2(cos q) = 1
q = cos
−1
1
2
= 60°
7. v
i
= 8.42 m/s
q = 55.2°
∆t = 1.40 s
a
y
=−g =−9.81 m/s
2
For first half of jump,
∆t
1
=
1.4
2
0s
= 0.700 s
∆y = v
i
(sin q)∆t
1
+
1
2
a
y
(∆t
1
)
2
= (8.42 m/s)(sin 55.2°)(0.700 s) +
1
2
(−9.81 m/s
2
)(0.700 s)
2
∆y = 4.84 m − 2.40 m = 2.44 m
∆x = v
i
(cos q)∆t
∆x = (8.42 m/s) (cos 55.2°)(1.40 s) = 6.73 m
The fence is 2.44 m high.
8. v
i
= 2.2 m/s
q = 21°
∆t = 0.16 s
a
y
=−g =−9.81 m/s
2
∆x = v
i
(cos q)∆t = (2.2 m/s) (cos 21°)(0.16 s) =
Maximum height is reached in a time interval of
∆
2
t
∆y
max
= v
i
(sin q)
∆
2
t
+
1
2
a
y
∆
2
t
2
∆y
max
= (2.2 m/s)(sin 21°)
0.1
2
6s
+
1
2
(−9.81 m/s
2
)
0.1
2
6s
2
∆y
max
= 6.3 × 10
−2
m − 3.1 × 10
−2
m = 3.2 × 10
−2
m = 3.2 cm
The flea’s maximum height is 3.2 cm.
0.33 m
Section Two — Problem Workbook Solutions II Ch. 3–9
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
1. v
se
= 126 km/h north
v
gs
= 40.0 km/h east
v
ge
= v
g
s
2
+
v
se
2
= (4
0.
0
km
/h
)
2
+
(
12
6
km
/h
)
2
v
ge
= 1.
60
×
1
0
3
k
m
2
/
h
2
+
1
.5
9
×
1
0
4
k
m
2
/
h
2
v
ge
= 1.
75
×
1
0
4
k
m
/h
=
q = tan
−1
v
v
g
se
s
= tan
−
1
4
1
0
2
.
6
0
k
k
m
m
/
/
h
h
= 72.4° north of east
132 km/h
Additional Practice F
2. v
we
=−3.00 × 10
2
km/h
v
pw
= 4.50 × 10
2
km/h
∆x = 250 km
v
pe
= v
pw
+ v
we
= 4.50 × 10
2
km/h − 3.00 × 10
2
km/h = 1.50 × 10
2
km/h
∆t =
v
∆
p
x
e
=
1.50
2
×
50
10
k
2
m
km/h
= 1.7 h
3. v
tw
= 9.0 m/s north
v
wb
= 3.0 m/s east
∆t = 1.0 min
v
tb
= v
tw
+ v
wb
v
tb
=
v
t
w
2
+
v
w
b
2
=
(9
.0
m
/s
)
2
+
(
3.
0
m
/s
)
2
=
81
m
2
/
s
2
+
9
.0
m
2
/
s
2
v
tb
=
9.
0
×
1
0
1
m
2
/
s
2
v
tb
= 9.5 m/s
∆x = v
tb
∆t = (9.5 m/s)(1.0 min)
1
6
m
0
i
s
n
=
q = tan
−1
v
v
w
tw
b
= tan
−1
3
9
.
.
0
0
m
m
/
/
s
s
= 18° east of north
570 m
4. v
sw
= 40.0 km/h forward
v
fw
= 16.0 km/h forward
∆x = 60.0 m
v
sf
= v
sw
− v
fw
= 40.0 km/h − 16.0 km/h = 24.0 km/h toward fish
∆t =
∆
v
s
x
f
==9.00 s
60.0 m
(24.0 km/h)
36
1
0
h
0s
1
1
0
k
3
m
m
5. v
1E
= 90.0 km/h
v
2E
=−90.0 km/h
∆t = 40.0 s
v
12
= v
1E
− v
2E
v
12
= 90.0 km/h − (−90.0 km/h) = 1.80 × 10
2
km/h
∆x = v
12
∆t = (1.80 × 10
2
km/h)
36
1
0
h
0s
1
1
0
k
3
m
m
(40.0 s) = 2.00 × 10
3
m = 2.00 km
The two geese are initially 2.00 km apart
6. v
me
= 18.0 km/h forward
V
re
= 0.333 V
me
= 6.00 km/h forward
∆x = 12.0 m
v
mr
= v
me
− v
re
v
mr
= 18.0 km/h − 6.0 km/h = 12.0 km/h
∆t =
v
∆
m
x
r
=
(12
1
.
2
0
.0
km
m
/h)
36
1
0
h
0s
1
1
0
k
3
m
m
∆t = 3.60 s
Section Two — Problem Workbook Solutions II Ch. 4–1
Forces and the
Laws of Motion
4
Problem Workbook Solutions
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Additional Practice A
Givens Solutions
1.
a. b.
F
Earth-on diver
F
air resistance-on diver
F
Earth-on diver
2.
F
chef-on-sack
F
scale-on-sack
F
Earth-on-sack
3.
F
floor-on-toy-vertical
F
floor-on-toy-horizontal
F
handlebars-on-toy
F
Earth-on-toy
1. m
w
= 75 kg
m
p
= 275 kg
g = 9.81 m/s
2
The normal force exerted by the platform on the weight lifter’s feet is equal to and
opposite of the combined weight of the weightlifter and the pumpkin.
F
net
= F
n
− m
w
g − m
p
g = 0
F
n
= (m
w
+ m
p
)g = (75 kg + 275 kg) (9.81 m/s
2
)
F
n
= (3.50 × 10
2
kg)(9.81 m/s
2
) = 3.43 × 10
3
N
F
n
= 3.43 × 10
3
N upward against feet
Additional Practice B
Holt Physics Solution ManualII Ch. 4–2
Givens Solutions
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. m
b
= 253 kg
m
w
= 133 kg
g = 9.81 m/s
2
F
net
= F
n,1
+ F
n,2
− m
b
g − m
w
g = 0
The weight of the weightlifter and barbell is distributed equally on both feet, so the
normal force on the first foot (F
n,1
) equals the normal force on the second foot (F
n,2
).
2F
n,1
= (m
b
+ m
w
)g = 2F
n,2
F
n,1
= F
n,2
=
(m
b
+
2
m
b
)g
=
F
n,1
= F
n,2
= = 1.89 × 10
3
N
F
n,1
= F
n,2
= 1.89 × 10
3
N upward on each foot
(386 kg)(9.81 m/s
2
)
2
(253 kg + 33 kg)
9.81
m
s
2
2
3. F
down
= 1.70 N
F
net
= 4.90 N
F
net
2
= F
forward
2
+ F
down
2
F
forward
=
F
ne
t
2
−
F
do
w
n
2
=
(4
.9
0
N
)
2
−
(
1.
70
N
)
2
F
forward
=
21
.1
N
2
= 4.59 N
4. m = 3.10 × 10
2
kg
g = 9.81 m/s
2
q
1
= 30.0°
q
2
= − 30.0°
F
x,net
=ΣF
x
= F
T, 1
(sin q
1
) + F
T, 2
(sin q
2
) = 0
F
y,net
=ΣF
y
= F
T, 1
(cos q
1
) + F
T, 2
(cos q
2
) + Fg = 0
F
T, 1
(sin 30.0°) =−F
T, 2
[sin (−30.0°)]
F
T, 1
= F
T, 2
F
T, 1
(cos q
1
) + F
T, 1
(cos q
2
) =−F
g
= mg
F
T, 1
(cos 30.0°) + F
T, 1
[cos (−30.0°)] = (3.10 × 10
2
kg)(9.81 m/s
2
)
F
T, 1
=
F
T, 1
= F
T, 2
=
As the angles q
1
and q
2
become larger, cos q
1
and cos q
2
become smaller. Therefore,
F
T, 1
and F
T, 2
must become larger in magnitude.
1.76 × 10
3
N
(3.10 × 10
2
kg)(9.81 m/s
2
)
(2)(cos 30.0°)[cos(−30.0°)]
Section Two — Problem Workbook Solutions II Ch. 4–3
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
5. m = 155 kg
F
T, 1
= 2F
T, 2
g = 9.81 m/s
2
q
1
= 90°−q
2
F
x,net
= F
T, 1
(cos q
1
) − F
T, 2
(cos q
2
) = 0
F
y,net
= F
T, 1
(sin q
1
) + F
T, 2
(sin q
2
) − mg = 0
F
T, 1
[(cos q
1
) −
1
2
(cos q
2
)] = 0
2 (cos q
1
) = cos q
2
= cos(90°−q
1
) = sin q
1
2 = tan q
1
q
1
= tan
−1
(2) = 63°
q
2
= 90°−63°=27°
F
T, 1
(sin q
1
) +
F
T
2
,1
(sin q
2
) = mg
F
T, 1
=
F
T, 1
= =
(155
0
k
.8
g
9
)(
+
9.
0
8
.
1
2
m
3
/s
2
)
=
(155 kg
1
)
.1
(9
2
.81 m)
F
T, 1
=
F
T, 2
= 6.80 × 10
2
N
1.36 × 1.36 × 10
3
N
(155 kg)(9.81 m/s
2
)
(sin 63°) +
(sin
2
27°)
mg
(sin θ
1
) +
1
2
(sin θ
2
)
1. v
i
= 173 km/h
v
f
= 0 km/h
∆x = 0.660 m
m = 70.0 kg
g = 9.81 m/s
2
a =
v
f
2
2∆
−
x
v
i
2
=
a =−1.75 × 10
3
m/s
2
F = ma = (70.0 kg)(−1.75 × 10
3
m/s
2
) =
F
g
= mg = (70.0 kg)(9.81 m/s
2
) =
The force of deceleration is nearly 178 times as large as David Purley’s weight.
6.87 × 10
2
N
−1.22°×10
5
N
[(0 km/h)
2
− (173 km/h)
2
](10
3
m/km)
2
(1 h/3600 s)
2
(2)(0.660 m)
2. m = 2.232 × 10
6
kg
g = 9.81 m/s
2
a
net
= 0 m/s
2
a. F
net
= ma
net
= F
up
− mg
F
up
= ma
net
+ mg = m(a
net
+ g) = (2.232 × 10
6
kg)(0 m/s
2
+ 9.81 m/s
2
)
F
up
==mg
b. F
down
= mg(sin q)
a
net
=
F
m
net
=
F
up
−
m
F
down
=
mg − m
m
g(sin q)
a
net
= g(1 − sin q) = (9.81 m/s
2
)[1.00 − (sin 30.0°)] =
9.81
2
m/s
2
= 4.90 m/s
2
a
net
= 4.90 m/s
2
up the incline
2.19 × 10
7
N
3. m = 40.00 mg
= 4.00 × 10
−5
kg
g = 9.807 m/s
2
a
net
= (400.0)g
F
net
= F
beetle
− F
g
= ma
net
= m(400.0) g
F
beetle
= F
net
+ F
g
= m(400.0 + 1)g = m(401)g
F
beetle
= (4.000 × 10
−5
kg)(9.807 m/s
2
)(401) =
F
net
= F
beetle
− F
g
= m(400.0) g = (4.000 × 10
−5
kg)(9.807 m/s
2
)(400.0)
F
net
=
The effect of gravity is negligible.
1.569 × 10
−1
N
1.573 × 10
−1
N
Additional Practice C
Holt Physics Solution ManualII Ch. 4–4
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
4. m
a
= 54.0 kg
m
w
= 157.5 kg
a
net
= 1.00 m/s
2
g = 9.81 m/s
2
The net forces on the lifted weight is
F
w,net
= m
w
a
net
= F′−m
w
g
where F′ is the force exerted by the athlete on the weight.
The net force on the athlete is
F
a,net
= F
n,1
+ F
n,2
− F′−m
a
g = 0
where F
n,1
and F
n,2
are the normal forces exerted by the ground on each of the ath-
lete’s feet, and −F′ is the force exerted by the lifted weight on the athlete.
The normal force on each foot is the same, so
F
n,1
= F
n,2
= F
n
and
F ′=2F
n
− m
a
g
Using the expression for F ′ in the equation for F
w,net
yields the following:
m
w
a
net
= (2F
n
− m
a
g) − m
a
g
2F
n
= m
w
(a
net
+ g) + m
a
g
F
n
=
m
w
(a
net
+
2
g) + m
a
g
=
F
n
=
F
n
==
223
2
2N
= 1116 N
F
n,1
− F
n,2
= F
n
= 1116 N upward
1702 N + 5.30 × 10
2
N
2
(157.5 kg)(10.81 m/s
2
) + (54.0 kg)(9.81 m/s
2
)
2
(157.5 kg)(1.00 m/s
2
+ 9.81 m/s
2
) + (54.0 kg)
2
5. m = 2.20 × 10
2
kg
a
net
= 75.0 m/s
2
g = 9.81 m/s
2
F
net
= ma
net
= F
avg
− mg
F
avg
= m(a
net
+ g) = (2.20 × 10
2
kg)(75.0 m/s
2
+ 9.81 m/s
2
)
F
avg
= (2.20 × 10
2
kg)(84.8 m/s
2
) = 1.87 × 10
4
N
F
avg
= 1.87 × 10
4
N upward
6. m = 2.00 × 10
4
kg
∆t = 2.5
v
i
= 0 m/s
v
f
= 1.0 m/s
g = 9.81 m/s
2
a
net
=
v
f
∆
−
t
v
i
=
(1.0 m/
2
s
.
−
5
0
s
.0 m/s)
= 0.40 m/s
2
F
net
= ma
net
= F
T
− mg
F
T
= ma
net
+ mg = m(a
net
+ g)
F
T
= (2.00 × 10
4
kg)(0.40 m/s
2
+ 9.81 m/s
2
)
F
T
= (2.00 × 10
4
kg)(10.21 m/s
2
) = 2.04 × 10
5
N
F
T
= 2.04 × 10
5
N
7. m = 2.65 kg
q
1
= q
2
= 45.0°
a
net
= 2.55 m/s
2
g = 9.81 m/s
2
F
x,net
= F
T, 1
(cos q
1
) − F
T, 2
(cos q
2
) = 0
F
T, 1
(cos 45.0°) = F
T, 2
(cos 45.0°)
F
T, 1
= F
T, 2
F
y,net
= ma
net
= F
T, 1
(sin q
1
) + F
T, 2
(sin q
2
) − mg
F
T
= F
T, 1
= F
T, 2
q = q
1
= q
2
F
T
(sin q) + F
T
(sin q) = m(a
net
+ g)
2F
T
(sin q) = m(a
net
+ g)
Section Two — Problem Workbook Solutions II Ch. 4–5
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
F
T
=
m
2
(a
(s
n
i
e
n
t
+
q)
g)
=
F
T
==23.2 N
F
T, 1
= 23.2 N
F
T, 2
= 23.2 N
(2.65 kg)(12.36 m/s
2
)
(2)(sin 45.0°)
(2.65 kg)(2.55 m/s
2
= 9.81 m/s
2
)
(2)(sin 45.0°)
Givens Solutions
8. m = 20.0 kg
∆x = 1.55 m
v
i
= 0 m/s
v
f
= 0.550 m/s
a
net
=
v
f
2
2∆
−
x
v
i
2
= = 9.76 × 10
−2
m/s
2
F
net
= ma
net
= (20.0 kg)(9.76 × 10
−2
m/s
2
) = 1.95 N
(0.550 m/s)
2
− (0.00 m/s)
2
(2)(1.55 m)
9. m
max
= 70.0 kg
m = 45.0 kg
g = 9.81 m/s
2
F
max
= m
max
g = F
T
F
max
= (70.0 kg)(9.81 m/s
2
) = 687 N
F
net
= ma
net
= F
T
− mg = F
max
− mg
a
net
=
F
m
m
ax
− g =
4
6
5
8
.
7
0
N
kg
− 9.81 m/s
2
= 15.3 m/s
2
− 9.81 m/s
2
= 5.5 m/s
2
a
net
= 5.5 m/s
2
upward
10. m = 3.18 × 10
5
kg
F
applied
= 81.0 × 10
3
N
F
friction
= 62.0 × 10
3
N
F
net
= F
applied
− F
friction
= (81.0 × 10
3
− 62.0 × 10
3
N)
F
net
= 19.0 × 10
3
N
a
net
=
F
m
net
=
3
1
.
9
1
.
8
0
×
×
1
1
0
0
5
3
k
N
g
= 5.97 × 10
−2
m/s
2
11. m = 3.00 × 10
3
kg
F
applied
= 4.00 × 10
3
N
q = 20.0°
F
opposing
= (0.120) mg
g = 9.81 m/s
2
F
net
= ma
net
= F
applied
(cos q) − F
opposing
a
net
=
a
net
=
a
net
= =
3
2
.0
.3
0
×
×
1
1
0
0
2
3
N
kg
a
net
= 7.7 × 10
−2
m/s
2
3.76 × 10
3
N − 3.53 × 10
3
N
3.00 × 10
3
kg
(4.00 × 10
3
N)(cos 20.0°) − (0.120)(3.00 × 10
3
kg)(9.81 m/s
2
)
3.00 × 10
3
kg
F
applied
(cos q) − (0.120) mg
m
12. m
c
= 1.600 × 10
3
kg
m
w
= 1.200 × 10
3
kg
v
i
= 0 m/s
g = 9.81 m/s
2
∆y = 25.0 m
For the counterweight: The tension in the cable is F
T
.
F
net
= F
T
− m
w
g = m
w
a
net
For the car:
F
net
= m
c
g − F
T
= m
c
a
net
Adding the two equations yields the following:
m
c
g − m
w
g = (m
w
+ m
c
)a
net
a
net
=
(m
m
c
c
−
+
m
m
w
w
)g
=
a
net
= = 1.40 m/s
2
(4.00 × 10
2
kg)(9.81 m/s
2
)
2.800 × 10
3
kg
(1.600 × 10
3
kg − 1.200 × 10
3
kg)(9.81 m/s
2
)
1.600 × 10
3
kg + 1.200 × 10
3
kg
Holt Physics Solution ManualII Ch. 4–6
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
13. m = 409 kg
d = 6.00 m
q = 30.0°
g = 9.81 m/s
2
F
applied
= 2080 N
v
i
= 0 m/s
a. F
net
= F
applied
− mg(sin q) = 2080 N − (409 kg)(9.81 m/s
2
)(sin 30.0°)
F
net
= 2080 N − 2010 N = 70 N
F
net
=
b. a
net
=
F
m
net
=
4
7
0
0
9
N
kg
= 0.2 m/s
2
a
net
=
c. d = v
i
∆t +
1
2
a
net
∆t
2
= (0 m/s)∆t +
1
2
(0.2 m/s
2
)∆t
2
∆t =
(
(
2
0
)
.
(
2
6
.
m
0
0
/s
m
2
)
)
= 8 s
0.2 m/s
2
at 30.0° above the horizontal
70 N at 30.0° above the horizontal
v
f
=
2a
ne
t
∆
y
+
v
i
2
=
(2
)(
1.
40
m
/s
2
)
(2
5.
0
m
)
+
(
0
m
/s
)
2
v
f
= 8.37 m/s
Givens Solutions
14. a
max
= 0.25 m/s
2
F
max
= 57 N
F
app
= 24 N
a. m =
F
a
m
m
a
a
x
x
=
0.2
5
5
7
m
N
/s
2
=
b. F
net
= F
max
− F
app
= 57 N − 24 N = 33 N
a
net
=
F
m
net
=
2.3
3
×
3
1
N
0
2
kg
= 0.14 m/s
2
2.3 × 10
2
kg
15. m = 2.55 × 10
3
kg
F
T
= 7.56 × 10
3
N
q
T
=−72.3°
F
buoyant
= 3.10 × 10
4
N
F
wind
=−920 N
g = 9.81 m/s
2
∆y =−45.0 m
v
i
= 0 m/s
a. F
x,net
=ΣF
x
= m
ax,net
= F
T
(cos q
T
) + F
wind
F
x,net
= (7.56 × 10
3
N)[cos(−72.3°)] − 920 N = 2.30 × 10
3
N − 920 N = 1.38 × 10
3
N
F
y,net
=ΣF
y
= ma
y,net
= F
T
(sin q
T
) + F
buoyant
+ F
g
= F
T
(sin q
T
) + F
buoyant
− mg
F
y,net
= (7.56 × 10
3
N)[sin(−72.3°)] = 3.10 × 10
4
N − (2.55 × 10
3
kg)(9.81 m/s
2
)
F
y,net
=−7.20 × 10
3
N + 3.10 × 10
4
N − 2.50 × 10
4
=−1.2 × 10
3
N
F
net
=
(F
x,
ne
t
)
2
+
(
F
y,n
et
)
2
=
(1
.3
8
×
1
0
3
N
)
2
+
(
−
1.
2
×
1
0
3
N
)
2
F
net
=
1.
90
×
1
0
6
N
2
+
1
.4
×
1
0
6
N
2
F
net
=
3.
3
×
1
0
6
N
2
= 1.8 × 10
3
N
q = tan
−1
F
F
x
y,
,
n
n
e
e
t
t
= tan
−1
−
1.
1
3
.
8
2
×
×
1
1
0
0
3
3
N
N
q =−41°
F
net
=
b. a
net
=
F
m
net
=
2
1
.5
.8
5
×
×
1
1
0
0
3
3
N
kg
a
net
=
c. Because v
i
= 0
∆y =
1
2
a
y,net
∆t
2
∆x =
1
2
a
x,net
∆t
2
∆x =
a
a
x
y,
,
n
n
e
e
t
t
∆y =∆y =
ta
∆
n
y
q
∆x =
ta
−
n
4
(
5
−
.0
41
m
°)
= 52 m
a
net
(cos q)
a
net
(sin q)
0.71 m/s
2
1.8 × 10
3
N at 41° below the horizontal
Section Two — Problem Workbook Solutions II Ch. 4–7
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. m = 11.0 kg
m
k
= 0.39
g = 9.81 m/s
2
Additional Practice D
Givens Solutions
2. m = 2.20 × 10
5
kg
m
s
= 0.220
g = 9.81 m/s
2
F
s,max
= m
s
F
n
= m
s
mg
F
s,max
= (0.220)(2.20 × 10
5
kg)(9.91 m/s
2
) = 4.75 × 10
5
N
3. m = 25.0 kg
F
applied
= 59.0 N
q = 38.0°
m
s
= 0.599
g = 9.81 m/s
2
F
s,max
= m
s
F
m
F
n
= mg(cos q) + F
applied
F
s,max
= m
s
[mg(cos q) = F
applied
] = (0.599)[(25.0 kg)(9.81 m/s
2
)(cos 38.0°+59.0 N]
F
s,max
= (0.599)(193 N + 59 N) = (0.599)(252 N) =
Alternatively,
F
net
= mg(sin q) − F
s,max
= 0
F
s,max
= mg(sin q) = (25.0 kg)(9.81 m/s
2
)(sin 38.0°) = 151 N
151 N
F
k
= m
k
F
n
= m
k
mg
F
k
= (0.39) (11.0 kg)(9.81 m/s
2
) = 42.1 N
4. q = 38.0°
g = 9.81 m/s
2
F
net
= mg(sin q) − F
k
= 0
F
k
= m
k
F
n
= m
k
mg(cos q)
m
k
mg(cos q) = mg(sin q)
m
k
=
c
si
o
n
s
q
q
= tan q = tan 38.0°
m
k
= 0.781
5. q = 5.2°
g = 9.81 m/s
2
F
net
= mg(sin q) − F
k
= 0
F
k
= m
k
F
n
= m
k
mg(cos q)
m
k
mg(cos q) = mg(sin q)
m
k
=
c
si
o
n
s
q
q
= tan q = tan 5.2°
m
k
= 0.091
Holt Physics Solution ManualII Ch. 4–8
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
10. m = 3.00 × 10
3
kg
q = 31.0°
g = 9.81 m/s
2
F
net
= mg(sin q) − F
k
= 0
F
k
= m
k
F
n
= m
k
mg(cos q)
m
k
mg(cos q) = mg(sin q)
m
k
=
c
si
o
n
s
q
q
= tan q = tan 31.0°
m
k
=
F
k
= m
k
mg(cos q) = (0.601)(3.00 × 10
3
kg)(9.81 m/s
2
)(cos 31.0°)
F
k
=
Alternatively,
F
k
= mg(sin q) = (3.00 × 10
3
kg)(9.81 m/s
2
)(sin 31.0°) = 1.52 × 10
4
N
1.52 × 10
4
N
0.601
6. m = 281.5 kg
q = 30.0°
F
net
= 3mg(sin q) − m
s
(3mg)(cos q) − F
applied
= 0
F
applied
= mg
m
s
===
m
s
=
(3
1
)
.
(
5
c
0
o
−
s3
1
0
.0
.0
0
°)
=
(3)(c
0
o
.
s
5
3
0
0.0°)
m
s
= 0.19
(3)(sin 30.0°) − 1.00
(3)(cos 30.0°)
3(sin q) − 1.00
3(cos q)
3mg(sin q) − mg
3mg(cos q)
Givens Solutions
7. m = 1.90 × 10
5
kg
m
s
= 0.460
g = 9.81 m/s
2
F
net
= F
applied
− F
k
= 0
F
k
= m
k
F
n
= m
k
mg
F
applied
= m
k
mg = (0.460)(1.90 × 10
5
kg)(9.81 m/s
2
)
F
applied
= 8.57 × 10
5
N
8. F
applied
= 6.0 × 10
3
N
m
k
= 0.77
g = 9.81 m/s
2
F
net
= F
applied
− F
k
= 0
F
k
= m
k
F
n
F
n
=
F
ap
m
p
k
lied
=
6.0
0
×
.7
1
7
0
3
N
=
F
n
= mg
m =
F
g
n
=
7
9
.8
.8
×
1
1
m
0
/
3
s
N
2
= 8.0 × 10
2
kg
7.8 × 10
3
N
9. F
applied
= 1.13 × 10
8
N
m
s
= 0.741
F
net
= F
applied
− F
s,max
= 0
F
s,max
= m
s
F
n
= m
s
mg
m =
F
a
m
pp
s
g
lied
=
(0.
1
7
.
4
1
1
3
)(
×
9
1
.8
0
1
8
m
N
/s
2
= 1.55 × 10
2
kg
Section Two — Problem Workbook Solutions II Ch. 4–9
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. F
applied
= 130 N
a
net
= 1.00 m/s
2
m
k
= 0.158
g = 9.81 m/s
2
F
net
= ma
net
= F
applied
− F
k
F
k
= m
k
F
n
= m
k
mg
ma
net
+ m
k
mg = F
applied
m(a
net
+ m
k
g) = F
applied
m =
a
n
F
e
a
t
p
+
pli
m
ed
k
g
=
m = = = 51 kg
130 N
2.55 m/s
2
130 N
1.00 m/s
2
+ 1.55 m/s
2
130 N
1.00 m/s
2
+ (0.158)(9.81 m/s
2
)
2. F
net
=−2.00 × 10
4
N
q = 10.0°
m
k
= 0.797
g = 9.81 m/s
2
F
net
= ma
net
= mg(sin q) − F
k
F
k
= m
k
F
n
= m
k
m
g
(cos q)
m[g(sin q) − m
k
g(cos q)] = F
net
m =
g[sin q −
F
n
m
e
k
t
(cos q)]
=
m = =
(9.8
−
1
2.
m
00
/s
×
2
)
1
(−
0
4
0.
N
611)
m =
F
n
= mg(cos q) = (3.34 × 10
3
kg)(9.81 m/s
2
)(cos 10.0°) = 3.23 × 10
4
N
3.34 × 10
3
kg
−2.00 × 10
4
N
(9.81 m/s
2
)(0.174 − 0.785)
−2.00 × 10
4
N
(9.81 m/s
2
)[(sin 10.0°) − (0.797)(cos 10.0°)]
3. F
net
= 6.99 × 10
3
N
q = 45.0°
m
k
= 0.597
F
net
= ma
net
= mg(sin q) − F
k
F
k
= m
k
F
n
= m
k
mg(cos q)
m[g(sin q) − m
k
g(cos q)] = F
net
m =
g[sin q −
F
n
m
e
k
t
(cos q)]
=
m = =
(9.8
6
1
.9
m
9
/
×
s
2
1
)
0
(
3
0.
N
285)
m =
F
n
= mg(cos q) = (2.50 × 10
3
kg)(9.81 m/s
2
)(cos 45.0°) = 1.73 × 10
4
N
2.50 × 10
3
kg
6.99 × 10
3
N
(9.81 m/s
2
)(0.707 − 0.422)
6.99 × 10
3
N
(9.81 m/s
2
)[(sin 45.0°) − (0.597)(cos 45.0°)]
4. m = 9.50 kg
q = 30.0 °
F
applied
= 80.0 N
a
net
= 1.64 m/s
2
g = 9.81 m/s
2
F
net
= ma
net
= F
applied
− F
k
− mg(sin q)
F
k
= m
k
F
n
= m
k
mg(cos q)
m
k
mg(cos q) = F
applied
− ma
net
− mg(sin q)
m
k
=
m
k
=
80.0 N − (9.50 kg)[1.64 m/s
2
+ (9.81 m/s
2
)(sin 30.0°)]
(9.50 kg)(9.81 m/s
2
)(cos 30.0°)
F
applied
− m[a
net
+ g (sin q)]
mg(cos q)
Additional Practice E
Givens Solutions
II
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualII Ch. 4–10
6. q = 38.0°
m
k
= 0.100
g = 9.81 m/s
2
F
net
= ma
net
= mg(sin q) − F
k
F
k
= m
k
F
n
= m
k
mg(cos q)
ma
net
= mg[sin q − m
k
(cos q)]
a
net
= g[sin q − m
k
(cos q)] = (9.81 m/s
2
)[(sin 38.0°) − (0.100)(cos 38.0°)]
a
net
= (9.81 m/s
2
)(0.616 − 7.88 × 10
−2
) = (9.81 m/s
2
)(0.537)
a
net
=
Acceleration is independent of the rider’s and sled’s masses. (Masses cancel.)
5.27 m/s
2
m
k
==
m
k
==
m
k
= 0.222
17.9 N
(9.50 kg)(9.81 m/s
2
)(cos 30.0°)
80.0 N − 62.1 N
(9.50 kg)(9.81 m/s
2
)(cos 30.0°)
80.0 N − (9.50 kg)(6.54 m/s
2
)
(9.50 kg)(9.81 m/s
2
)(cos 30.0°)
80.0 N − (9.50 kg)[1.64 m/s
2
+ 4.90 m/s
2
)
(9.50 kg)(9.81 m/s
2
)(cos 30.0°)
5. m = 1.89 × 10
5
kg
F
applied
= 7.6 × 10
5
N
a
net
= 0.11 m/s
2
F
net
= ma
net
= F
applied
− F
k
F
k
= F
applied
− ma
net
= 7.6 × 10
5
N − (1.89 × 10
5
)(0.11 m/s
2
) = 7.6 × 10
5
N − 2.1 × 10
4
N
F
k
= 7.4 × 10
5
N
7. ∆t = 6.60 s
q = 34.0°
m
k
= 0.198
g = 9.81 m/s
2
v
i
= 0 m/s
F
net
= ma
net
= mg(sin q) − F
k
F
k
= m
k
F
n
= m
k
mg(cos q)
ma
net
= mg[sin q − m
k
(cos q)]
a
net
= g[sin q − m
k
(cos q)] = (9.81 m/s
2
)[(sin 34.0°) − (0.198)(cos 34.0°)]
a
net
= (9.81 m/s
2
)(0.559 − 0.164) = (9.81 m/s
2
)(0.395)
a
net
=
v
f
= v
i
+ a
net
∆t = 0 m/s + (3.87 m/s
2
)(6.60 s)
v
f
= 25.5 m/s
2
= 92.0 km/h
3.87 m/s
2
Section Two — Problem Workbook Solutions II Ch. 5–1
Work and Energy
Problem Workbook Solutions
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. W = 1.15 × 10
3
J
m = 60.0 kg
g = 9.81 m/s
2
q = 0°
W = Fd(cos q) = mgd(cos q)
d =
mg(
W
cos q)
=
d = 195 m
1.15 × 10
5
J
(60.0 kg)(9.81 m/s
2
)(cos 0°)
Additional Practice A
Givens Solutions
2. m = 1.45 × 10
6
kg
g = 9.81 m/s
2
q = 0°
W = 1.00 × 10
2
MJ
F = (2.00 × 10
−2
) mg
W = Fd(cos q)
d =
F(c
W
os q)
=
d = 352 m
1.00 × 10
8
J
(2.00 × 10
−2
)(1.45 × 10
6
kg)(9.81 m/s
2
)(cos 0.00°)
3. m = 1.7 g
W = 0.15 J
a
net
= 1.2 m/s
2
q = 0°
g = 9.81 m/s
2
4. m = 5.40 × 10
2
kg
W = 5.30 × 10
4
J
g = 9.81 m/s
2
q = 30.0°
q′=0°
W = Fd(cos q′) = Fd
F = mg(sin q)
W = mg(sin q)d
d =
mg(
W
sin q)
=
d = 20.0 m
5.30 × 10
4
J
(5.40 × 10
2
kg)(9.81 m/s
3
)(sin 30.0°)
F
net
= ma
net
= F − mg
F = ma
net
+ mg
W = Fd(cos q) = m(a
net
+ g)d(cos q)
d =
m(a
net
+
W
g)(cos q)
=
d =
d = 8.0 m
0.15 J
(1.7 × 10
−3
kg)(11.0 m/s
2
)
0.15 J
(1.7 × 10
−3
kg)(1.2 m/s
2
+ 9.81 m/s
2
)(cos 0°)
Holt Physics Solution ManualII Ch. 5–2
II
5. d = 5.45 m
W = 4.60 × 10
4
J
q = 0°
F
net
= F
lift
− F
g
= 0
F = F
lift
= F
g
W = Fd(cos q) = F
g
d(cos q)
F
g
=
d(c
W
os q)
=
(5.
4
4
.
5
60
m
×
)(
1
c
0
o
4
s
J
0°)
= 8.44 10
3
N
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
6. d = 52.0 m
m = 40.0 kg
W = 2.04 × 10
4
J
q = 0°
F =
d(c
W
os q)
=
(5
2
2
.
.
0
0
4
m
×
)
1
(c
0
o
4
s
J
0°)
= 392 N
7. d = 646 m
W = 2.15 × 10
5
J
q = 0°
F =
d(c
W
os q)
=
(64
2
6
.1
m
5 ×
)(
1
co
0
s
5
0
J
°)
= 333 N
8. m = 1.02 × 10
3
kg
d = 18.0 m
angle of incline = q = 10.0°
q′=0°
g = 9.81 m/s
2
m
k
= 0.13
F
net
= F
g
− F
k
= mg (sin q) − m
k
mg(cos q)
W
net
= F
net
d(cos q′) = mgd(cos q′)[(sin q) − m
k
(cos q)]
W
net
= (1.02 × 10
3
kg)(9.81 m/s
2
)(18.0 m)(cos 0°)[(sin 10.0°) − (0.13)(cos 10.0°)]
W
net
= (1.02 × 10
3
kg)(9.81 m/s
2
)(18.0 m)(0.174 − 0.128)
W
net
= (1.02 × 10
3
kg)(9.81 m/s
2
)(18.0 m)(0.046)
W
net
= 8.3 × 10
3
J
9. d = 881.0 m
F
applied
= 40.00 N
q = 45.00°
F
k
= 28.00 N
q′=0°
W
net
= F
net
d(cos q′)
F
net
= F
applied
(cos q) − F
k
W
net
= [F
applied
(cos q) − F
k
]d(cos q′)
W
net
= [40.00 N(cos 45.00°) − 28.00° N](881.0 m)(cos q)
W
net
= (28.28 N − 28.00 N)(881.0 m) = (0.28 N)(881.0 m)
W
net
= 246.7 J
10. m = 9.7 × 10
3
kg
q = 45°
F = F
1
= F
2
= 1.2 × 10
3
N
d = 12 m
W
net
= F
net
d(cos q) = (F
1
+ F
2
)d(cos q) = 2Fd(cos q)
W
net
= (2)(1.2 × 10
3
N)(12 m)(cos 45°) = 2.0 × 10
4
J
11. m = 1.24 × 10
3
kg
F
1
= 8.00 × 10
3
N east
F
2
= 5.00 × 10
3
N 30.0°
south of east
d = 20.0 m south
Only F
2
contributes to the work done in moving the flag south.
q = 90.0°−30.0°=60.0°
W
net
= F
net
d(cos q) = F
2
d(cos q) = (5.00 × 10
3
N)(20.0 m)(cos 60.0°)
W
net
= 5.00 × 10
4
J
Section Two — Problem Workbook Solutions II Ch. 5–3
II
1. ∆x = 1.00 × 10
2
m
∆t = 9.85 s
KE = 3.40 × 10
3
J
v =
∆
∆t
x
KE =
1
2
mv
2
=
1
2
m
∆
∆
x
t
2
m =
2K
∆
E
x
∆
2
t
2
==66.0 kg
(2)(3.40 × 10
3
J)(9.85 s)
2
(1.00 × 10
2
m)
2
Additional Practice B
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. v = 4.00 × 10
2
km/h
KE = 2.10 × 10
7
J
m =
2
v
K
2
E
==3.40 × 10
3
kg
(2)(2.10 × 10
7
J)
(4.00 × 10
2
km/h)
2
(10
3
m km)
2
(1 h/3600 s)
2
3. v = 50.3 km/h
KE = 6.54 × 10
3
J
m =
2
v
K
2
E
==67.0 kg
(2)(6.54 × 10
3
J)
(50.3 km/h)
2
(10
3
m/km)
2
(1 h/3600 s)
4. v = 318 km/h
KE = 3.80 MJ
m =
2
v
K
2
E
==974 kg
(2)(3.80 × 10
6
J)
(318 km/h)
2
(10
3
m/km)
2
(1 h/3600 s)
5. m = 51.0 kg
KE = 9.96 × 10
4
J
v =
2
m
K
E
=
(2
)(
9
5
.
9
1
6
.
0
×
kg
10
4
J)
= 62.5 m/s = 225 km/h
6. ∆x = 93.625 km
∆t = 24.00 h
m = 55 kg
a. v
avg
=
∆
∆
x
t
=
(24
9
.
.
0
3
0
62
h
5
)(
×
3
1
6
0
0
4
0
m
s/h)
=
b. KE =
1
2
mv
2
=
1
2
(55 kg)(1.084 m/s)
2
= 32 J
1.084 m/s
7. m = 3.38 × 10
31
kg
KE = 1.10 × 10
42
J
v =
2
m
K
E
=
(2
3
)
.
(
3
1
8
.1
×
0
1
×
0
1
3
1
0
4
k
2
g
J
)
= 2.55 × 10
5
m/s = 255 km/s
8. m = 680 kg
v = 56.0 km/h
KE
LB
= 3.40 × 10
3
J
a. KE =
1
2
mv
2
=
1
2
(680 kg)[(56.0 km/h)(10
3
m/km)(1 h/3600 s)]
2
= 8.23 × 10
4
J
b.
K
K
E
E
L
p
B
b
=
3
8
.
.
4
2
0
×
×
1
1
0
0
4
3
J
J
=
2
1
4
9. v = 11.2 km/s
m = 2.3 × 10
5
kg
KE =
1
2
mv
2
=
1
2
(2.3 × 10
5
kg)(11.2 × 10
3
m/s)
2
= 1.4 × 10
13
J
Holt Physics Solution ManualII Ch. 5–4
II
Additional Practice C
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. d = 227 m
m = 655 g
g = 9.81 m/s
2
F
resistance
= (0.0220)mg
q = 0°
KE
i
= 0 J
W
net
=∆KE = KE
f
− KE
i
= KE
f
W
net
= F
net
d(cos q)
F
net
= F
g
− F
resistance
= mg − (0.0220)mg = mg(1 − 0.0220)
KE
f
= mg(1 − 0.0220)d(cos q) = (655 × 10
−3
kg)(9.81 m/s
2
)(1 − 0.0220)(227 m)(cos 0°)
KE
f
= (0.655 kg)(9.81 m/s
2
)(0.9780)(227 m)
KE
f
= 1.43 × 10
3
J
2. v
i
= 12.92 m/s
W
net
=−2830 J
m = 55.0 kg
W
net
is the work done by friction.
W
net
=∆KE = KE
f
− KE
i
= KE
f
−
1
2
mv
i
2
KE
f
= W
net
+
1
2
mv
i
2
=−2830 J +
1
2
(55.0 kg)(12.92 m/s)
2
=−2830 J + 4590 J
KE
f
= 1.76 × 10
3
J
3. m = 25.0 g
h
i
= 553 m
h
f
= 353 m
v
i
= 0 m/s
v
f
= 30.0 m/s
g = 9.81 m/s
2
q = 0°
W
net
=∆KE = KE
f
− KE
i
=
1
2
mv
f
2
−
1
2
mv
i
2
W
net
= F
net
d(cos q)
F
net
= F
g
− F
r
= mg − F
r
d = h
i
− h
f
W
net
= (mg − F
r
)(h
i
− h
f
)(cos q)
mg − F
r
=
1
2
m (v
f
2
− v
i
2
)
(h
i
– h
f
)(cos q)
F
r
= m
g −
2(h
(
i
v
−
f
2
h
−
f
)(
v
c
i
2
o
)
s q)
= (25.0 × 10
−3
kg)
9.81 m/s
2
−
F
r
= (25.0 × 10
−3
kg)
9.81 m/s
2
−
(
9
2
.
)
0
(
0
2.
×
00
10
×
2
1
m
0
2
2
/
m
s
2
)
F
r
= (25.0 × 10
−3
kg)(9.81 m/s
2
− 2.25 m/s
2
) = (25.0 × 10
−3
kg)(7.56 m/s
2
)
F
r
= 0.189 N
(30.0 m/s)
2
− (0 m/s)
2
(2)(553 m − 353 m)(cos 0°)
4. v
i
= 404 km/h
W
net
=−3.00 MJ
m = 1.00 × 10
3
kg
W
net
=∆KE = KE
f
− KE
i
=
1
2
mv
f
2
−
1
2
mv
i
2
1
2
mv
f
2
=
1
2
mv
i
2
+ W
net
v
f
=
v
i
2
+
2
W
m
ne
t
=
[(
40
4
km
/h
)(
10
3
m
/k
m
)(
1
h
/3
60
0
s)
]
2
+
(
2)
1
(
.
−
0
0
3.
0
×
0
1
×
0
3
1
k
0
g
6
J)
v
f
=
1.
26
×
1
0
4
m
2
/
s
2
−
6
.0
0
×
1
0
3
m
2
/
s
2
=
6.
6
×
1
0
3
m
2
/
s
2
v
f
= 81 m/s = 290 km/h
5. m = 45.0 g
h
i
= 8848.0 m
h
f
= 8806.0 m
v
i
= 0 m/s
v
f
= 27.0 m/s
g = 9.81 m/s
2
q = 0°
W
net
=∆KE = KE
f
− KE
i
=
1
2
mv
f
2
−
1
2
mv
i
2
W
net
= F
net
d(cos q)
F
net
= F
g
− F
r
= mg − F
r
d = h
i
− h
f
W
net
= mg(h
i
− h
f
)(cos q) − F
r
(h
i
− h
f
)(cos q)
− F
r
(h
i
− h
f
)(cos q) = F
r
(h
i
− h
f
)(cos 180°+q) = W
r
1
2
m(v
f
2
− v
i
2
) = mg(h
i
− h
f
)(cos q) + W
r
Section Two — Problem Workbook Solutions II Ch. 5–5
II
6. v
f
= 35.0 m/s
v
i
= 25.0 m/s
W
net
= 21 kJ
W
net
=∆KE = KE
f
− KE
i
=
1
2
mv
f
2
−
1
2
mv
i
2
m =
v
2
f
2
W
−
n
v
et
i
2
==
m =
6.0
4
×
2
1
×
0
1
2
0
m
3
J
2
/s
2
= 7.0 × 10
1
kg
42 × 10
3
J
1220 m
2
/s
2
− 625 m
2
/s
2
(2)(21 × 10
3
J)
(35.0 m/s)
2
− (25.0 m/s)
2
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
7. v
i
= 104.5 km/h
v
f
=
1
2
v
i
m
k
= 0.120
g = 9.81 m/s
2
q = 180°
W
net
=∆KE = KE
f
− KE
i
=
1
2
mv
f
2
−
1
2
mv
i
2
W
net
= W
k
d(cos q) = F
k
d(cos q) = m
k
mgd(cos q)
1
2
m(v
f
2
− v
i
2
) = m
k
mgd(cos q)
d =
2m
v
k
f
g
2
(
−
co
v
s
i
2
q)
=
d = =
d = 268 m
−(3)
1
3
0
.6
4
0
.5
0
m/s
2
−(8)(0.120)(9.81 m/s
2
)
1
3
0
.6
4
0
.5
0
m/s
2
1
4
− 1
−(2)(0.120)(9.81 m/s
2
)
(2)(0.120)(9.81 m/s
2
)(cos 180°)
Additional Practice D
W
r
= m[
1
2
(v
f
2
− v
i
2
) − g(h
i
− h
f
)(cos q)] = (45.0 × 10
−3
kg)
1
2
(27.0 m/s)
2
−
1
2
(0 m/s)
2
−(9.81 m/s
2
)(8848.0 m − 8806.0 m)(cos 0°)
W
r
= (45.0 × 10
−3
kg)[364 m
2
/s
2
− (9.81 m/s
2
)(42.0 m)]
W
r
= (45.0 × 10
−3
kg)(364 m
2
/s
2
− 412 m
2
/s
2
)
W
r
= (45.0 × 10
−3
kg)(−48 m
2
/s
2
) =−2.16 J
1. h = 6.13/2 m = 3.07 m
PE
g
= 4.80 kJ
g = 9.81 m/s
2
m =
P
g
E
h
g
=
(9.81
4.
m
80
/s
×
2
)
1
(
0
3
3
.0
J
7m)
= 1.59 × 10
2
kg
2. h = 1.70 m
PE
g
= 3.04 × 10
3
J
g = 9.81 m/s
2
m =
P
g
E
h
g
=
(9.81
3.
m
04
/s
×
2
)
1
(
0
1
3
.7
J
0m)
= 182 kg
3. PE
g
= 1.48 × 10
7
J
h = (0.100)(180 km)
g = 9.81 m/s
2
m =
P
g
E
h
g
= = 83.8 kg
1.48 × 10
7
J
(9.81 m/s
2
)(0.100)(180 × 10
3
m)
4. m = 3.6 × 10
4
kg
PE
g
= 8.88 × 10
8
J
g = 9.81 m/s
2
h =
P
m
E
g
g
==2.5 × 10
3
m = 2.5 km
8.88 × 10
8
J
(3.6 × 10
4
kg)(9.81 m/s
2
)
[(104.5 km/h)(10
3
m/km)(1 h/3600 s)]
2
[
1
2
2
− (1)
2
]
Holt Physics Solution ManualII Ch. 5–6
II
5.
P
m
E
g
= 20.482 m
2
/s
2
g = 9.81 m/s
2
P
m
E
g
= gh = 20.482 m
2
/s
2
h =
20.482
g
m
2
/s
2
=
20
9
.
.
4
8
8
1
2
m
m
/
2
s
/
2
s
2
= 2.09 m
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
6. k = 3.0 × 10
4
N/m
PE
elastic
= 1.4 × 10
2
J
x =±
2P
E
k
el
as
tic
=±
(
3
2
.
)
0
(1
×
.4
1
0
×
4
1
N
0
/
2
m
J)
=+9.7 × 10
−2
m = 9.7 cm
7. m = 51 kg
g = 9.81 m/s
2
h = 321 m − 179 m = 142 m
k = 32 N/m
x = 179 m − 104 m = 75 m
PE
tot
= PE
g
+ PE
elastic
Set PE
g
= 0 J at the river level.
PE
g
= mgh = (51 kg)(9.81 m/s
2
)(142 m) = 7.1 × 10
4
J
PE
elastic
=
1
2
kx
2
=
1
2
(32 N/m)(75 m)
2
= 9.0 × 10
4
J
PE
tot
= (7.1 × 10
4
J) + (9.0 × 10
4
J) = 1.6 × 10
5
J
8. h
2
= 4080 m
h
1
= 1860 m
m = 905 kg
g = 9.81 m/s
2
∆PE
g
= PE
g,2
− PE
g,1
= mg(h
2
− h
1
) = (905 kg)(9.81 m/s
2
)(4080 m − 1860 m)
∆PE
g
= (905 kg)(9.81 m/s
2
)(2220 m) = 1.97 × 10
7
J
9. m = 286 kg
k = 9.50 × 10
3
N/m
g = 9.81 m/s
2
x = 59.0 cm
h
1
= 1.70 m
h
2
= h
1
− x
a. PE
elastic
=
1
2
kx
2
=
1
2
(9.50 × 10
3
N/m)(0.590 m)
2
=
b. PE
g,1
= mgh
1
= (286 kg)(9.81 m/s
2
)(1.70 m) =
c. h
2
= 1.70 m − 0.590 m = 1.11 m
PE
g,2
= mgh
2
= (286 kg)(9.81 m/s
2
)(1.11 m) =
d. ∆PE
g
= PE
g,2
− PE
g,1
= (3.11 × 10
3
J) − (4.77 × 10
3
J) =
The answer in part (d) is approximately equal in magnitude to that in (a); the
slight difference arises from rounding. The increase in elastic potential energy
corresponds to a decrease in gravitational potential energy; hence the difference
in signs for the two answers.
−1.66 × 10
3
J
3.11 × 10
3
J
4.77 × 10
3
J
1.65 × 10
3
J
Section Two — Problem Workbook Solutions II Ch. 5–7
II
10. ∆x = 9.50 × 10
2
m
q = 45.0°
m = 65.0 g
g = 9.81 m/s
2
x = 55.0 cm
a. v
x
= v
i
(cos q) =
∆
∆
x
t
∆t =
v
i
(c
∆
o
x
s q)
vertical speed of the arrow for the first half of the flight = v
i
(sin q) = g
∆
2
t
v
i
(sin q) =
2v
i
(
g
c
∆
o
x
s q)
v
i
=
2(
si
n
g
q
∆
)
(
x
c
o
s
q
)
=
= 96.5 m/s
KE
i
=
1
2
mv
i
2
=
1
2
(65.0 × 10
−3
kg)(96.5 m/s)
2
=
b. From the conservation of energy,
PE
elastic
= KE
i
1
2
kx
2
= KE
i
k =
2K
x
2
E
i
=
(55.
(
0
2)
×
(3
1
0
0
3
−2
J)
m)
2
=
c. KE
i
= PE
g,max
+ KE
f
KE
f
=
1
2
mv
x
2
=
1
2
m[(v
i
(cos q)]
2
=
1
2
(65.0 × 10
−3
kg)(96.5 m/s)
2
(cos 45.0°)
2
= 151 J
PE
g,max
= KE
i
− KE
f
= 303 J − 151 J = 152 J
h
max
=
PE
m
g
,m
g
ax
=
h = 238 m
152 J
(65.0 × 10
−3
kg)(9.81 m/s
2
)
2.00 × 10
3
N/m
303 J
(9.81 m/s
2
)(9.50 × 10
2
m)
(2)(sin 45.0°)(cos 45.0°)
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. m = 118 kg
h
i
= 5.00 m
g = 9.81 m/s
2
v
i
= 0 m/s
KE
f
= 4.61 kJ
PE
i
+ KE
i
= PE
f
+ KE
f
mgh
i
+
1
2
mv
i
2
= mgh
f
+ KE
f
mgh
f
= mgh
i
+
1
2
mv
i
2
− KE
f
h
f
= h
i
+
v
2
i
g
2
−
K
m
E
g
f
= 5.00 m +
(2)
(
(
0
9.
m
81
/s
m
)
2
/s
2
)
−
(118
4
k
.6
g
1
)(
×
9.
1
8
0
1
3
m
J
/s
2
)
h
f
= 5.00 m − 3.98 m = 1.02 m above the ground
Additional Practice E
2. v
f
= 42.7 m/s
h
f
= 50.0 m
v
i
= 0 m
g = 9.81 m/s
2
PE
i
+ KE
i
= PE
f
+ KE
f
mgh
i
+
1
2
mv
i
2
= mgh
f
+
1
2
mv
f
2
h
i
= h
f
+
v
f
2
2
−
g
v
i
2
= 50.0 m +=50.0 m + 92.9 m
h
i
=
The mass of the nut is not needed for the calculation.
143 m
(42.7 m/s)
2
− (0 m/s)
2
(2)(9.81 m/s
2
)
Holt Physics Solution ManualII Ch. 5–8
II
3. h
i
= 3150 m
v
f
= 60.0 m/s
KE
i
= 0 J
g = 9.81 m/s
2
PE
i
+ KE
i
= PE
f
+ KE
f
mgh
i
= mgh
f
+
1
2
mv
f
2
h
f
= h
i
−
v
2
f
g
2
= 3150 m −
(2
(
)
6
(
0
9
.
.
0
81
m
m
/s
/
)
s
2
2
)
= 3150 m − 183 m
h
f
= 2970 m
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
4. h
i
= 1.20 × 10
2
m
h
f
= 30.0 m
m = 72.0 kg
g = 9.81 m/s
2
KE
i
= 0 J
5. h
f
= 250.0 m
∆ME =−2.55 × 10
5
J
m = 250.0 kg
g = 9.81 m/s
2
∆ME = PE
f
− KE
i
= mgh
f
−
1
2
mv
i
2
v
i
=
2g
h
f
−
2
∆
m
M
E
=
(2
)(
9.
81
m
/s
2
)
(2
50
.0
m
)
−
(
2)
(−
2
2
5
.
0
5
.
5
0
×
k
g
1
0
5
J
)
v
i
=
4.
90
×
1
0
3
m
2
/
s
2
+
2
.0
4
×
1
0
3
m
2
/
s
2
=
6.
94
×
1
0
3
m
2
/
s
2
v
i
= 83.3 m/s = 3.00 × 10
2
km/h
6. h
i
= 12.3 km
m = 120.0 g
g = 9.81 m/s
2
KE
i
= 0 J
∆h = h
i
− h
f
= 3.2 km
PE
i
+ KE
i
= PE
f
+ KE
f
PE
i
− PE
f
= KE
f
KE
f
= PE
i
− PE
f
= mgh
i
− mgh
f
= mg∆h
KE
f
= mg∆h = (0.1200 kg)(9.81 m/s
2
)(3.2 × 10
3
m) =
PE
f
= mgh
f
= mg(h
i
−∆h) = (0.1200 kg)(9.81 m/s
2
)(12.3 × 10
3
m − 3.2 × 10
3
m)
PE
f
= (0.1200 kg)(9.81 m/s
2
)(9.1 × 10
3
m) =
Alternatively,
PE
f
= PE
i
− KE
f
= mgh
i
− KE
f
PE
f
= (0.1200 kg)(9.81 m/s
2
)(12.3 × 10
3
m) − 3.8 × 10
3
J = 1.45 × 10
4
J − 3.8 × 10
3
J
PE
f
= 1.07 × 10
4
J
1.1 × 10
4
J
3.8 × 10
3
J
7. h = 68.6 m
v = 35.6 m/s
g = 9.81 m/s
2
PE
f
= 0 J
KE
i
= 0 J
ME
i
= PE
i
= mgh
ME
f
= KE
f
=
1
2
mv
2
percent of energy dissipated =
(ME
i
−
M
M
E
E
i
f
)(100)
=
(100)
percent of energy dissipated =
(100)
percent of energy dissipated =
(100)
percent of energy dissipated =
(673 J −
6
6
7
3
3
4
J
J)(100)
=
(39
6
J
7
)
3
(1
J
00)
= 5.8 percent
(9.81 m/s
2
)(68.6 m) −
1
2
(35.6 m/s)
2
(9.81 m/s
2
)(68.6 m)
gh −
1
2
v
2
gh
mgh −
1
2
mv
2
)
mgh
PE
i
+ KE
i
= PE
f
+ KE
f
PE
i
− PE
f
= KE
f
KE
f
=∆PE = mg(h
i
− h
f
)
KE
f
= (72.0 kg)(9.81 m/s
2
)(1.20 × 10
2
m − 30.0 m) = (72.0 kg)(9.81 m/s
2
)(9.0 × 10
1
m)
KE
f
=
v
f
=
2K
m
E
f
=
(2
)(
6
7
.
2
4
.0
×
k
1
g
0
4
J
)
v
f
= 42 m/s
6.4 × 10
4
J
II
1. P = 56 MW
∆t = 1.0 h
W = P∆t = (56 × 10
6
W)(1.0 h)(3600 s/h) = 2.0 × 10
11
J
Additional Practice F
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section Two — Problem Workbook Solutions II Ch. 5–9
2. ∆t = 62.25 min
P = 585.0 W
W = P∆t = (585.0 W)(62.25 min)(60 s/min) = 2.185 × 10
6
J
3. h = 106 m
m = 14.0 kg
g = 9.81 m/s
2
P = 3.00 × 10
2
W
q = 0°
W = F
g
d(cos q) = F
g
d = mgh
∆t =
W
P
=
m
P
gh
==48.5 s
(14.0 kg)(9.81 m/s
2
)(106 m)
3.00 × 10
2
W
4. P = 2984 W
W = 3.60 × 10
4
J
∆t =
W
P
=
3.6
2
0
98
×
4
1
W
0
4
J
= 12.1 s
5. ∆t = 3.0 min
W = 54 kJ
P =
∆
W
t
==3.0 × 10
2
W
54 × 10
3
J
(3.0 min)(60 s/min)
6. ∆t = 16.7 s
h = 18.4 m
m = 72.0 kg
g = 9.81 m/s
2
q = 0°
W = F
g
d (cos q) = mgh
P =
∆
W
t
=
m
∆
g
t
h
=
P = 778 W
(72.0 kg)(9.81 m/s
2
)(18.4 m)
16.7 s
Section Two—Problem Workbook Solutions II Ch. 6–1
II
HRW material copyrighted under notice appearing earlier in this book.
Momentum
and Collisions
Problem Workbook Solutions
Additional Practice A
Givens Solutions
1. v = 40.3 km/h
p = 6.60 × 10
2
kg
•
m/s
m =
v
p
==59.0 kg
6.60 × 10
2
kg
•
m/s
(40.3 × 10
3
m/h)(1 h/3600 s)
2. m
h
= 53 kg
v = 60.0 m/s to the east
p
tot
= 7.20 × 10
3
kg
•
m/s to
the east
p
tot
= m
h
v + m
p
v
m
p
=
p
tot
−
v
m
h
v
=
m
p
===67 kg
4.0 × 10
3
kg
•
m/s
60.0 m/s
7.20 × 10
3
kg
•
m/s − 3.2 × 10
3
kg
•
m/s
60.0 m/s
7.20 × 10
3
kg
•
m/s − (53 kg)(60.0 m/s)
60.0 m/s
3. m
1
= 1.80 × 10
2
kg
m
2
= 7.0 × 10
1
kg
p
tot
= 2.08 × 10
4
kg•m/s to
the west
=−2.08 × 10
4
kg•m/s
v =
m
1
p
+
tot
m
2
==
v =−83.2 m/s = 83.2 m/s to the west
−2.08 × 10
4
kg•m/s
2.50 × 10
2
kg
−2.08 × 10
4
kg•m/s
1.80 × 10
2
kg + 7.0 × 10
1
kg
4. m = 83.6 kg
p = 6.63 × 10
5
kg•m/s
v =
m
p
=
6.63 ×
83
1
.
0
6
5
k
k
g
g
•
m/s
= 7.93 × 10
3
m/s = 7.93 km/s
1. m = 9.0 × 10
4
kg
v
i
= 0 m/s
v
f
= 12 cm/s upward
F = 6.0 × 10
3
N
∆t ==
∆t ==1.8 s
(9.0 × 10
4
kg)(0.12 m/s)
6.0 × 10
3
N
(9.0 × 10
4
kg)(0.12 m/s) − (9.0 × 10
4
kg)(0 m/s)
6.0 × 10
3
N
mv
f
− mv
i
F
Additional Practice B
5. m = 6.9 × 10
7
kg
v = 33 km/h
6. h = 22.13 m
m = 2.00 g
g = 9.81 m/s
2
p = mv = (6.9 × 10
7
kg)(33 × 10
3
m/h)(1 h/3600 s) = 6.3 × 10
8
kg
•
m/s
mgh =
1
2
mv
f
2
v
f
=
2g
h
p = mv
f
= m
2g
h
= (2.00 × 10
−3
kg)
(2
)(
9.
81
m
/s
2
)
(2
2.
13
m
)
p = 4.17 × 10
−2
kg
•
m/s downward
Holt Physics Solution ManualII Ch. 6–2
II
HRW material copyrighted under notice appearing earlier in this book.
2. m = 1.00 × 10
6
kg
v
i
= 0 m/s
v
f
= 0.20 m/s
F = 12.5 kN
∆p = mv
f
− mv
i
= (1.00 × 10
6
kg)(0.20 m/s) − (1.00 × 10
6
kg)(0 m/s)
∆p =
∆t =
∆
F
p
==16 s
2.0 × 10
5
kg
•
m/s
12.5 × 10
3
N
2.0 × 10
5
kg
•
m/s
Givens Solutions
3. h = 12.0 cm
F = 330 N, upward
m = 65 kg
g = 9.81 m/s
2
The speed of the pogo stick before and after it presses against the ground can be de-
termined from the conservation of energy.
PE
g
= KE
mgh =
1
2
mv
2
v =±
2g
h
For the pogo stick’s downward motion,
v
i
=−
2g
h
For the pogo stick’s upward motion,
v
f
=+
2g
h
∆p = mv
f
− mv
i
= m
2g
h
− m
−
2g
h
∆p = 2m
2g
h
∆t =
∆
F
p
=
2m
F
2g
h
=
∆t = 0.60 s
(2)(65 kg)
(2
)(
9.
81
m
/s
2
)
(0
.1
20
m
)
330 N
4. m = 6.0 × 10
3
kg
F = 8.0 kN to the east
∆t = 8.0 s
v
i
= 0 m/s
v
f
==
v
f
= 11 m/s, east
(8.0 × 10
3
N)(8.0 s) + (6.0 × 10
3
kg)(0 m/s)
6.0 × 10
3
kg
F∆t + mv
i
m
5. v
i
= 125.5 km/h
m = 2.00 × 10
2
kg
F =−3.60 × 10
2
N
∆t = 10.0 s
v
f
=
v
f
=
v
f
===
or v
f
= (16.8 × 10
−3
km/s)(3600 s/h) = 60.5 km/h
16.8 m/s
3.37 10
3
kg
•
m/s
2.00 10
2
kg
−3.60 × 10
3
N
•
s + 6.97 × 10
3
kg
•
m/s
2.00 × 10
2
kg
(−3.60 × 10
2
N)(10.0 s) + (2.00 × 10
2
kg)(125.5 × 10
3
m/h)(1 h/3600 s)
2.00 × 10
2
kg
F∆t + mv
i
m
6. m = 45 kg
F = 1.6 × 10
3
N
∆t = 0.68 s
v
i
= 0 m/s
v
f
=
F∆t
m
+ mv
i
=
v
f
==24 m/s
(1.6 × 10
3
N)(0.68 s)
45 kg
(1.6 × 10
3
N)(0.68 s) + (45 kg)(0 m/s)
45 kg
Section Two—Problem Workbook Solutions II Ch. 6–3
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
7. m = 4.85 × 10
5
kg
v
i
= 20.0 m/s northwest
v
f
= 25.0 m/s northwest
∆t = 5.00 s
F ==
F ==
F = 4.8 × 10
5
N northwest
2.4 × 10
6
kg•m/s
5.00 s
1.21 × 10
7
kg•m/s − 9.70 × 10
6
kg•m/s
5.00 s
(4.85 × 10
5
kg)(25.0 m/s) − (4.85 × 10
5
kg)(20.0 m/s)
5.00 s
mv
f
− mv
i
∆t
Givens Solutions
8. v
f
= 12.5 m/s upward
m = 70.0 kg
∆t = 4.00 s
v
i
= 0 m/s
F == =219 N
F = 219 N upward
(70.0 kg)(12.5 m/s) − (70.0 kg)(0 m/s)
4.00 s
mv
f
− mv
i
∆t
9. m = 12.0 kg
h = 40.0 m
∆t = 0.250 s
v
f
= 0 m/s
g = 9.81 m/s
2
From conservation of energy, v
i
=−
2g
h
∆p = mv
f
− mv
i
= mv
f
− m
–
2g
h
∆p = (12.0 kg)(0 m/s) + (12.0 kg)
(2
)(
9.
81
m
/s
2
)
(4
0.
0
m
)
= 336 kg
•
m/s
F =
∆
∆
t
p
==1340 N = 1340 N upward
336 kg
•
m/s
0.250 s
1. F = 2.85 × 10
6
N backward
=−2.85 × 10
6
N
m = 2.0 × 10
7
kg
v
i
= 3.0 m/s forward
=+3.0 m/s
v
f
= 0 m/s
∆t = 21 s
∆p = F∆t = (−2.85 × 10
6
N)(21 s)
∆p =
∆x =
1
2
(v
i
+ v
f
)∆t =
1
2
(3.0 m/s + 0 m/s)(21 s) = 32 m forward
−6.0 × 10
7
kg•m/s forward or 6.0 × 10
7
kg•m/s backward
Additional Practice C
2. m = 6.5 × 10
4
kg
F =−1.7 × 10
6
N
v
i
= 1.0 km/s
∆t = 30.0 s
∆p = F∆t = (−1.7 × 10
6
N)(30.0 s) =
v
f
=
∆p +
m
mv
i
=
v
f
===220 m/s
∆x =
1
2
(v
i
+ v
f
)∆t =
1
2
(1.0 × 10
3
m/s + 220 m/s)(30.0 s) =
1
2
(1.2 × 10
3
m/s)(30.0 s)
∆x = 1.8 × 10
4
m = 18 km
1.4 × 10
7
kg•m/s
6.5 × 10
4
kg
−5.1 × 10
7
kg•m/s + 6.5 × 10
7
kg•m/s
6.5 × 10
4
kg
−5.1 × 10
7
kg•m/s + (6.5 × 10
4
kg)(1.0 × 10
3
m/s)
6.5 × 10
4
kg
−5.1 × 10
7
kg•m/s
Givens Solutions
Holt Physics Solution ManualII Ch. 6–4
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
3. m = 2.03 × 10
4
kg
v
i
= 5.00 m/s to the east
= 5.00 m/s
∆t = 20.3 s
F = 1.20 × 10
3
N to the west
∆p = F∆t = (−1.20 × 10
3
N)(20.3 s) =
v
f
=
∆p +
m
mv
i
=
v
f
==
v
f
= 3.73 m/s
∆x =
1
2
(v
i
+ v
f
)∆t =
1
2
[5.00 m/s + (3.73 m/s)](20.3 s) =
1
2
(8.73 m/s)(20.3 s)
∆x = 88.6 m = 88.6 m to the east
7.58 × 10
4
kg•m/s
2.03 × 10
4
kg
−2.44 × 10
4
kg•m/s + 1.02 × 10
5
kg•m/s
2.03 × 10
4
kg
−2.44 × 10
4
kg•m/s + (2.03 × 10
4
kg)(5.00 m/s)
2.3 × 10
4
kg
2.44 × 10
4
kg•m/s to the west
4. m = 113 g
v
i
= 2.00 m/s to the right
v
f
= 0 m/s
∆t = 0.80 s
F =
mv
f
∆
−
t
mv
i
==
F =−0.28 N =
∆x =
1
2
(v
i
+ v
f
)∆t =
1
2
(2.00 m/s + 0 m/s)(0.80 s)
∆x = 0.80 m to the right
0.28 N to the left
−(0.113 kg)(2.00 m/s)
0.80 s
(0.113 kg)(0 m/s) − (0.113 kg)(2.00 m/s)
0.80 s
6. h = 68.6 m
m = 1.00 × 10
3
kg
F =−2.24 × 10
4
N
g = 9.81 m/s
2
v
f
= 0 m/s
From conservation of energy,
v
i
=
2g
h
∆p = mv
f
− mv
i
= mv
f
− m
2g
h
∆t =
∆
F
p
=
mv
f
−
F
m
2g
h
=
∆t ==
∆x =
1
2
(v
i
+ v
f
)∆t =
1
2
(
2g
h
+ v
f
)∆t
∆x =
1
2
(2
)(
9.
81
m
/s
2
)
(6
8.
6
m
)
+ 0 m/s
(1.64 s) = 30.1 m
1.64 s
−(1.00 × 10
3
kg)
(2
)(
9.
81
m
/s
2
)
(6
8.
6
m
)
−2.24 × 10
4
N
(1.00 × 10
3
kg)(0 m/s) − (1.00 × 10
3
kg)
(2
)(
9.
81
.m
/s
2
)
(6
8.
6
m
)
−2.24 × 10
4
N
5. m = 4.90 × 10
6
kg
v
i
= 0.200 m/s
v
f
= 0 m/s
∆t = 10.0 s
F =
∆
∆
p
t
=
mv
f
∆
−
t
mv
i
=
F = –9.80 10
4
N
F =
∆x =
1
2
(v
i
+ v
f
)∆t =
1
2
(0.200 m/s + 0 m/s)(10.0 s)
∆x = 1.00 m
9.80 × 10
4
N opposite the palace’s direction of motion
–(4.90 10
6
kg)(0.200 m/s)
10.0 s
(4.90 × 10
6
kg)(0 m/s) − (4.90 × 10
6
kg)(0.200 m/s)
10.0 s
Section Two—Problem Workbook Solutions II Ch. 6–5
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
7. m = 100.0 kg
v
i
= 4.5 × 10
2
m/s
v
f
= 0 m/s
F =−188 N
∆t =
mv
f
F
− mv
i
=
∆t ==
∆x =
1
2
(v
i
+ v
f
)∆t =
1
2
(4.5 × 10
2
m/s + 0 m/s)(240 s) = 5.4 × 10
4
m = 54 km
The tunnel is long.54 km
240 s
−(100.0 kg)(4.5 × 10
2
m/s)
−188 N
(100.0 kg)(0 m/s) − (100.0 kg)(4.5 × 10
2
m/s)
−188 N
Givens Solutions
1. m
1
= 3.3 × 10
3
kg
v
1,i
= 0 m/s
v
2,i
= 0 m/s
v
2,f
= 2.5 m/s to the right
= 2.5 m/s
v
1,f
= 0.050 m/s to the left
= –0.050 m/s
Because the initial momentum is zero, the final momentum is also zero, and so
m
2
=
−m
v
2
1
v
,f
1,f
==66 kg
−(3.3 × 10
3
kg)(−0.050 m/s)
2.5 m/s
2. m
1
= 1.25 × 10
3
kg
v
1,i
= 0 m/s
v
2,i
= 0 m/s
v
2,f
= 1.40 m/s backward
= –1.40 m/s
∆t
1
= 4.0 s
∆x
1
= 24 cm forward
= 24 cm
Because the initial momentum is zero, the final momentum is also zero, and so
v
1,f
=
∆
∆
x
t
1
1
=
0
4
.2
.0
4
s
m
= 0.060 m/s forward
m
2
=
−m
v
2
1
v
,f
1,f
==54 kg
−(1.25 × 10
3
kg)(0.060 m/s)
−1.40 m/s
3. m
1
= 114 kg
v
2, f
= 5.32 m/s backward
=−5.32 m/s
v
1, f
= 3.41 m/s forward
=+3.41 m/s
m
2
= 60.0 kg
m
1
v
i
+ m
2
v
i
= m
1
v
1, f
+ m
2
v
2, f
v
i
=
m
1
v
m
1,
1
f
+
+
m
m
2
2
v
2, f
=
v
i
==
7.0 ×
1
1
7
0
4
1
k
k
g
g
•
m/s
= 0.40 m/s
v
i
= 0.40 m/s forward
389 kg•m/s − 319 kg•m/s
174 kg
(114 kg)(3.41 m/s) + (60.0 kg)(−5.32 m/s)
114 kg + 60.0 kg
4. m
1
= 5.4 kg
v
1, f
= 7.4 m/s forward
=+7.4 m/s
v
2, f
= 1.4 m/s backward
=−1.4 m/s
m
2
= 50.0 kg
m
1
v
i
+ m
2
v
i
= m
1
v
1, f
+ m
2
v
2, f
v
i
==
v
i
==
−3.0 ×
55
1
.
0
4
1
k
k
g
g
•
m/s
= –0.54 m/s
v
i
= 0.54 m/s backward
4.0 × 10
1
kg•m/s − 7.0 × 10
1
kg•m/s
55.4 kg
(5.4 kg)(7.4 m/s) + (50.0 kg)(−1.4 m/s)
5.4 kg + 50.0 kg
m
1
v
1, f
+ m
2
v
2, f
m
1
+ m
2
Additional Practice D
5. m
1
= 3.4 × 10
2
kg
v
2, f
= 9.0 km/h northwest
=−9.0 km/h
v
1, f
= 28 km/h southeast
=+28 km/h
m
2
= 2.6 × 10
2
kg
m
1
v
i
+ m
2
v
i
= m
1
v
1, f
+ m
2
v
2, f
v
i
==
v
i
==
v
i
= 12 km/h to the southeast
7.2 × 10
3
kg•km/h
6.0 × 10
2
kg
9.5 × 10
3
kg•km/h − 2.3 × 10
3
kg•km/h
6.0 × 10
2
kg
(3.4 × 10
2
kg)(28 km/h) + (2.6 × 10
2
kg)(−9.0 km/h)
3.4 × 10
2
kg + 2.6 × 10
2
kg
m
1
v
1, f
+ m
2
v
2, f
m
1
+ m
2
Givens Solutions
6. m
i
= 3.6 kg
m
2
= 3.0 kg
v
1,i
= 0 m/s
v
2,i
= 0 m/s
v
2,f
= 2.0 m/s to the left
= –2.0 m/s
Because the initial momentum is zero, the final momentum must also equal zero.
m
i
v
1,f
=−m
2
v
2,f
v
1,f
=
−m
m
2
v
1
2,f
==1.7 m/s = 1.7 m/s to the right
−(3.0 kg)(−2.0 m/s)
3.6 kg
7. m
1
= 449 kg
v
1,i
= 0 m/s
v
2,i
= 0 m/s
v
2,f
= 4.0 m/s backward
= –4.0 m/s
m
2
= 60.0 kg
∆t = 3.0 s
Because the initial momentum is zero, the final momentum must also equal zero.
v
1,f
=
−m
m
2
1
v
2,f
==0.53 m/s = 0.53 m/s forward
∆x = v
1,f
∆t = (0.53 m/s)(3.0 s) = 1.6 m forward
−(60.0 kg)(−4.0 m/s)
449 kg
Additional Practice E
1. m
1
= 155 kg
v
1,i
= 6.0 m/s forward
v
2,i
= 0 m/s
v
f
= 2.2 m/s forward
m
2
==
m
2
==
m
2
= 270 kg
590 kg•m/s
2.2 m/s
930 kg•m/s –340 kg•m/s
2.2 m/s
(155 kg)(6.0 m/s) − (155 kg)(2.2 m/s)
2.2 m/s − 0 m/s
m
1
v
1,i
− m
1
v
f
v
f
− v
2,i
Holt Physics Solution ManualII Ch. 6–6
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. v
1,i
= 10.8 m/s
v
2,i
= 0 m/s
v
f
= 10.1 m/s
m
1
= 63.0 kg
m
2
==
m
2
===4.4 kg
44 kg
•
m/s
10.1 m/s
6.80 × 10
2
kg
•
m/s − 6.36 × 10
2
kg
•
m/s
10.1 m/s
(63.0 kg)(10.8 m/s) − (63.0 kg)(10.1 m/s)
10.1 m/s − 0 m/s
m
1
v
1,i
− m
1
v
f
v
f
− v
2,i
3. v
1, i
= 4.48 m/s to the right
v
2, i
= 0 m/s
v
f
= 4.00 m/s to the right
m
2
= 54 kg
m
1
==
(54 k
0
g
.
)
4
(
8
4
m
.00
/s
m/s)
m
1
= 450 kg
(54 kg)(4.00 m/s) − (54 kg)(0 m/s)
4.48 m/s − 4.00 m/s
Section Two—Problem Workbook Solutions II Ch. 6–7
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
6. m
1
= 9.50 kg
v
1, i
= 24.0 km/h to the north
m
2
= 32.0 kg
v
f
= 11.0 km/h to the north
v
2, i
=
v
2, i
=
v
2, i
==
=
228
32
k
.
g
0
•
k
k
m
g
/h
v
2, i
= 7.12 km/h to the north
456 kg•km/h − 228 kg•km/h
32.0 kg
(41.5 kg)(11.0 km/h) − 228 kg
•km/h
32.0 kg
(9.5 kg + 32.0 kg)(11.0 km/h) − (9.50 kg)(24.0 km/h)
32.0 kg
(m
1
+ m
2
)v
f
− m
1
v,
1
m
2
7. m
1
= m
2
v
1,i
= 89 km/h
v
2,i
= 69 km/h
Because m
1
= m
2
, v
f
=
v
1,i
+
2
v
2,i
==
158 k
2
m/h
= 79 km/h
v
f
= 79 km/h
89 km/h + 69 km/h
2
8. m
1
= 3.0 × 10
3
kg
m
2
= 2.5 × 10
2
kg
v
2,i
= 3.0 m/s down
= –3.0 m/s
v
1,i
= 1.0 m/s up =+1.0 m/s
v
f
==
v
f
==
v
f
= 0.69 m/s = 0.69 m/s upward
2.2 10
3
kg•m/s
3.2 10
3
kg
3.0 10
3
kg•m/s –7.5 10
2
kg•m/s
3.2 10
3
kg
(3.0 × 10
3
kg)(1.0 m/s) + (2.5 × 10
2
kg)(−3.0 m/s)
(3.0 × 10
3
kg) + (2.5 × 10
2
kg)
m
1
v
1,i
+ m
2
v
2,i
m
1
+ m
2
9. m
1
= (2.267 × 10
3
kg) +
(5.00 × 10
2
kg) = 2.767 ×
10
3
kg
m
2
= (1.800 × 10
3
kg) +
(5.00 × 10
2
kg) = 2.300 ×
10
3
kg
v
1,i
= 2.00 m/s to the left
= –2.00 m/s
v
2,i
= 1.40 m/s to the right
=+1.40 m/s
v
f
==
v
f
==
–23
5
1
0
0
67
kg
k
•
g
m/s
= –0.456 m/s
v
f
= 0.456 m/s to the left
–5.53 10
3
kg
•
m/s + 3220 kg
•
m/s
5.067 × 10
3
kg
(2.767 × 10
3
kg)(−2.00 m/s) + (2.300 × 10
3
kg)(1.40 m/s)
2.767 × 10
3
kg + 2.300 × 10
3
kg
m
1
v
1,i
+ m
2
v
2,i
m
1
+ m
2
4. m
1
= 28 × 10
3
kg
m
2
= 12 × 10
3
kg
v
1,i
= 0 m/s
v
f
= 3.0 m/s forward
v
2,i
=
v
2,i
=
v
2,i
=
v
2,i
= 1.0 × 10
1
m/s forward
(4.0 10
4
kg)(3.0 m/s)
12 10
3
kg
(28 × 10
3
kg + 12 × 10
3
kg)(3.0 m/s) − (28 × 10
3
kg)(0 m/s)
12 × 10
3
kg
(m
1
+ m
2
)v
f
− m
1
v
1,i
m
2
5. m
1
= 227 kg
m
2
= 267 kg
v
1,i
= 4.00 m/s to the left
= –4.00 m/s
v
f
= 0 m/s
v
2,i
=
v
2,i
==3.40 m/s
v
2,i
= 3.40 m/s to the right
(227 kg + 267 kg)(0 m/s) − (227 kg)(–4.00 m/s)
267 kg
(m
1
+ m
2
)v
f
− m
1
v
1,i
m
2
Givens Solutions
Additional Practice F
Givens Solutions
1. m
1
= 2.0 g
v
1,i
= 2.0 m/s forward
=+2.0 m/s
m
2
= 0.20 g
v
2,i
= 8.0 m/s backward
= −8.0 m/s forward
v
f
=
v
f
=
v
f
=
v
f
=
2.4
2
.2
10
–
1
3
0
k
–3
g
•
k
m
g
/s
= 1.1 m/s forward
KE
i
=
1
2
m
1
v
1,i
2
+
1
2
m
2
v
2,i
2
KE
i
=
2
1
(2.0 × 10
−3
kg)(2.0 m/s)
2
+
2
1
(0.20 × 10
−3
kg)(−8.0 m/s)
2
KE
i
= 4.0 × 10
−3
J + 6.4 × 10
−3
J = 1.04 × 10
−3
J
KE
f
=
2
1
(m
1
+ m
2
)v
f
2
=
2
1
(2.0 × 10
−3
kg + 0.20 × 10
−3
kg)(1.1 m/s)
2
KE
f
=
2
1
(2.2 × 10
−3
kg)(1.1 m/s)
2
∆KE = KE
f
− KE
i
= 1.3 × 10
−3
J − 1.04 × 10
−2
J =−9.1 × 10
−3
J
fraction of total KE dissipated =
∆
K
K
E
E
i
==0.88
9.1 × 10
−3
J
1.04 × 10
−2
J
4.0 10
–3
kg•m/s − 1.6 10
–3
kg•m/s
2.2 10
–3
kg
(2.0 10
–3
kg)(2.0 m/s) + (0.20 10
–3
kg)(−8.0 m/s)
2.0 10
–3
kg + 0.20 10
–3
kg
m
1
v
1,i
+ m
2
v
2,i
m
1
+ m
2
Holt Physics Solution ManualII Ch. 6–8
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. m
1
= 313 kg
v
1,i
= 6.00 m/s away from
shore
v
2,i
= 0 m/s
v
f
= 2.50 m/s away from
shore
m
2
==
m
2
===4.4 × 10
2
kg
KE
i
=
2
1
m
1
v
1,i
2
+
2
1
m
2
v
2,i
2
KE
i
=
2
1
(313 kg)(6.00 m/s)
2
+
2
1
(4.40 × 10
2
kg)(0 m/s)
2
= 5630 J
KE
f
=
2
1
(m
1
+ m
2
)v
f
2
KE
f
=
2
1
(313 kg + 4.40 × 10
2
kg)(2.50 m/s)
2
=
2
1
(753 kg)(2.50 m/s)
2
= 2350 J
∆KE = KE
f
− KE
i
= 2350 J − 5630 J =−3280 J
1.10 × 10
3
kg
•
m/s
2.50 m/s
1880 kg
•
m/s − 782 kg
•
m/s
2.50 m/s
(313 kg)(6.00 m/s) − (313 kg)(2.50 m/s)
2.50 m/s − 0 m/s
m
1
v
1,i
− m
1
v
f
v
f
− v
2,i
3. m
1
= m
2
= 111 kg
v
1, i
= 9.00 m/s to the right
=+9.00 m/s
v
2, i
= 5.00 m/s to the left
=−5.00 m/s
v
f
=
m
1
v
m
1,
1
i
+
+
m
m
2
2
v
2, i
=
v
f
==
44
2
4
2
k
2
g
k
•
m
g
/s
= 2.00 m/s to the right
KE
i
=
2
1
m
1
v
1,i
2
+
2
1
m
2
v
2,i
2
=
2
1
(111 kg)(9.00 m/s)
2
+
2
1
(111 kg)(–5.00 m/s)
2
KE
i
= 4.50 × 10
3
J + 1.39 × 10
3
J = 5.89 × 10
3
J
KE
f
=
1
2
(m
1
+ m
2
)v
f
2
=
2
1
(111 kg 111 kg)(2.00 m/s)
2
=
2
1
(222 kg)(2.00 m/s)
KE
f
= 444 J
∆KE = KE
f
− KE
i
= 444 J − 5.89 × 10
3
J =−5450 J
999 kg•m/s − 555 kg•m/s
222 kg
(111 kg)(9.00 m/s) + (111 kg)(−5.00 m/s)
111 kg + 111 kg
Section Two—Problem Workbook Solutions II Ch. 6–9
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
5. m
1
= 4.00 × 10
5
kg
v
1, i
= 32.0 km/h
m
2
= 1.60 × 10
5
kg
v
2, i
= 45.0 km/h
v
f
=
m
1
v
m
1,
1
i
+
+
m
m
2
2
v
2,i
=
v
f
==
v
f
= 35.7 km/h
KE
i
=
1
2
m
1
v
1,i
2
+
1
2
m
2
v
2,i
2
KE
i
=
1
2
(4.00 × 10
5
kg)(32.0 × 10
3
m/h)(1 h/3600 s)
2
+
1
2
(1.60 × 10
5
kg)
(45.0 × 10
3
m/h)
2
(1 h/3600 s)
2
KE
i
= 1.58 × 10
7
J + 1.25 × 10
7
J = 2.83 × 10
7
J
KE
f
=
1
2
(m
1
+ m
2
)v
f
2
KE
f
=
1
2
(4.00 × 10
5
kg + 1.60 × 10
5
kg)(35.7 × 10
3
m/h)
2
(1 h/3600 s)
2
=
1
2
(5.60 × 10
5
kg)(35.7 × 10
3
m/h)
2
(1 h/3600 s)
2
KE
f
= 2.75 × 10
7
J
∆KE = KE
f
− KE
i
= 2.75 × 10
7
J − 2.83 × 10
7
J =−8 × 10
5
J
2.00 × 10
7
kg•km/h
5.60 × 10
5
kg
1.28 × 10
7
kg•km/h + 7.20 × 10
6
kg•km/h
5.60 × 10
5
kg
(4.00 × 10
5
kg)(32.0 km/h) + (1.60 × 10
5
kg)(45.0 km/h)
4.00 × 10
5
kg + 1.60 × 10
5
kg
4. m
1
= m
2
= 60.0 kg + 50.0 kg
= 110.0 kg
v
1, i
= 106.0 km/h to the east
=+106.0 km/h
v
2, i
= 75.0 km/h to the west
=−75.0 km/h
v
f
==
v
f
==
3.41 ×
22
1
0
0
.
3
0
k
k
g
g
•
km/h
v
f
= 15.5 km/h to the east
KE
i
=
1
2
m
1
v
1, i
2
+
1
2
m
2
v
2, i
2
KE
i
=
1
2
(110.0 kg)(106.0 × 10
3
m/h)
2
(1 h/3600 s)
2
+
1
2
(110.0 kg)(−75.0 × 10
3
m/h)
2
(1 h/3600 s)
2
KE
i
= 4.768 × 10
4
J + 2.39 × 10
4
J = 7.16 × 10
4
J
KE
f
=
1
2
(m
1
+ m
2
)v
f
2
KE
f
=
1
2
(110.0 kg + 110.0 kg)(15.5 × 10
3
m/h)
2
(1 h/3600 s)
2
=
1
2
(220.0 kg)(15.5 × 10
3
m/h)
2
(1 h/3600 s)
2
KE
f
= 2.04 × 10
3
J
∆KE = KE
f
− KE
i
= 2.04 × 10
3
J − 7.16 × 10
4
J =−6.96 × 10
4
J
1.166 × 10
4
kg•km/h − 8.25 × 10
3
kg•km/h
220.0 kg
(110.0 kg)(106.0 km/h) + (110.0 kg)(−75.0 km/h)
110.0 kg + 110.0 kg
m
1
v
1,i
+ m
2
v
2,i
m
1
+ m
2
Givens Solutions
Holt Physics Solution ManualII Ch. 6–10
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
6. m
1
= 21.3 kg
v
1,i
= 0 m/s
m
2
= 1.80 × 10
−1
kg
v
f
= 6.00 × 10
−2
m/s
v
2,i
=
(m
1
+ m
m
2
)
2
v
f
–m
1
v
1,i
v
2,i
=
v
2,i
= 7.17 m/s
KE
i
=
1
2
m
1
v
1,i
2
+
1
2
m
2
v
2,i
2
KE
i
=
1
2
(21.3 kg)(0 m/s)
2
+
1
2
(1.80 × 10
−1
kg)(7.17 m/s)
2
KE
i
= 0 J 4.63 J = 4.63 J
KE
f
=
1
2
(m
1
+ m
2
)v
f
2
KE
f
=
1
2
(21.3 kg 0.180 kg)(6.00 × 10
−2
m/s)
2
=
1
2
(21.5 kg)(6.00 × 10
−2
m/s)
2
KE
f
= 3.87 × 10
−2
J
∆KE = KE
f
− KE
i
= 3.87 × 10
−2
J − 4.63 J =−4.59 J
(21.5 kg)(6.00 10
−2
m/s)
1.80 10
–1
kg
(21.3 kg + 1.80 × 10
−1
kg)(6.00 × 10
−2
m/s) – (21.3 kg)(0 m/s)
1.80 × 10
−1
kg
7. m
1
= 122 g
m
2
= 96.0 g
v
2,i
= 0 m/s
Because v
2,i
= 0 m/s, m
1
v
1,i
= (m
1
+ m
2
)v
f
v
1,i
=
fraction of KE dissipated =
∆
K
K
E
E
i
=
KE
f
K
−
E
i
KE
i
=
fraction of KE dissipated =
fraction of KE dissipated =
m
1
v
f
2
+ m
2
v
f
2
−
(m
1
v
f
)
2
+ 2m
1
m
2
v
f
2
+ (m
2
v
f
)
2
m
1
(m
1
+ m
2
)v
f
2
− m
1
(m
1
+
m
m
1
2
)v
f
2
m
1
(m
1
+
m
m
1
2
)v
f
2
1
2
m
1
+ m
2
v
f
2
−
1
2
m
1
v
1,i
2
1
2
m
1
v
1,i
2
(m
1
+ m
2
)v
f
m
1
(m
1
v
f
)
2
+ 2m
1
m
2
v
f
2
+ (m
2
v
f
)
2
m
1
fraction
of KE
dissipated =
fraction of KE dissipated ==
fraction of KE dissipated ===
The fraction of kinetic energy dissipated can be determined without the initial veloc-
ity because this value cancels, as shown above. The initial velocity is needed to find
the decrease in kinetic energy.
−0.440
−171.5 g
3.90 × 10
2
g
−96.0 g − 75.5 g
122 g + 192 g + 75.5 g
−96.0 g −
(9
1
6
2
.0
2
g
g
)
2
122 g + (2)(96.0 g) +
(9
1
6
2
.0
2
g
g
)
2
−m
2
−
m
m
2
1
2
m
1
+ 2m
2
+
m
m
2
1
2
v
f
2
m
1
+ m
2
− m
1
− 2m
2
−
m
m
2
1
2
v
f
2
m
1
+ 2m
2
+
m
m
2
1
2
Section Two—Problem Workbook Solutions II Ch. 6–11
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Additional Practice G
Givens Solutions
2. m
1
= 18.40 kg
m
2
= 56.20 kg
v
2, i
= 5.000 m/s to the left
=−5.000 m/s
v
2, f
= 6.600 × 10
−2
m/s to
the left
=−6.600 × 10
−2
m/s
v
1, f
= 10.07 m/s to the left
=−10.07 m/s
Momentum conservation
m
1
v
1, i
+ m
2
v
2, i
= m
1
v
1, f
+ m
2
v
2, f
v
1, i
=
v
1, i
=
v
1, i
==
92
1
.
8
0
.4
k
0
g
•
k
m
g
/s
= 5.00 m/s
v
1, i
=
Conservation of kinetic energy (check)
1
2
m
1
v
1, i
2
+
1
2
m
2
v
2, i
2
=
1
2
m
1
v
1, f
2
+
1
2
m
2
v
2, f
2
1
2
(18.40 kg)(5.00 m/s)
2
+
1
2
(56.20)(−5.000 m/s)
2
=
1
2
(18.40 kg)(−10.07 ms)
2
+
1
2
(56.20 kg)(−6.600 × 10
−2
m/s)
2
2.30 × 10
2
J + 702.5 J = 932.9 J + 0.1224 J
932 J = 933 J
The slight difference arises from rounding.
5.00 m/s to the right
−185.3 kg•m/s − 3.709 kg•m/s + 281.0 kg•m/s
18.40 kg
(18.40 kg)(−10.07 m/s) + (56.20 kg)(−6.600 × 10
−2
m/s) − (56.20 kg)(−5.000 m/s)
18.40 kg
m
1
v
1, f
+ m
2
v
2, f
− m
2
v
2, i
m
1
1. m
2
= 0.500 m
1
v
1, i
= 3.680 × 10
3
km/h
v
1, f
=−4.40 × 10
2
km/h
v
2, f
= 5.740 × 10
3
km/h
Momentum conservation
m
1
v
1, i
+ m
2
v
2, i
= m
1
v
1, f
+ m
2
v
2, f
v
2, i
==
v
2, i
= (2.00)v
1, f
+ v
2, f
− (2.00)v
1, i
= (2.00)(−4.40 × 10
2
km/h) + 5.740 × 10
3
km/h
− (2.00)(3.680 × 10
3
km/h) =−8.80 × 10
2
km/h + 5.740 × 10
3
km/h
− 7.36 × 10
3
km/h
v
2, i
=
Conservation of kinetic energy (check)
1
2
m
1
v
1, i
2
+
1
2
m
2
v
2, i
2
=
1
2
m
1
v
1, f
2
+
1
2
m
2
v
2, f
2
1
2
m
1
v
1, i
2
+
1
2
(0.500)m
1
v
2, i
2
=
1
2
m
1
v
1, f
2
+
1
2
(0.500)m
1
v
2, f
2
v
1, i
2
+ (0.500)v
2, i
2
= v
1, f
2
+ (0.500)v
2, f
2
(3.680 × 10
3
km/h)
2
+ (0.500)(−2.50 × 10
3
km/h)
2
= (−4.40 × 10
2
km/h)
2
+ (0.500)
(5.740 × 10
3
km/h)
2
1.354 × 10
7
km
2
/h
2
+ 3.12 × 10
6
km
2
/h
2
= 1.94 × 10
5
km
2
/h
2
+ 1.647 × 10
7
km
2
/h
2
1.666 × 10
7
km
2
/h
2
= 1.666 × 10
7
km
2
/h
2
−2.50 × 10
3
km/h
m
1
v
1,
f
+ (0.500)m
1
v
2,
f
− m
1
v
1, i
(0.500)m
1
m
1
v
1,
f
+ m
2
v
2,
f
− m
1
v
1, i
m
2
Givens Solutions
Holt Physics Solution ManualII Ch. 6–12
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
3. m
1
= m
2
v
1, i
= 5.0 m/s to the right
=+5.0 m/s
v
1, f
= 2.0 m/s to the left
=−2.0 m/s
v
2, f
= 5.0 m/s to the right
=+5.0 m/s
Momentum conservation
m
1
v
1, i
+ m
2
v
2, i
= m
1
v
1, f
+ m
2
v
2, f
v
2, i
==v
1, f
+ v
2, f
− v
1, i
v
2, i
=−2.0 m/s + 5.0 m/s − 5.0 m/s =−2.0 m/s
v
2, i
=
Conservation of kinetic energy (check)
1
2
m
i
v
1, i
2
+
1
2
m
2
v
2, i
2
=
1
2
m
1
v
1, f
2
+
1
2
m
2
v
2, f
2
v
1,i
2
+ v
2,i
2
= v
1,f
2
+ v
2,f
2
(5.0 m/s)
2
+ (−2.0 m/s)
2
= (−2.0 m/s)
2
+ (5.0 m/s)
2
25 m
2
/s
2
+ 4.0 m
2
/s
2
= 4.0 m
2
/s
2
+ 25 m
2
/s
2
29 m
2
/s
2
= 29 m
2
/s
2
2.0 m/s to the left
m
1
v
1, f
+ m
2
v
2, f
− m
1
v
1, i
m
2
4. m
1
= 45.0 g
v
1, i
= 273 km/h to the right
=+273 km/h
v
2, i
= 0 km/h
v
1, f
= 91 km/h to the left
=−91 km/h
v
2, f
= 182 km/h to the right
=+182 km/h
Momentum conservation
m
1
v
1, i
+ m
2
v
2, i
= m
1
v
1, f
+ m
2
v
2, f
m
2
=
m
1
v
v
1
2
,
,
f
i
−
−
v
m
2
1
,
v
f
1, i
=
m
2
==
m
2
=
Conservation of kinetic energy (check)
1
2
m
1
v
1,i
2
+
1
2
m
2
v
2,i
2
=
1
2
m
1
v
1, f
2
+
1
2
m
2
v
2, f
1
2
(45.0 g)(273 10
3
m/h)
2
(1 h/3600 s)
2
+
1
2
(90.1 g)(0 m/s)
2
=
1
2
(45.0 g)(−91 × 10
3
m/h)
2
(1 h/3600 s)
2
+
1
2
(90.1 g)(182 × 10
3
m/h)
2
(1 h/3600 s)
2
129 J + 0 J = 14 J + 115 J
129 J = 129 J
90.1 g
−16.4 10
3
g
•
km/h
−182 km/h
−4.1 10
3
g •km/h − 12.3 10
3
g •km/h
−182 km/h
(45.0 g)(−91 km/h) − (45.0 g)(273 km/h)
0 km/h − 182 km/h
5. v
1,i
= 185 km/h to the right
185 km/h
v
2,i
= 0 km/h
v
i,f
= 80.0 km/h to the left
=−80.0 km/h
m
1
= 5.70 10
–2
kg
Momentum conservation
m
1
v
1, i
+ m
2
v
2,i
= m
1
v
1,f
+ m
2
v
2,f
m
m
1
2
v
1,i
−
m
m
1
2
v
1,f
= v
2,f
–v
2,i
m
m
1
2
[185 km/h − (−80.0 km/h)] = v
2,f
− 0 km/h
v
2,f
=
m
m
1
2
(265 km/h) to the right
Conservation of kinetic energy
KE
i
=
1
2
m
1
v
1,i
2
+
1
2
m
2
v
2,i
2
=
1
2
m
1
v
1,i
2
KE
f
=
1
2
m
1
v
1,f
2
+
1
2
m
2
v
2,f
2
1
2
m
1
v
1,i
2
=
1
2
m
1
v
1,f
2
+
1
2
m
2
v
2,f
2
m
m
1
2
(v
1,i
)
2
=
m
m
1
2
(v
1,f
)
2
+ v
2,f
2
m
m
1
2
(185 km/h)
2
=
m
m
1
2
(−80.0 km/h)
2
+ v
2,f
2
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section Two—Problem Workbook Solutions II Ch. 6–13
Givens Solutions
m
m
1
2
(3
.4
2
×
1
0
4
k
m
2
/
h
2
)
−
m
m
1
2
(6
.4
0
×
1
0
3
k
m
2
/
h
2
)
= v
2,f
v
2,f
=
m
m
1
2
(2
.7
8
×
1
0
4
k
m
2
/h
2
) =
m
m
1
2
167 km/h
Equating the two results for v
2,f
yields the ratio of m
1
to m
2
.
m
m
1
2
(265 km/h) =
m
m
1
2
(167 km/h)
265 km/h =
m
m
2
1
(167 km/h)
m
m
2
1
=
2
1
6
6
5
7
k
k
m
m
/
/
h
h
2
= 2.52
m
2
= (2.52) m
1
(2.52)(5.70 10
–2
kg)
m
2
=
0.144 kg
6. m
1
= 4.00 × 10
5
kg
m
2
= 1.60 × 10
5
kg
v
1, i
= 32.0 km/h to the right
v
2, i
= 36.0 km/h to the right
v
1, f
= 35.5 km/h to the right
Momentum conservation
m
1
v
1, i
+ m
2
v
2, i
= m
1
v
1, f
+ m
2
v
2, f
v
2, f
=
v
2, f
=
v
2, f
=
v
2, f
=
4.4
1
×
.6
1
0
0
×
6
1
k
0
g
5
•
k
k
m
g
/h
v
2, f
=
Conservation of kinetic energy (check)
1
2
m
1
v
1, i
2
+
1
2
m
2
v
2, i
2
=
1
2
m
1
v
1, f
2
+
1
2
m
2
v
2, f
2
1
2
(4.00 × 10
5
kg)(32.0 × 10
3
m/h)
2
(1 h/3600 s)
2
+
1
2
(1.60 × 10
5
kg)(36.0 × 10
3
m/h)
2
(1 h/3600 s)
2
=
1
2
(4.00 × 10
5
kg)(35.5 × 10
3
m/h)
2
(1 h/3600 s)
2
+
1
2
(1.60 × 10
5
kg)
(28 10
3
m/h)
2
(1 h/3600 s)
2
1.58 × 10
7
J + 8.00 × 10
6
J = 1.94 × 10
7
J + 4.8 × 10
6
J
2.38 × 10
7
J = 2.42 × 10
7
J
The slight difference arises from rounding.
28 km/h to the right
1.28 × 10
7
kg•km/h + 5.76 × 10
6
kg•km/h − 1.42 × 10
7
kg•km/h
1.60 × 10
5
kg
(4.00 × 10
5
kg)(32.0 km/h) + (1.60 × 10
5
kg)(36.0 km/h) − (4.00 × 10
5
kg)(35.5 km/h)
1.60 × 10
5
kg
m
1
v
1, i
+ m
2
v
2, i
− m
1
v
1, f
m
2
7. m
1
= 5.50 × 10
5
kg
m
2
= 2.30 × 10
5
kg
v
1, i
= 5.00 m/s to the right
=+5.00 m/s
v
2, i
= 5.00 m/s to the left
=−5.00 m/s
v
2, f
= 9.10 m/s to the right
=+9.10 m/s
Momentum conservation
m
1
v
1,i
+ m
2
v
2,i
= m
1
v
1,f
+ m
2
v
2,f
v
1,f
=
v
1,f
=
v
1,f
==−0.89 m/s right
v
1,f
=
Conservation of kinetic energy (check)
1
2
m
1
v
1, i
2
+
1
2
m
2
v
2, i
2
=
1
2
m
1
v
1, f
2
+
1
2
m
2
v
2, f
2
1
2
(5.50 × 10
5
kg)(5.00 m/s)
2
+
1
2
(2.30 × 10
5
kg)(−5.00 m/s)
2
=
1
2
(5.50 × 10
5
kg)
(−0.89 m/s)
2
+
1
2
(2.30 × 10
5
kg)(9.10 × m/s)
2
6.88 × 10
6
J + 2.88 × 10
6
J = 2.2 × 10
5
J + 9.52 × 10
6
J
9.76 × 10
6
J = 9.74 × 10
6
J
The slight difference arises from rounding.
0.89 m/s left
2.75 10
6
kg•m/s – 1.15 10
6
kg•m/s –2.09 × 10
6
kg•m/s
5.50 × 10
5
kg
(5.50 × 10
5
kg)(5.00 m/s) + (2.30 × 10
5
kg)(−5.00 m/s) − (9.10 m/s)
5.50 × 10
5
kg
m
1
v
1,i
+ m
2
v
2,i
− m
2
v
2,f
m
1
Givens Solutions
Holt Physics Solution ManualII Ch. 6–14
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section Two—Problem Workbook Solutions II Ch. 7–1
Circular Motion
and Gravitation
Problem Workbook Solutions
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Additional Practice A
Givens Solutions
1. v
t
= 0.17 m/s
a
c
= 0.29 m/s
2
r =
v
a
t
c
2
=
(0
0
.
.
1
2
7
9
m
m
/
/
s
s
)
2
2
= 0.10 m
2. v
t
= 465 m/s
a
c
= 3.4 × 10
−2
m/s
2
r =
v
a
t
c
2
=
3.4
(4
×
6
1
5
0
m
−2
/s
m
)
2
/s
2
= 6.4 × 10
6
m
3. r =
58.4
2
cm
= 29.2 cm
a
c
= 8.50 × 10
−2
m/s
2
v
t
=
ra
c
=
(2
9.
2
×
1
0
−
2
m
)(
8.
50
×
1
0
−
2
m
/s
2
v
t
= 0.158 m/s
4. r =
12
2
cm
= 6.0 cm
a
c
= 0.28 m/s
2
v
t
=
ra
c
=
(6
.0
×
1
0
−
2
m
)(
0.
28
m
/s
2
)
= 0.13 m/s
5. v
t
= 7.85 m/s
r = 20.0 m
a
c
=
v
r
t
2
=
(7.
2
8
0
5
.0
m
m
/s)
2
= 3.08 m/s
2
6. ∆t = 1.000 h
∆s = 47.112 km
r = 6.37 × 10
3
km
a
c
=
v
r
t
2
==
r
∆
∆
s
t
2
2
a
c
==2.69 × 10
−5
m/s
2
(47 112 m)
2
(6.37 × 10
6
m)
[(1.000 h)(3600 s/h)]
2
∆
∆
s
t
2
r
Additional Practice B
1. m
1
= 235 kg
m
2
= 72 kg
r = 25.0 m
F
c
= 1850 N
m
tot
= m
1
+ m
2
= 235 kg + 72 kg = 307 kg
F
c
= m
tot
a
c
= m
tot
v
r
t
2
v
t
=
m
r
F
to
c
t
=
(2
5.
0
3
m
0
)
7
(
1
k
8
g
5
0
N
)
= 12.3 m/s
2. m = 30.0 g
r = 2.4 m
F
T
= 0.393 N
g = 9.81 m/s
2
F
T
= F
g
+ F
c
= mg + m
v
r
t
2
v
t
=
r(
F
T
m
−
m
g)
=
v
t
=
=
v
t
= 2.8 m/s
(2.4 m)(0.099 N)
30.0 × 10
−3
kg
(2.4 m)(0.393 N − 0.294 N)
30.0 × 10
−3
kg
(2.4 m)[0.393 N − (30.0 × 10
−3
kg)(9.81 m/s
2
)]
30.0 × 10
−3
kg
Holt Physics Solution ManualII Ch. 7–2
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
2. m
1
= 3.08 × 10
4
kg
r = 1.27 × 10
7
m
F
g
= 2.88 × 10
−16
N
G = 6.673 × 10
−11
N
•
m
2
kg
2
m
2
==
m
2
= 2.26 × 10
4
kg
(2.88 × 10
−16
N)(1.27 × 10
7
m)
2
6.673 × 10
−11
N
k
•
g
m
2
2
(3.08 × 10
4
kg)
F
g
r
2
Gm
1
3. v
t
= 8.1 m/s
r = 4.23 m
m
1
= 25 g
g = 9.81 m/s
2
F
g
= F
c
m
1
g =
m
2
r
v
t
2
m
2
=
m
v
1
t
2
gr
m
2
==1.6 × 10
−2
kg
(25 × 10
−3
kg)(9.81 m/s
2
)(4.23 m)
(8.1 m/s)
2
4. v
t
= 75.57 km/h
m = 92.0 kg
F
c
= 12.8 N
F
c
= m
v
r
t
2
r =
m
F
v
c
t
2
=
r = 3.17 × 10
3
m = 3.17 km
(92.0 kg)[(75.57 km/h)(10
3
m/km)(1 h/3600 s)]
2
12.8 N
5. m = 75.0 kg
r = 446 m
v
t
= 12 m/s
g = 9.81 m/s
2
F
c
=
m
r
v
t
2
==
F
T
= F
c
+ mg = 24 N + (75.0 kg)(9.81 m/s
2
)
F
T
= 24 N + 736 N = 7.60 × 10
2
N
24 N
(75.0 kg)(12 m/s)
2
446 m
1. r = 6.3 km
F
g
= 2.5 × 10
−2
N
m
1
= 3.0 kg
G = 6.673 × 10
−11
N
•
m
2
kg
2
m
2
==
m
2
= 5.0 × 10
15
kg
(2.5 × 10
−2
N)(6.3 × 10
3
m)
2
6.673 × 10
−11
N
k
•
g
m
2
2
(3.0 kg)
F
g
r
2
Gm
1
3. m
1
= 5.81 × 10
4
kg
r = 25.0 m
F
g
= 5.00 × 10
−7
N
G = 6.673 × 10
−11
N
•
m
2
kg
2
m
2
==
m
2
= 80.6 kg
(5.00 × 10
−7
N)(25.0 m)
2
6.673 ×10
−11
N
k
•
g
m
2
2
(5.81 × 10
4
kg)
F
g
r
2
Gm
1
Additional Practice C
Section Two—Problem Workbook Solutions II Ch. 7–3
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
7. m
1
= 318m
E
m
2
= 50.0 kg
V
J
= 1323V
E
m
E
= 5.98 × 10
24
kg
r
E
= 6.37 × 10
6
m
G = 6.673 × 10
−11
N
•
m
2
kg
2
If V
J
= 1323 V
E
, then r
J
=
3
13
23
r
E
.
F
g
=
Gm
r
J
1
2
m
2
=
F
g
= 1.30 × 10
3
N
(6.673 × 10
−11
N
•
m
2
/kg
2
)(318)(5.98 × 10
24
kg)(50.0 kg)
[(
3
13
23
)(6.37 × 10
6
m)]
2
4. m
1
= 621 g
m
2
= 65.0 kg
F
g
= 1.0 × 10
−12
N
G = 6.673 × 10
−11
N
•
m
2
kg
2
r =
G
m
F
1
g
m
2
r =
= 52 m
(6.673 × 10
−11
N
•
m
2
/kg
2
)(0.621 kg)(65.0 kg)
1.0 × 10
−12
N
5. m
1
= m
2
= 1.0 × 10
8
kg
F
g
= 1.0 × 10
−3
N
G = 6.673 × 10
−11
N
•
m
2
kg
2
r =
G
m
F
1
g
m
2
r =
r = 2.6 × 10
4
m = 26 km
(6.673 × 10
−11
N
•
m
2
/kg
2
)(1.0 × 10
8
kg
)
2
1.0 × 10
−3
N
6. m
s
= 25 × 10
9
kg
m
1
= m
2
=
1
2
m
s
r = 1.0 × 10
3
km
G = 6.673 × 10
−11
N
•
m
2
kg
2
F
g
=
Gm
r
1
2
m
2
==1.0 × 10
−2
N
6.673 × 10
−11
N
k
•
g
m
2
2
1
2
(25 × 10
9
kg)
2
(1.0 × 10
6
m)
2
Additional Practice D
1. T = 88 643 s
m = 6.42 × 10
23
kg
r
m
= 3.40 × 10
6
m
r =
3
=
3
r = 2.04 × 10
7
m
r
s
= r − r
m
= 2.04 × 10
7
m − 3.40 × 10
6
m = 1.70 × 10
7
m
6.673 × 10
−11
N
k
•
g
m
2
2
(6.42 × 10
23
kg)(88 643 s)
2
4p
2
GmT
2
4p
2
2. T = 5.51 × 10
5
s
m = 1.25 × 10
22
kg
r =
3
=
3
r = 1.86 × 10
7
m
6.673 × 10
−11
N
k
•
g
m
2
2
(1.25 × 10
22
kg)(5.51 × 10
5
s)
2
4p
2
GmT
2
4p
2
6.673
× 10
−1
1
N
k
•
g
m
2
2
5
6
.9
.7
7
4
×
×
1
1
0
0
2
6
4
m
kg
6.673
× 10
−1
1
N
k
•
g
m
2
2
5
6
.9
.7
7
4
×
×
1
1
0
0
2
6
4
m
kg
Holt Physics Solution ManualII Ch. 7–4
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
3. r = 4.22 × 10
7
m
m = 5.97 × 10
24
kg
v
t
=
G
m
r
=
6.673 × 10
−11
N
k
•
g
m
2
2
= 3.07 × 10
3
m/s
(5.97 × 10
24
kg)
(4.22 × 10
7
m)
4. r = 3.84 × 10
8
m
m = 5.97 × 10
24
kg
v
t
=
G
m
r
=
6.673 × 10
−11
N
k
•
g
m
2
2
= 1.02 × 10
3
m/s
(5.97 × 10
24
kg)
(3.84 × 10
8
m)
5. r = 3.84 × 10
8
m
m = 5.97 × 10
24
kg
T = 2p
G
r
m
3
= 2p
= 2.37 × 10
6
s = 27.4 d
(3.84 × 10
8
m)
3
6.673 × 10
−11
N
k
•
g
m
2
2
(5.97 × 10
24
kg)
6. r = 4.50 × 10
12
m
m = 1.99 × 10
30
kg
T = 2p
G
r
m
3
= 2p
= 5.20 × 10
9
s = 165 years
(4.50 × 10
12
m)
3
6.673 × 10
−11
N
k
•
g
m
2
2
(1.99 × 10
30
kg)
7. r = 1.19 × 10
6
m
T = 4.06 × 10
5
s
m = 4p
2
G
r
T
3
2
= 4p
2
= 6.05 × 10
18
kg
(1.19 × 10
6
m)
3
6.673 × 10
−11
N
k
•
g
m
2
2
(4.06 × 10
5
s)
2
8. r = 2.30 × 10
10
m
T = 5.59 × 10
5
s
m
s
= 1.99 × 10
30
kg
m = 4p
2
G
r
T
3
2
= 4p
2
=
m
m
s
=
2
1
.
.
3
9
0
9
×
×
1
1
0
0
3
3
1
0
k
k
g
g
= 11.6
2.30 × 10
31
kg
(2.30 × 10
10
m)
3
6.673 × 10
−11
N
k
•
g
m
2
2
(5.59 × 10
5
s)
2
1. m = 3.00 × 10
5
kg
q = 90.0°−45.0° = 45.0°
t = 3.20 × 10
7
N
•
m
g = 9.81 m/s
2
t = Fd(sin q) = mgl (sin q)
l
=
mg(s
t
in q)
l
=
l
= 15.4 m
3.20 × 10
7
N
•
m
(3.00 × 10
5
kg)(9.81 m/s
2
)(sin 45.0°)
Additional Practice E
II
2. t
net
= 9.4 kN
•
m
m
1
= 80.0 kg
m
2
= 120.0 kg
g = 9.81 m/s
2
t
net
= t
1
+ t
2
= F
1
d
1
(sin q
1
) + F
2
d
2
(sin q
2
)
q
1
= q
2
= 90°, so
t
net
= F
1
d
1
+ F
2
d
2
= m
1
g
+ m
2
gl
l
=
l
=
9.4 × 10
3
N
•
m
+ (120.0 kg)(9.81 m/s
2
)
=
l
= = 6.0 m
9.4 × 10
3
N
•
m
1.57 × 10
3
N
9.4 × 10
3
N
•
m
392 N + 1.18 × 10
3
N
(80.0 kg)(9.81 m/s
2
)
2
t
net
m
2
1
g
+ m
2
g
l
2
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section Two—Problem Workbook Solutions II Ch. 7–5
3. t
net
= 56.0 N
•
m
m
1
= 3.9 kg
m
2
= 9.1 kg
d
1
= 1.000 m − 0.700 m =
0.300 m
g = 9.81 m/s
2
t
net
= t
1
+ t
2
= F
1
d
1
(sin q
1
) + F
2
d
2
(sin q
2
)
q
1
= q
2
= 90°, so
t
net
= F
1
d
1
+ F
2
d
2
= m
1
gd
1
+ m
2
g(1.000 m − x)
x = 1.000 m −
t
net
m
−
2
m
g
1
gd
1
x = 1.000 m −
x == =1.000 m − 0.50 m
x = 0.50 m = 5.0 × 10
1
cm
45 N
•
m
(9.1 kg)(9.81 m/s
2
)
56.0 N
•
m − 11 N
•
m
(9.1 kg)(9.81 m/s
2
)
56.0 N
•
m − (3.9 kg)(9.81 m/s
2
)(0.300 m)
(9.1 kg)(9.81 m/s
2
)
4. t =−1.3 × 10
4
N
•
m
l
= 6.0 m
d = 1.0 m
q = 90.0°−30.0°=60.0°
t = Fd(sin q) =−F
g
(
l
− d)(sin q)
F
g
= = =
F
g
= 3.0 × 10
3
N
1.3 × 10
4
N
•
m
(5.0 m)(sin 60.0°)
−(−1.3 × 10
4
N
•
m)
(6.0 m − 1.0 m)(sin 60.0°)
−t
(
l
− d)(sin q)
5. R =
76
2
m
= 38 m
q = 60.0°
t =−1.45 × 10
6
N
•
m
t = Fd(sin q) =−F
g
R(sin q)
F
g
=
R(s
−
in
t
q)
=
F
g
= 4.4 × 10
4
N
−(−1.45 × 10
6
N
•
m)
(38 m)(sin 60.0°)
II
6. m
1
= 102 kg
m
2
= 109 kg
l
= 3.00 m
l
1
= 0.80 m
l
2
= 1.80 m
g = 9.81 m/s
2
t
net
= t
1
+ t
2
= F
1
d
1
(sin q
1
) + F
2
d
2
(sin q
2
)
q
1
= q
2
= 90°,so
t
net
= F
1
d
1
+ F
2
d
2
= m
1
g
−
l
1
+ m
2
g
−
l
2
t
net
= (102 kg)(9.81 m/s
2
)
3.0
2
0m
− 0.80 m
+ (109 kg)(9.81 m/s
2
)
3.0
2
0m
− 1.80 m
t
net
= (102 kg)(9.81 m/s
2
)(1.50 m − 0.80 m) + (109 kg)(9.81 m/s
2
)(1.50 m − 1.80 m)
t
net
= (102 kg)(9.81 m/s
2
)(0.70 m) + (109 kg)(9.81 m/s
2
)(−0.30 m)
t
net
= 7.0 × 10
2
N
•
m − 3.2 × 10
2
N
•
m
t
net
= 3.8 × 10
2
N
•
m
l
2
l
2
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualII Ch. 7–6
7. m = 5.00 × 10
2
kg
d
1
= 5.00 m
t = 6.25 × 10
5
N
•
m
g = 9.81 m/s
2
q
1
= 90.0°−10.0°=80.0°
d
2
= 4.00 m
q
2
= 90°
a. t = Fd(sin q) = mgd
1
(sin q
1
)
t = (5.00 × 10
2
kg)(9.81 m/s
2
)(5.00 m)(sin 80.0°)
t =
b. t
net
= Fd
2
(sin q
2
) − t = Fd
2
(sin q
2
) − mgd
1
(sin q
1
)
F =
F ==
F = 1.62 × 10
5
N
6.49 × 10
5
N
•
m
4.00 m
6.25 × 10
5
N
•
m + 2.42 × 10
4
N
•
m
4.00 m (sin 90°)
t
net
+ mgd
1
(sin q
1
)
d
2
(sin q
2
)
2.42 × 10
4
N
•
m
Section Two—Problem Workbook Solutions II Ch. 8–1
Fluid Mechanics
Problem Workbook Solutions
II
1. m
p
= 1158 kg
V = 3.40 m
3
ρ
= 1.00 × 10
3
kg/m
3
g = 9.81 m/s
2
F
B
= F
g
ρ
Vg = (m
p
+ m
r
)g
m
r
=
ρ
V − m
p
= (1.00 × 10
3
kg/m
3
)(3.40 m
3
) − 1158 kg = 3.40 × 10
3
kg − 1158 kg
m
r
= 2.24 × 10
3
kg
Additional Practice A
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. V = 4.14 × 10
−2
m
3
apparent weight =
3.115 × 10
3
N
ρ
sw
= 1.025 × 10
3
kg/m
3
g = 9.81 m/s
2
F
B
= F
g
− apparent weight
ρ
sw
Vg = mg − apparent weight
m =
ρ
sw
V +
apparen
g
tweight
= (1.025 × 10
3
kg/m
3
)(4.14 × 10
−2
m
3
) +
3.1
9
1
.8
5
1
×
m
1
/
0
s
3
2
N
m = 42.4 kg + 318 kg = 3.60 × 10
2
kg
3.
l
= 3.00 m
A = 0.500 m
2
r
fw
= 1.000 × 10
3
kg/m
3
r
sw
= 1.025 × 10
3
kg/m
3
F
net,1
= F
net,2
= 0
F
B,1
− F
g,1
= F
B,2
− F
g,2
r
fw
Vg − mg = r
sw
Vg − (m + m
ballast
)g
m
ballast
g = (r
sw
− r
fw
)Vg
m
ballast
= (r
sw
− r
fw
)A
l
m
0
= (1.025 × 10
3
kg/m
3
− 1.000 × 10
3
kg/m
3
)(0.500 m
2
)(3.00 m)
m
0
= (25 kg/m
3
)(0.500 m
2
)(3.00 m) = 38 kg
4. A = 3.10 × 10
4
km
2
h = 0.84 km
r = 1.025 × 10
3
kg/m
3
g = 9.81 m/s
2
F
B
= rVg = rAhg
F
B
= (1.025 × 10
3
kg/m
3
)(3.10 × 10
10
m
2
)(840 m)(9.81 m/s
2
) = 2.6 × 10
17
N
5. m = 4.80 × 10
2
kg
g = 9.81 m/s
2
apparent weight = 4.07 × 10
3
N
F
B
= F
g
− apparent weight = mg − apparent weight
F
B
= (4.80 × 10
2
kg)(9.81 m/s
2
) − 4.07 × 10
3
N = 4.71 × 10
3
N − 4.07 × 10
3
N
F
B
= 640 N
Holt Physics Solution ManualII Ch. 8–2
II
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
6. h = 167 m
H = 1.50 km
r
sw
= 1.025 × 10
3
kg/m
3
F
g,i
= F
B
r
i
V
i
g = r
sw
V
sw
g
r
i
(h + H)Ag = r
sw
HAg
r
i
=
h
r
s
+
w
H
H
r
i
===921 kg/m
3
(1.025 × 10
3
kg/m
3
)(1.50 × 10
3
m)
1670 m
(1.025 × 10
3
kg/m
3
)(1.50 × 10
3
m)
167 m + 1.50 × 10
3
m
7.
l
= 1.70 × 10
2
m
r =
13.
2
9m
= 6.95 m
m
sw
= 2.65 × 10
7
kg
a = 2.00 m/s
2
g = 9.81 m/s
2
F
net
= F
g
− F
B
m
sub
a = m
sub
g − m
sw
g
ρ
sub
Va =
ρ
sub
Vg − m
sw
g
ρ
sub
(g − a)V = m
sw
g
ρ
sub
=
(g
m
−
sw
a
g
)V
=
(g −
m
a)
s
(
w
π
g
r
2
l
)
ρ
sub
=
ρ
sub
=
ρ
sub
= 1.29 × 10
3
kg/m
3
(2.65 × 10
7
kg)(9.81 m/s
2
)
(9.81 m/s
2
)(
π
)(6.95 m)
2
(1.70 × 10
2
m)
(2.65 × 10
7
kg)(9.81 m/s
2
)
(9.81 m/s
2
− 2.00 m/s
2
)(
π
)(6.95 m)
2
(1.70 × 10
2
m)
8. V = 6.00 m
3
∆ apparent weight = 800 N
ρ
water
= 1.00 × 10
3
kg/m
3
g = 9.81 m/s
2
F
g,1
= F
g,2
F
B,1
+ apparent weight in water = F
B,2
+ apparent weight in PEG solution
ρ
water
Vg + apparent weight in water − apparent weight in PEG solution =
ρ
soln
Vg
ρ
soln
=
ρ
soln
=
ρ
soln
==
ρ
soln
= 1.01 × 10
3
kg/m
3
5.97 × 10
4
N
(6.00 m
3
)(9.81 m/s
2
)
5.89 × 10
4
N + 800 N
(6.00 m
3
)(9.81 m/s
2
)
(1.00 × 10
3
kg/m
3
)(6.00 m
3
)(9.81 m/s
2
) + 800 N
(6.00 m
3
)(9.81 m/s
2
)
ρ
water
Vg +∆ apparent weight
Vg
Additional Practice B
1. P = 1.01 × 10
5
Pa
A = 3.3 m
2
F = PA (1.01 × 10
5
Pa)(3.3 m
2
) = 3.3 × 10
5
N
Section Two—Problem Workbook Solutions II Ch. 8–3
II
2. P = 4.0 × 10
11
Pa
r = 50.0 m
F = PA = P(
π
r
2
)
F = (4.0 × 10
11
Pa)(
π
)(50.0 m)
2
F = 3.1 × 10
15
N
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
3. m
1
= 181 kg
m
2
= 16.0 kg
A
1
= 1.8 m
2
g = 9.81 m/s
2
P
1
= P
2
A
F
1
1
=
A
F
2
2
A
2
=
F
2
F
A
1
1
=
3m
m
2
1
g
g
A
1
=
3m
m
2
1
A
1
A
2
==0.48 m
2
(3)(16.0 kg)(1.8 m
2
)
181 kg
4. m = 4.0 × 10
7
kg
F
2
= 1.2 × 10
4
N
A
2
= 5.0 m
2
g = 9.81 m/s
2
P
1
= P
2
A
F
1
1
=
A
F
2
2
A
1
=
A
F
2
F
2
1
=
A
F
2
m
2
g
A
1
==1.6 × 10
5
m
2
(5.0 m
2
)(4.0 × 10
7
kg)(9.81 m/s
2
)
1.2 × 10
4
N
5. P = 2.0 × 10
16
Pa
F = 1.02 × 10
31
N
A =
P
F
=
1
2
.
.
0
0
2
×
×
1
1
0
0
1
3
6
1
P
N
a
=
A = 4
π
r
2
r =
=
r = 6.4 × 10
6
m
5.1 × 10
14
m
2
4
π
A
4
π
5.1 × 10
14
m
2
6. F = 4.6 × 10
6
N
r =
38
2
cm
= 19 cm
P =
A
F
Assuming the squid’s eye is a sphere, its total surface area is 4
π
r
2
. The outer half of
the eye has an area of
A = 2
π
r
2
P
=
2
π
F
r
2
=
(2
4
π
.6
)(
×
0.
1
1
0
9
6
m
N
)
2
= 2.0 × 10
7
Pa
7. A = 26.3 m
2
F = 1.58 × 10
7
N
P
o
= 1.01 × 10
5
Pa
P =
A
F
=
1.5
2
8
6.
×
3
1
m
0
7
2
N
=
P
gauge
= P − P
o
= 6.01 × 10
5
Pa − 1.01 × 10
5
Pa = 5.00 × 10
5
Pa
6.01 × 10
5
Pa
II
1. h = (0.800)(16.8 m)
P = 2.22 × 10
5
Pa
P
o
= 1.01 × 10
5
Pa
g = 9.81 m/s
2
P = P
o
+
ρ
gh
ρ
=
P
g
−
h
P
o
==
ρ
= 918 kg/m
3
1.21 × 10
5
Pa
(9.81 m/s
2
)(0.800)(16.8 m)
2.22 × 10
5
Pa − 1.01 × 10
5
Pa
(9.81 m/s
2
)(0.800)(16.8 m)
Additional Practice C
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. h =−950 m
P = 8.88 × 10
4
Pa
P
o
= 1.01 × 10
5
Pa
g = 9.81 m/s
2
P = P
o
+
ρ
gh
ρ
== =
ρ
= 1.3 kg/m
3
−1.2 × 10
4
Pa
(9.81 m/s
2
)(−950 m)
8.88 × 10
4
Pa − 1.01 × 10
5
Pa
(9.81 m/s
2
)(−950 m)
P − P
o
g
1
h
3. P = 13.6P
0
P
0
= 1.01 × 10
5
Pa
r = 1.025 × 10
3
kg/m
3
g = 9.81 m/s
2
P = P
0
+ rgh
h =
13.6P
r
0
g
− P
0
=
12
r
.6
g
P
0
h ==127 m
(12.6)(1.01 × 10
5
Pa)
(1.025 × 10
3
kg/m
3
)(9.81 m/s
2
)
4. P = 4.90 × 10
6
Pa
P
0
= 1.01 × 10
5
Pa
r = 1.025 × 10
3
kg/m
3
g = 9.81 m/s
2
P = P
0
+ rgh
h =
P
r
−
g
P
0
=
h ==477 m
4.80 × 10
6
Pa
(1.025 × 10
3
kg/m
3
)(9.81 m/s
2
)
4.90 × 10
6
Pa − 1.01 × 10
5
Pa
(1.025 × 10
3
kg/m
3
)(9.81 m/s
2
)
6. h = 10 916 m
P
0
= 1.01 × 10
5
Pa
r = 1.025 × 10
3
kg/m
3
g = 9.81 m/s
2
P = P
0
+ rgh = 1.01 × 10
5
Pa + (1.025 × 10
3
kg/m
3
)(9.81 m/s
2
)(10 916 m)
P = 1.01 × 10
5
Pa + 1.10 × 10
8
Pa = 1.10 × 10
8
Pa
5. h = 245 m
P
o
= 1.01 × 10
5
Pa
ρ
= 1.025 × 10
3
kg/m
3
g = 9.81 m/s
2
P = P
o
+
ρ
gh
P = 1.01 × 10
5
Pa + (1.025 × 10
3
kg/m
3
)(9.81 m/s
2
)(245 m)
P = 1.01 × 10
5
Pa + 2.46 × 10
6
Pa
P = 2.56 × 10
6
Pa
Holt Physics Solution ManualII Ch. 8–4
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section Two—Problem Workbook Solutions II Ch. 9–1
1. T
C
= 14°C
T = T
C
+ 273.15
T = (14 + 273.15) K
T =
T
F
=
9
5
T
C
+ 32.0
T
F
=
9
5
(14) + 32.0
°F = (25 + 32.0)°F
T
F
= 57°F
287 K
Additional Practice A
Givens Solutions
2. T
F
= (4.00 × 10
2
)°F
T
C
=
5
9
(T
F
− 32.0)
T
C
=
5
9
[(4.00 × 10
2
) − 32.0]°C =
5
9
(368)°C
T
C
=
T = T
C
+ 273.15
T = (204 + 273.15) K
T = 477 K
204°C
3. T
C,1
= 117°C
T
C,2
=−163°C
∆T
C
= T
C,1
− T
C,2
= 117°C − (−163°C)
∆T
C
= (2.80 × 10
2
)°C
∆T
F
=
5
9
∆T
C
∆T
F
=
5
9
(2.80 × 10
2
)°F
∆T
F
= 504°F
Heat
Problem Workbook Solutions
4. T
F
= 860.0°F
T
C
=
5
9
(T
F
− 32.0)
T
C
=
9
5
(860.0 − 32.0)°C =
9
5
(828.0)°C
T
C
= 460.0°C
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualII Ch. 9–2
5. ∆T
F
= 49.0°F
T
C,2
= 7.00°C
T
F
=
9
5
T
C
+ 32.0
T
F,2
=
9
5
(7.00) + 32.0
°F = (12.6 + 32.0)°F
T
F,2
=
T
F,1
= T
F,2
−∆T
F
= 44.6°F − 49.0°F
T
F,1
=
T
C,1
=
5
9
(T
F,1
− 32.0)
T
C,1
=
5
9
(−4.4 − 32.0)°C =
5
9
(−36.4)°C
T
C,1
=−20.2°C
−4.4°F
44.6°F
Givens Solutions
6. ∆T
C
= 56°C
T
C,2
=−49°C
T
C,1
= T
C,2
+∆T
C
T
C,1
=−49°C + 56°C
T
C,1
= 7°C
T
1
= T
C,1
+ 273.15
T
1
= (7 + 273.15) K
T
1
=
T
2
= T
C,2
+ 273.15
T
2
= (−49 + 273.15) K
T
2
= 2.24 × 10
2
K
2.80 × 10
2
K
1. m
H
= 3.05 × 10
5
kg
v
i
= 120.0 km/h
v
f
= 90.0 km/h
∆T = 10.0°C
k =
m
∆
w
U
∆T
=
(1.00 k
4
g
1
)
8
(
6
1.
J
00°C)
∆PE +∆KE +∆U = 0 ∆PE = 0
∆KE =
1
2
m
H
v
f
2
−
1
2
m
H
v
i
2
=
m
2
H
(v
f
2
− v
i
2
)
∆U =−∆KE =
m
2
H
(v
i
2
− v
f
2
)
m
w
=
m
∆
w
U
∆T
∆
∆
U
T
=
1
k
∆
∆
U
T
=
2
m
k∆
H
T
(v
i
2
− v
f
2
)
m
w
=
120.
h
0km
2
−
90.0
h
km
2
36
1
0
h
0s
1
1
0
k
3
m
m
2
m
w
= (3.64 kg
•
s
2
/m
2
)(1110 m
2
/s
2
− 625 m
2
/s
2
)
m
w
= (3.64 kg
•
s
2
/m
2
)(480 m
2
/s
2
)
m
w
= 1.7 × 10
3
kg
3.05 × 10
5
kg
(2
(1
)(
.0
4
0
18
k
6
g)
J
(
)
1
(1
.0
0
0
.0
°C
°C
)
)
Additional Practice B
7. T
F
= 116 °F
T = T
C
+ 273.15 =
5
9
(T
F
− 32.0) + 273.15
T =
5
9
(116 − 32.0) + 273.15
K =
5
9
(84) + 273.15
K = (47 + 273.15) K
T = 3.20 × 10
2
K
Section Two—Problem Workbook Solutions II Ch. 9–3
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. h = 228 m
T
i
= 0.0°C
g = 9.81 m/s
2
fraction of ME
f
converted
to U = 0.500
k = (∆U/m)= energy
needed to melt ice =
3.33 × 10
5
J/1.00 kg
∆PE =−mgh
When the ice lands, its kinetic energy is tranferred to the internal energy of the
ground and the ice. Therefore, ∆KE = 0 J.
∆U = (0.500)(ME
f
) =−(0.500)(∆PE) = (0.500)(mgh)
∆
m
U
= (0.500)(gh)
f =
∆
km
U
=
(0.500
k
)(gh)
f =
f = 3.36 × 10
−3
(0.500)(9.81 m/s
2
)(228 m)
(3.33 × 10
5
J/1.00 kg)
Givens Solutions
3. v
i
= 2.333 × 10
3
km/h
h = 4.000 × 10
3
m
g = 9.81 m/s
2
fraction of ME converted
to U = 0.0100
k =
m
∆
∆
U
T
=
(1.00 k
(3
g
5
)(
5
1
J
.
)
00°C)
4. h = 8848 m
g = 9.81 m/s
2
fraction of ME
f
converted
to U = 0.200
T
i
=−18.0°C
∆U
∆T
/m
=
4
1
4
.
8
00
J
°
/k
C
g
∆PE =−mgh
ME
f
=−∆PE
When the hook lands, its kinetic energy is transferred to the internal energy of the
hook and the ground. Therefore, ∆KE = 0 J.
∆U = (0.200)(ME
f
) = (−0.200)(∆PE) = (0.200)(mgh)
∆U/m = (0.200)(gh)
∆T =
∆U
∆T
/m
∆
m
U
=
4
1
4
.
8
00
J
°
/k
C
g
[(0.200)(gh)]
∆T =
4
1
4
.
8
00
J
°
/k
C
g
(0.200)(9.81 m/s
2
)(8848 m) = 38.7°C
T
f
= T
i
+∆T =−18.0°C + 38.7°C
T
f
= 20.7°C
(0.0100)(∆PE +∆KE) +∆U = 0
∆PE = PE
f
− PE
i
= 0 − mgh =−mgh
∆KE = KE
f
− KE
i
= 0 −
1
2
mv
i
2
=−
1
2
mv
i
2
∆U =−(0.0100)(∆PE +∆KE) =−(0.0100)(m)
−gh −
1
2
v
2
= (0.0100)(m)
gh +
1
2
v
2
∆T ==
∆T =
∆T =
∆T = 7.02°C
(0.0100)[(3.92 × 10
4
m
2
/s
2
) + (2.100 × 10
5
m
2
/s
2
)]
355 m
2
/s
2
•
°C
(0.0100)
(9.81 m/s
2
)(4.000 × 10
3
m) +
1
2
2.33
3
3
6
×
00
10
s/
6
h
m/h
2
355 m
2
/s
2
•
°C
(0.0100)
gh +
1
2
v
2
(1.00 k
3
g
5
)
5
(1
J
.00°C)
∆
m
U
k
Holt Physics Solution ManualII Ch. 9–4
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
7. ∆T = 0.230°C
g = 9.81 m/s
2
fraction of ME
f
converted
to U = 0.100
∆
∆
U
T
/m
=
41
1
8
.0
6
0
J
°
/
C
kg
∆
m
U
=∆T
∆
∆
U
T
/m
=
(0.100
m
)(ME
f
)
=
(0.100
m
)(∆PE)
= (0.100)(gh)
Because the kinetic energy at the bottom of the falls is converted to the internal en-
ergy of the water and the ground, ∆KE = 0 J.
h =
h =
41
1
8
.0
6
0
J
°
/
C
kg
h = 981 m
0.230°C
(0.100)(9.81 m/s
2
)
∆T
∆
∆
U
T
/m
(0.100)(g)
5. h
i
= 629 m
g = 9.81 m/s
2
v
f
= 42 m/s
fraction of ME converted
to U = 0.050
m = 3.00 g
Because h
f
= 0 m, PE
f
= 0 J. Further, v
i
= 0 m/s, so KE
i
= 0 J.
∆U =−(0.050)(∆ME) =−(0.050)(∆PE +∆KE)
∆PE = PE
f
− PE
i
= 0 J − PE
i
=−mgh
∆KE = KE
f
− KE
i
= KE
f
− 0 J =
1
2
mv
f
2
∆U = (0.050)(−∆PE −∆KE) = (0.050)(mgh −
1
2
mv
f
2
) = (0.050)(m)(gh −
1
2
v
f
2
)
∆U = (0.050)(3.00 × 10
−3
kg)[(9.81 m/s
2
)(629 m) − (0.5)(42 m/s)
2
]
∆U = (0.050)(3.00 × 10
−3
kg)(6170 m
2
/s
2
− 880 m
2
/s
2
)
∆U = (0.050)(3.00 × 10
−3
kg)(5290 m
2
/s
2
)
∆U = 0.79 J
Givens Solutions
6. h = 2.49 m
g = 9.81 m/s
2
m = 312 kg
v = 0.50 m/s
fraction of ME converted
to U = 0.500
(0.500)(∆PE +∆KE) +∆U = 0
∆PE = PE
f
− PE
i
= 0 − mgh =−mgh
∆KE = KE
f
− KE
i
= 0 −
2
1
mv
2
=
−m
2
v
2
∆U =−(0.500)(∆PE +∆KE) =−(0.500)
−mgh −
m
2
v
2
= (0.500)
mgh +
m
2
v
2
∆U = (0.500)[(312 kg)(9.81 m/s
2
)(2.49 m) + (0.5)(312 kg)(0.50 m/s)
2
]
∆U = (0.500)[(7.62 × 10
3
J) + 39 J]
∆U = 3.83 × 10
3
J
Section Two—Problem Workbook Solutions II Ch. 9–5
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. Q = (2.8 × 10
9
W)(1.2 s)
c
p,c
= 387 J/kg
•
°C
T
c
= 26.0°C
T
f
= 21.0°C
Q =−m
c
c
p,c
(T
f
− T
c
) = m
c
c
p,c
(T
c
− T
f
)
m
c
=
c
p,c
(T
Q
c
− T
f
)
m
c
=
m
c
= = 1.7 × 10
6
kg
(2.8 × 10
9
W)(1.2 s)
(387 J/kg
•
°C)(5.0°C)
(2.8 × 10
9
W)(1.2 s)
(387 J/kg
•
°C)(26.0°C − 21.0°C)
2. m
w
= 143 × 10
3
kg
T
w
= 20.0°C
T
x
= temperature of
burning wood = 280.0°C
T
f
= 100.0°C
c
p,x
= specific heat
capacity of wood =
1.700 × 10
3
J/kg
•
°C
c
p,w
= 4186 J/kg
•
°C
− c
p,x
m
x
(T
f
− T
x
) = c
p,w
m
w
(T
f
− T
w
)
m
x
=
m
x
=
m
x
=
m
x
= 1.56 × 10
5
kg
(4186 J/kg
•
°C)(143 × 10
3
kg)(80.0°C)
(1.700 × 10
3
J/kg
•
°C)(180.0°C)
(4186 J/kg
•
°C)(143 × 10
3
kg)(100.0°C − 20.0°C)
(1.700 × 10
3
J/kg
•
°C)(280.0°C − 100.0°C)
c
p,w
m
w
(T
f
− T
w
)
c
p,x
(T
x
− T
f
)
Additional Practice C
Givens Solutions
3. ∆U = Q = (0.0100)
(1.450 GW)(1.00 year)
c
p,x
= specific heat capacity
of iron = 448 J/kg
•
°C
m
x
= mass of steel =
25.1 × 10
9
kg
Q = c
p,x
m
x
∆T
∆T =
c
p,x
Q
m
x
∆T =
365
1
.2
y
5
ea
d
r
ays
1
2
d
4
a
h
y
36
1
0
h
0 s
∆T = 40.7°C
(0.0100)(1.450 × 10
9
W)(1.00 year)
(448 J/kg
•
°C)(25.1 × 10
9
kg)
4. m
l
= 2.25 × 10
3
kg
T
l,i
= 28.0°C
c
p,l
= c
p,w
= 4186 J/kg
•
°C
m
i
= 9.00 × 10
2
kg
T
i,i
=−18.0°C
c
p,i
= 2090 J/kg
•
°C
T
i,f
= 0.0°C
−m
l
c
p,l
(T
l,f
− T
l,i
) = m
i
c
p,i
(T
i,f
− T
i,i
)
T
l,f
= T
l,i
−
m
m
l
i
c
c
p
p
,
,
l
i
(T
i,f
− T
i,i
)
T
l,f
= (28.0°C) −
2
9
.
.
2
0
5
0
×
×
1
1
0
0
3
2
k
k
g
g
[(0.0°C) − (−18.0°C)]
T
l,f
= 28.0°C − 3.59°C = 24.4°C
2090 J/kg
•
°C
4186 J/kg
•
°C
5. m
w
= 1.33 × 10
19
kg
T
w
= 4.000°C
c
p,w
= 4186 J/kg
•
°C
P = 1.33 × 10
10
W
∆t = 1.000 × 10
3
years
P∆t = Q = m
w
c
p,w
(T
f
− T
w
)
T
f
=
m
P
w
∆
c
p
t
,w
+ T
w
T
f
=+4.000°C
T
f
= (7.54 × 10
−3
)°C + 4.000°C
T
f
= 4.008°C
(1.33 × 10
10
W)(1.000 × 10
3
years)
36
1
5.
y
2
e
5
a
d
r
ay
1
2
d
4
a
h
y
36
1
0
h
0 s
(1.33 × 10
19
kg)(4186 J/kg
•
°C)
Holt Physics Solution ManualII Ch. 9–6
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
7. T
m
=−62.0°C
T
w
= 38.0°C
m
m
= 180 g
m
w
= 0.500 kg
T
f
= 36.9°C
c
p,w
= 4186 J/kg
•
°C
m
m
c
p,m
(T
f
− T
m
) =−m
w
c
p,w
(T
f
− T
w
)
c
p,m
=
m
m
m
w
(c
p,w
)
T
T
f
w
−
−
T
T
m
f
c
p,m
=
0
0
.5
.1
0
8
0
k
k
g
g
(4186 J/kg
•
°C)
c
p,m
=
The metal could be gold (c
p
= 129 J/kg
•
°C) or lead (c
p
= 128 J/kg
•
°C).
1.3 × 10
2
J/kg
•
°C
(38.0°C) − (36.9°C)
(36.9°C) − (−62.0°C)
Givens Solutions
6. T
i
= 18.0°C
T
f
= 32.0°C
Q = 20.8 kJ
m
x
= 0.355 kg
Q = m
x
c
p,x
∆T
c
p,x
=
m
x
Q
∆T
=
m
x
(T
Q
f
− T
i
)
c
p,x
=
c
p,x
= 4190 J/kg
•
°C
20.8 × 10
3
J
(0.355 kg)(32.0°C − 18.0°C)
1. m
w,S
= 1.20 × 10
16
kg
m
w,E
= 4.8 × 10
14
kg
T
E
= 0.0°C
T
S
= 100.0°C
c
p,w
= 4186 J/kg
•
°C
L
f
of ice = 3.33 × 10
5
J/kg
Q
S
= energy transferred by heat from Lake Superior = c
p,w
m
w,S
(T
S
− T
f
)
Q
E
= energy transferred by heat to Lake Erie = m
w,E
L
f
+ m
w,E
c
p,w
(T
f
− T
E
)
From the conservation of energy,
Q
S
= Q
E
c
p,w
m
w,S
(T
S
− T
f
) = m
w,E
L
f
+ m
w,E
c
p,w
(T
f
− T
E
)
(m
w,E
c
p,w
+ c
p,w
m
w,S
)T
f
= c
p,w
m
w,S
T
S
+ m
w,E
c
p,w
T
E
− m
w,E
L
f
T
f
= ,where T
E
= 0.0°C
T
f
=
T
f
=
T
f
=
T
f
= 92.9°C
(5.02 × 10
21
J) − (1.6 × 10
20
J)
(4186 J/kg
•
°C)(1.25 × 10
16
kg)
(4186 J/kg
•
°C)(1.20 × 10
16
kg)(100.0°C) − (4.8 × 10
14
kg)(3.33 × 10
5
J/kg)
(4186 J/kg
•
°C)[(4.8 × 10
14
kg) + (1.20 × 10
16
kg)]
c
p,w
m
w,S
T
S
− m
w,E
L
f
c
p,w
(m
w,E
+ m
w,S
)
c
p,w
(m
w,S
T
S
+ m
w,E
T
E
) − m
w,E
L
f
c
p,w
(m
w,E
+ m
w,S
)
Additional Practice D
2. T
f
=−235°C
T
freezing
= 0.0°
m
w
= 0.500 kg
c
p,w
= 4186 J/kg
•
°C
c
p,ice
= c
p,i
= 2090 J/kg
•
°C
L
f
of ice = 3.33 × 10
5
J/kg
Q
tot
= 471 kJ
Q
tot
= c
p,w
m
w
(T
i
− 0.0°) + L
f
m
w
+ m
w
c
p,i
(0.0°− T
f
) = c
p,w
m
w
T
i
+ L
f
m
w
− c
p,i
m
w
T
f
T
i
=
T
i
=
T
i
=
T
i
= 28°C
(4.71 × 10
5
J) − (1.66 × 10
5
J) − (2.46 × 10
5
J)
2093 J/°C
(4.71 × 10
5
J) − (3.33 × 10
5
J/kg)(0.500 kg) + (−235°C)(2090 J/kg
•
°C)(0.500 kg)
(4186 J/kg
•
°C)(0.500 kg)
Q
tot
− L
f
m
w
+ c
p,i
m
w
T
f
c
p,w
m
w
Section Two—Problem Workbook Solutions II Ch. 9–7
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
3. T
i
= 0.0°C
m
i
= 4.90 × 10
6
kg
L
f
of ice = 3.33 × 10
5
J/kg
T
s
= 100.0°C
L
v
of steam = 2.26 × 10
6
J/kg
m
s
L
v
= m
i
L
f
m
s
=
m
L
i
v
L
f
m
s
=
m
s
= 7.22 × 10
5
kg
(4.90 × 10
6
kg)(3.33 × 10
5
J/kg)
2.26 × 10
6
J/kg
Givens Solutions
4. m
s
= 1.804 × 10
6
kg
L
f
of silver = L
f,s
=
8.82 × 10
4
J/kg
L
f
of ice = L
f,i
=
3.33 × 10
5
J/kg
m
s
L
f,s
= m
i
L
f,i
m
i
=
m
L
s
L
f,i
f,s
m
i
=
m
i
= 4.78 × 10
5
kg
(1.804 × 10
6
kg)(8.82 × 10
4
J/kg)
3.33 × 10
5
J/kg
5. m
g
= 12.4414 kg
T
g,i
= 5.0°C
Q = 2.50 MJ
c
p,g
= 129 J/kg
•
°C
T
g,f
= 1063°C
Q = m
g
c
p,g
(T
g,f
− T
g,i
) + m
g
L
f
L
f
=
L
f
=
L
f
=
L
f
= 6.4 × 10
4
J/kg
(2.50 × 10
6
J) − (1.70 × 10
6
J)
12.4414 kg
(2.50 × 10
6
J) − (12.4414 kg)(129 J/kg
•
°C)(1063°C − 5.0°C)
12.4414 kg
Q − m
g
c
p,g
(T
g,f
− T
g,i
)
m
g
6. V
p
= 7.20 m
3
V
c
= (0.800)(V
p
)
r
c
= 8.92 × 10
3
kg/m
3
L
f
= 1.34 × 10
5
J/kg
a. m
c
= r
c
V
c
m
c
= (8.92 × 10
3
kg/m
3
)(0.800)(7.20 m
3
)
m
c
=
b. fraction of melted coins =
m
Q
c
L
f
=
1
1
0
5
0
Q =
1
1
0
5
0
m
c
L
f
=
Q = 1.03 × 10
9
J
15(5.14 × 10
4
kg)(1.34 × 10
5
J/kg)
100
5.14 × 10
4
kg
Holt Physics Solution ManualII Ch. 9–8
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
7. m
w
= 3.5 × 10
19
kg
T
i
= 10.0°C
T
f
= 100.0°C
c
p,w
= 4186 J/kg
•
°C
L
v
of water = 2.26 × 10
6
J/kg
P = 4.0 × 10
26
J/s
a. Q = m
w
c
p,w
(T
f
− T
i
) + m
w
L
v
Q = (3.5 × 10
19
kg)(4186 J/kg
•
°C)(100.0°C − 10.0°C)
+ (3.5 × 10
19
kg)(2.26 × 10
6
J/kg)
Q = 1.3 × 10
25
+ 7.9 × 10
25
J =
b. Q = P∆t
∆t =
Q
P
=
4
9
.0
.2
×
×
1
1
0
0
2
2
6
5
J/
J
s
= 0.23 s
9.2 × 10
25
J
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section Two—Problem Workbook Solutions II Ch. 10–1
1. P = 5.1 kPa
W = 3.6 × 10
3
J
V
i
= 0.0 m
3
W = P∆V
∆V =
W
P
=
5
3
.1
.6
×
×
1
1
0
0
3
3
P
J
a
= 7.1 × 10
−1
m
3
V = V
i
+∆V = 0.0 m
3
+ 7.1 × 10
−1
m
3
= 7.1 × 10
−1
m
3
Additional Practice A
Givens Solutions
2. m = 207 kg
g = 9.81 m/s
2
h = 3.65 m
P = 1.8 × 10
6
Pa
W = mgh =−P∆V
∆V =
m
−
g
P
h
∆V ==−4.1 × 10
−3
m
3
(207 kg)(9.81 m/s
2
)(3.65 m)
−(1.8 × 10
6
Pa)
3. r
f
= 1.22 m
r
i
= 0.0 m
W = 642 kJ
W = P∆V
P =
∆
W
V
∆V =
3
4
p(r
f
3
− r
i
3
)
P == =8.44 × 10
4
Pa
642 × 10
3
J
3
4
p
(1.22 m)
3
− (0.0 m)
3
W
3
4
p(r
f
3
− r
i
3
)
4. r
f
= 7.0 × 10
5
km
r
f
= 7.0 × 10
8
m
r
i
= 0.0 m
W = 3.6 × 10
34
J
W = P∆V
V =
3
4
pr
3
∆V = V
f
− V
i
=
3
4
p(r
f
3
− r
i
3
)
W = (P)(
3
4
p)(r
f
3
− r
i
3
)
P =
W
(
3
4
p)(r
f
3
− r
i
3
)
5. P = 87 kPa
∆V =−25.0 × 10
−3
m
3
W = P∆V
W = (87 × 10
3
Pa)(−25.0 × 10
−3
m
3
) =−2.2 × 10
3
J
Thermodynamics
Problem Workbook Solutions
P ==2.5 × 10
7
Pa
(3.6 × 10
34
J)
(
3
4
p )[(7.0 × 10
8
m)
3
− (0.0 m)
3
]
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualII Ch. 10–2
6. r
f
= 29.2 cm
r
i
= 0.0 m
P = 25.0 kPa
m = 160.0 g
W = P∆V
∆V =
3
4
p(r
f
3
− r
i
3
)
W =
1
2
mv
2
1
2
mv
2
= (P)
4
3
p
(r
f
3
− r
i
3
)
v =
8
3
p
m
P
(r
f
3
− r
i
3
)
v =
(
29
.2
×
1
0
−
2
m
)
3
−
(
0.
0
m
)
3
v = 181 m/s
(8p)(25.0 × 10
3
Pa)
(3)(160.0 × 10
−3
kg)
Givens Solutions
1. m = 227 kg
h = 8.45 m
g = 9.81 m/s
2
U
i
= 42.0 kJ
Q = 4.00 kJ
∆U = U
f
− U
i
= Q − W
W = mgh
U
f
= U
i
+ Q − W = U
i
+ Q − mgh
U
f
= (42.0 × 10
3
J) + (4.00 × 10
3
J) − (227 kg)(9.81 m/s
2
)(8.45 m)
U
f
= (42.0 × 10
3
J) + (4.00 × 10
3
J) − (18.8 × 10
3
J)
U
f
= 27.2 × 10
3
J = 27.2 kJ
Additional Practice B
2. m = 4.80 × 10
2
kg
Q = 0 J
v = 2.00 × 10
2
m/s
U
f
= 12.0 MJ
a. Assume that all work is transformed to the kinetic energy of the cannonball.
W =
1
2
mv
2
W =
1
2
(4.80 × 10
2
kg)(2.00 × 10
2
m/s)
2
W =
b. ∆U = Q − W =−W
U
f
− U
i
=−W
U
i
= U
f
+ W
U
i
= (12.0 × 10
6
J) + (9.60 × 10
6
J)
U
i
= 21.6 × 10
6
J = 21.6 MJ
9.60 × 10
6
J = 9.60 MJ
3. m = 4.00 × 10
4
kg
c
p
= 4186 J/kg
•
°C
∆T =−20.0°C
W = 1.64 × 10
9
J
a. Q = mc
p
∆T
Q = (4.00 × 10
4
kg)(4186 J/kg
•
°C)(−20.0°C)
Q =
b. Q of gas =−Q of jelly =−(−3.35 × 10
9
J) = 3.35 × 10
9
J
∆U = Q − W
∆U = (3.35 × 10
9
J) − (1.64 × 10
9
J)
∆U = 1.71 × 10
9
J
−3.35 × 10
9
J
Section Two—Problem Workbook Solutions II Ch. 10–3
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
6. P =
∆
Q
t
= 5.9 × 10
9
J/s
∆t = 1.0 s
∆U = 2.6 × 10
9
J
∆U = Q − W = P∆t − W
W = P∆t −∆U
W = (5.9 × 10
9
J/s)(1.0 s) − (2.6 × 10
9
J)
W = 3.3 × 10
9
J
Givens Solutions
5. m = 5.00 × 10
3
kg
v = 40.0 km/h
U
i
= 2.50 × 10
5
J
U
f
= 2U
i
W =
1
2
mv
2
∆U = U
f
− U
i
= Q − W
U
f
= 2U
i
∆U = 2U
i
− U
i
= U
i
Q =∆U + W = U
i
+
1
2
mv
2
Q = (2.50 × 10
5
J) +
1
2
(5.00 × 10
3
kg)
40.0
h
km
36
1
0
h
0s
1
1
0
k
3
m
m
2
Q = (2.50 × 10
5
J) + (3.09 × 10
5
J)
Q = 5.59 × 10
5
J
4. m = 1.64 × 10
15
kg
h = 75.0 m
g = 9.81 m/s
2
T
i
= 6.0°C
T
f
= 100.0°C
c
p,w
= 4186 J/kg
•
°C
L
v
of water = 2.26 × 10
6
J/kg
∆U = (−0.900)(U
i
)
W = mgh = (1.64 × 10
15
kg)(9.81 m/s
2
)(75.0 m)
W = 1.21 × 10
18
J
Q =−mc
p,w
(T
f
− T
i
) − mL
v
=−m[c
p,w
(T
f
− T
i
) + L
v
]
T
f
− T
i
= 100.0°C − 6.0°C = 94.0°C
Q =−(1.64 × 10
15
kg)[(4186 J/kg
•
°C)(94.0°C) + (2.26 × 10
6
J/kg)]
Q =−4.35 × 10
21
J
∆U = U
f
− U
i
= (−0.900)(U
i
) = Q − W
U
f
= (1 − 0.900)U
i
= (0.100)(U
i
)
−∆U = U
i
− U
f
=
0.
U
10
f
0
− U
f
= (0.900)
0.
U
10
f
0
= W − Q
U
f
=
0
0
.
.
1
9
0
0
0
0
(W − Q)
U
f
=
0
0
.
.
1
9
0
0
0
0
[(1.21 × 10
18
J) − (−4.35 × 10
21
J)]
U
f
=
(Note: Nearly all of the energy is used to increase the temperature of the water
and to vaporize the water.)
4.83 × 10
20
J
Holt Physics Solution ManualII Ch. 10–4
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
7. h = 1.00 × 10
2
m
v = 141 km/h
U
i
= 40.0 ΜJ
m = 76.0 kg
a. ∆U = Q − W
All energy is transferred by heat, so W =
b. ∆U = Q =
1
2
mv
2
∆
U
U
i
× 100
=
m
2U
v
2
i
(100)
∆
U
U
i
× 100
=
∆
U
U
i
× 100
= 0.146 percent
(76.0 kg)
141
h
km
2
36
1
0
h
0 s
2
1
1
0
k
3
m
m
2
(100)
(2)(40.0 × 10
6
J)
0 J
Givens Solutions
1. eff = 8 percent = 0.080
Q
h
= 2.50 kJ
eff =
Q
h
Q
−
h
Q
c
= 1 −
Q
Q
h
c
−Q
c
= Q
h
(eff − 1)
Q
c
= Q
h
(1 − eff )
Q
c
= (2.50 kJ)(1 − 0.08) = (2.50 kJ)(0.92)
Q
c
=
W = Q
h
− Q
c
W = 2.50 kJ − 2.3 kJ
W = 0.2 kJ
2.3 kJ
Additional Practice C
2. P
net
= 1.5 MW
eff = 16 percent = 0.16
Q
h
= 2.0 × 10
9
J
eff =
W
Q
n
h
et
=
P
n
Q
et
h
∆t
∆t =
(eff
P
)
n
(
e
Q
t
h
)
∆t =
∆t = 2.1 × 10
2
s
(0.16)(2.0 × 10
9
J)
1.5 × 10
6
W
3. P
net
= 19 kW
eff = 6.0 percent = 0.060
∆t = 1.00 h
W
net
= P
net
∆t
eff =
W
Q
n
h
et
Q
h
=
W
ef
n
f
et
=
P
n
e
e
f
t
f
∆t
Q
h
=
Q
h
= 1.1 × 10
6
kJ = 1.1 × 10
9
J
(19 kW)(1.00 h)
3.6 ×
1h
10
3
s
(0.060)
Section Two—Problem Workbook Solutions II Ch. 10–5
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
4. P
net
= 370 W
∆t = 1.00 min = 60.0 s
eff = 0.19
eff =
W
Q
n
h
et
=
P
n
Q
et
h
∆t
Q
h
=
P
n
e
e
f
t
f
∆t
Q
h
=
Q
h
= 1.2 × 10
5
J = 120 kJ
(370 W)(60.0 s)
0.19
Givens Solutions
5. W
net
= 2.6 MJ
Qh/m = 32.6
M
kg
J
m = 0.80 kg
eff =
W
Q
n
h
et
=
eff =
eff = 0.10 = 10 percent
2.6 MJ
32.6
M
kg
J
(0.80 kg)
W
net
Q
m
h
(m)
6. m = 3.00 × 10
4
kg
g = 9.81 m/s
2
h = 1.60 × 10
2
m
Q
c
= 3.60 × 10
8
J
W
net
= mgh = Q
h
− Q
c
Q
h
= W
net
+ Q
c
eff =
W
Q
n
h
et
=
W
n
W
et
n
+
et
Q
c
=
mg
m
h
g
+
h
Q
c
eff =
eff = 0.12
(3.00 10
4
kg)(9.81 m/s
2
)(1.60 10
2
m)
(3.00 10
4
kg)(9.81 m/s
2
)(1.60 10
2
m) + 3.60 10
8
J
Vibrations and Waves
Problem Workbook Solutions
II
1. m = 0.019 kg
g = 9.81 m/s
2
k = 83 N/m
k =
x
F
=
m
x
g
x =
x = 2.25 × 10
−3
m
(0.019 kg)(9.81 m/s
2
)
83 N/m
Additional Practice A
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. m = 187 kg
k = 1.53 × 10
4
N/m
g = 9.81 m/s
2
k =
x
F
=
m
x
g
x =
(18
1
7
.5
k
3
g
×
)(
1
9
0
.8
4
1
N
m
/m
/s
2
)
= 0.120 m
3. m
1
= 389 kg
x
2
= 1.2 × 10
−3
m
m
2
= 1.5 kg
x
F
1
1
=
F
x
2
2
x
1
=
F
F
1
2
x
2
=
m
m
1
g
2
x
g
2
x
1
==0.31 m
(389 kg)(1.2 × 10
−3
m)
(1.5 kg)
4. m = 18.6 kg
x = 3.7 m
g = 9.81 m/s
2
k =
x
F
=
m
x
g
=
k = 49 N/m
(18.6 kg)(9.81 m/s
2
)
(3.7 m)
5. h = 533 m
x
1
=
1
3
h
m = 70.0 kg
x
2
=
2
3
h
g = 9.81 m/s
2
k =
x
F
=
(x
2
m
−
g
x
1
)
=
3m
h
g
k ==3.87 N/m
3(70.0 kg)(9.81 m/s
2
)
(533 m)
6. k = 2.00 × 10
2
N/m
x = 0.158 m
g = 9.81 m/s
2
a. F = kx = (2.00 × 10
2
N/m)(0.158 m) =
b. m =
F
g
=
k
g
x
m =
m = 3.22 kg
(2.00 × 10
2
N/m)(0.158 m)
(9.81 m/s
2
)
31.6 N
Section Two—Problem Workbook Solutions II Ch. 11–1
Holt Physics Solution ManualII Ch. 11–2
II
7. h = 1.02 × 10
4
m
L = 4.20 × 10
3
m
k = 3.20 × 10
−2
N/m
F = kx = k(h − L)
F = (3.20 × 10
−2
N/m)(6.0 × 10
3
m) = 190 N
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. L = 6.7 m
a
g
= g = 9.81 m/s
2
T = 2π
a
L
g
= 2π
(9
(
.8
6
1
.7
m
m
/
)
s
2
)
= 5.2 s
Additional Practice B
2. L = 0.150 m
a
g
= g = 9.81 m/s
2
T = 2p
a
L
g
= 2p
= 0.777 s
(0.150 m)
(9.81 m/s
2
)
3. x = 0.88 m
a
g
= g = 9.81 m/s
2
T = 2p
4
a
x
g
= 2p
T = 3.8 s
4(0.88 m)
(9.81 m/s
2
)
4. f = 6.4 × 10
−2
Hz
a
g
= g = 9.81 m/s
2
T =
1
f
= 2p
a
L
g
L =
4p
a
2
g
f
2
=
L = 61 m
(9.81 m/s
2
)
4π
2
(6.4 × 10
−2
Hz)
2
5. t = 3.6 × 10
3
s
N = 48 oscillations
a
g
= g = 9.81 m/s
2
T = 2p
a
L
g
=
N
t
L ==
L = 1.4 × 10
3
m
(3.6 × 10
3
s)
2
(9.81 m/s
2
)
4p
2
(48)
2
N
t
2
a
g
4p
2
8. h = 348 m
L = 2.00 × 10
2
m
k = 25.0 N/m
g = 9.81 m/s
2
F = kx = k(h − L) = mg
m ==377 kg
(25.0 N/m)(148 m)
(9.81 m/s
2
)
6. L = 1.00 m
T = 10.5 s
a
g
=
4p
T
2
2
L
==0.358 m/s
2
4p
2
(1.00 m)
(10.5 s)
2
Section Two—Problem Workbook Solutions II Ch. 11–3
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. f
1
= 90.0 Hz
k = 2.50 × 10
2
N/m
T = 2p
m
k
=
3.00 ×
1
10
−2
f
1
m ==
m = 0.869 kg
(2.50 × 10
2
N/m)
4p
2
(3.00 × 10
−2
)
2
(90.0 Hz)
2
k
4p
2
(3.00 × 10
−2
)
2
f
1
2
Additional Practice C
Givens Solutions
2. m
1
= 3.5 × 10
6
kg
f = 0.71 Hz
k = 1.0 × 10
6
N/m
T =
1
f
= 2p
m
1
k
+
m
2
m
2
=
4p
k
2
f
2
− m
1
m
2
=−3.5 × 10
4
kg = 1.5 × 10
4
kg
(1.0 × 10
6
N/m)
4p
2
(0.71 Hz)
2
3. m = 20.0 kg
f =
4
6
2
0
.7
s
= 0.712 Hz
k =
4p
T
2
2
m
= 4p
2
mf
2
k = 4p
2
(20.0 kg)(0.712 Hz)
2
k = 4.00 × 10
2
N/m
4. m = 2.00 × 10
5
kg
T = 1.6 s
T = 2p
m
k
k =
4p
T
2
2
m
==3.1 × 10
6
N/m
4p
2
(2.00 × 10
5
kg)
(1.6 s)
2
5. m = 2662 kg
x = 0.200 m
g = 9.81 m/s
2
T = 2p
m
k
= 2p
m
m
x
g
T = 2p
(
(
9
0
.8
.
2
1
0
m
0
m
/
s
2
)
)
= 0.897 s
1. f = 2.50 × 10
2
Hz
v = 1530 m/s
l =
v
f
=
2.5
1
0
53
×
0
1
m
0
2
/s
Hz
= 6.12 m
Additional Practice D
6. m = 10.2 kg
k = 2.60 × 10
2
N/m
T = 2p
m
k
= 2p
= 1.24 s
(10.2 kg)
(2.60 × 10
2
N/m)
Holt Physics Solution ManualII Ch. 11–4
II
2. f = 123 Hz
v = 334 m/s
l =
v
f
=
(
(
3
1
3
2
4
3
m
H
/
z
s
)
)
= 2.72 m
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
3. l = 2.0 × 10
−2
m
v = 334 m/s
f =
l
v
=
(2.
(
0
33
×
4
1
m
0
−
/
2
s)
m)
= 1.7 × 10
4
Hz
4. l = 2.54 m
v = 334 m/s
f =
l
v
=
(
(
3
2
3
.5
4
4
m
m
/s
)
)
= 131 Hz
5. f = 73.4 Hz
l = 4.50 m
v = fl = (73.4 Hz)(4.50 m) = 3.30 × 10
2
m/s
6. f = 2.80 × 10
5
Hz
l = 5.10 × 10
−3
m
∆x = 3.00 × 10
3
m
v = fl = (2.80 × 10
5
Hz)(5.10 × 10
−3
m)
v =
∆t =
∆
v
x
=
(
(
1
3
.4
.0
3
0
×
×
1
1
0
0
3
3
m
m
/s
)
)
∆t = 2.10 s
1.43 × 10
3
m/s
Sound
Problem Workbook Solutions
II
1. Intensity = 3.0 × 10
−3
W/m
2
r = 4.0 m
Intensity =
4p
P
r
2
P = 4pr
2
(Intensity) = 4p(4.0 m)
2
(3.0 × 10
−3
W/m
2
)
P = 0.60 W
Additional Practice A
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. r = 8.0 × 10
3
m
Intensity = 1.0 × 10
−12
W/m
2
Intensity =
4p
P
r
2
P = 4pr
2
(Intensity)
P = 4p(8.0 × 10
3
m)
2
(1.0 × 10
−12
W/m
2
) = 8.0 × 10
−4
W
3. Intensity = 1.0 × 10
−12
W/m
2
P = 2.0 × 10
−6
W
Intensity =
4p
P
r
2
r =
4p
(I
n
P
te
n
si
ty
)
r =
= 4.0 × 10
2
m
2.0 × 10
−6
W
4p(1.0 × 10
−12
W/m
2
)
4. Intensity = 1.1 × 10
−13
W/m
2
P = 3.0 × 10
−4
W
r
2
=
4p In
P
tensity
r =
=
= 1.5 × 10
4
m
(3.0 × 10
−4
W)
4p(1.1 × 10
−
13
W/m
2
)
P
4p Intensity
5. P = 1.0 × 10
−4
W
r = 2.5 m
Intensity =
4p
P
r
2
Intensity ==1.3 × 10
−6
W/m
2
(1.0 × 10
−4
W)
4p(2.5 m)
2
6. Intensity = 2.5 × 10
−6
W/m
2
r = 2.5 m
P = 4pr
2
(Intensity)
P = 4p(2.5 m)
2
(2.5 × 10
−6
W/m
2
)
P = 2.0 × 10
−4
W
Section Two—Problem Workbook Solutions II Ch. 12–1
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. f
15
= 26.7 Hz
v = 334 m/s
n = 15
L =
4
15
f
1
v
5
=
L = 46.9 m
15(334 m/s)
4(26.7 Hz)
Additional Practice B
Givens Solutions
2. l = 3.47 m
v
s
= 5.00 × 10
2
m/s
n = 3
v
a
= 334 m/s
L =
l
2
v
v
s
a
n
=
L = 7.79 m
(3.47 m)(5.00 × 10
2
m/s)(3)
2(334 m/s)
3. n = 19
L = 86 m
v = 334 m/s
f
19
=
2
n
L
v
=
19
2
(
(
3
8
3
6
4
m
m
)
/s)
f
19
= 37 Hz
4. L = 3.50 × 10
2
m
f
75
= 35.5 Hz
n = 75
f
75
=
7
2
5
L
v
v =
2L
7
f
5
75
=
v = 331 m/s
2(3.50 × 10
2
m)(35.5 Hz)
75
5. L = 4.7 × 10
−3
m
l = 3.76 × 10
−3
m
l
n
=
4
n
L
n =
l
4L
n
==5
4(4.7 × 10
−3
m)
(3.76 × 10
−3
m)
Holt Physics Solution ManualII Ch. 12–2
Light and Reflection
Problem Workbook Solutions
II
1. f = 9.00 × 10
8
Hz
d = 60.0 m
c = 3.00 × 10
8
m/s
c = fl
l
d
==
d
c
f
l
d
=
l
d
= 1.80 × 10
2
wavelengths
(60.0 m)(9.00 × 10
8
Hz)
(3.00 × 10
8
m/s)
d
f
c
Additional Practice A
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. f = 5.20 × 10
14
Hz
d = 2.00 × 10
−4
m
c = 3.00 × 10
8
m/s
c = fl
l
d
==
d
c
f
l
d
=
l
d
= 347 wavelengths
(2.00 × 10
−4
m)(5.20 × 10
14
Hz)
(3.00 × 10
8
m/s)
d
f
c
3. f = 2.40 × 10
10
Hz
c = 3.00 × 10
8
m/s
c = fl
l =
c
f
l =
l = 1.25 × 10
−2
m = 1.25 cm
(3.00 × 10
8
m/s)
(2.40 × 10
10
Hz)
4. l = 1.2 × 10
−6
m
c = 3.00 × 10
8
m/s
c = fl
f =
l
c
f =
f = 2.5 × 10
14
Hz = 250 TH
(3.00 × 10
8
m/s)
(1.2 × 10
−6
m)
Section Two—Problem Workbook Solutions II Ch. 13–1
Holt Physics Solution ManualII Ch. 13–2
II
5. l
1
= 2.0 × 10
−3
m
l
2
= 5.0 × 10
−3
m
c = 3.00 × 10
8
m/s
c = fl
f
1
=
l
c
1
=
f
1
= 1.5 × 10
11
Hz = 15 × 10
10
Hz
f
2
=
l
c
2
=
f
2
= 6.0 × 10
10
Hz
6.0 × 10
10
Hz < f < 15 × 10
10
Hz
(3.00 × 10
8
m/s)
(5.0 × 10
−3
m)
(3.00 × 10
8
m/s)
(2.0 × 10
−3
m)
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
6. f = 10.0 Hz
c = 3.00 × 10
8
m/s
c = fl
l =
c
f
l =
l = 3.00 × 10
7
m = 3.00 × 10
4
km
(3.00 × 10
8
m/s)
(10.0 Hz)
1. p = 3.70 × 10
5
m
f = 2.50 × 10
5
m
q
1
=
1
f
−
p
1
q
1
=
(2.50 ×
1
10
5
m)
−
(3.70 ×
1
10
5
m)
=
(4.00
1
×
m
10
−6
)
−
(2.70
1
×
m
10
−6
)
q =
1.30
1
×
m
10
−6
−1
= 7.69 × 10
5
m =
M =−
p
q
=
−
3
7
.7
.6
0
9
×
×
1
1
0
0
5
5
m
m
M =−2.08
769 km
Additional Practice B
2. h = 8.00 × 10
−5
m
f = 2.50 × 10
−2
m
q =−5.9 × 10
−1
m
p
1
+
1
q
=
1
f
p
1
=
1
f
−
1
q
p
1
=
(2.50 ×
1
10
−2
m)
−
(−5.9 ×
1
10
−1
m)
=
4
1
0
m
.0
−
1
1
.6
m
9
=
4
1
1
m
.7
p =
M =
h
h
=−
p
q
=−
(
(
−
2.
5
4
.
0
9
×
×
1
1
0
0
−
−
2
1
m
m
)
)
= 24.6
2.40 × 10
−2
m
II
3. h =−28.0 m
h = 7.00 m
f = 30.0 m
Image is real, so q > 0 and
h < 0.
M =−
p
q
=
h
h
q =−
p
h
h
p
1
+
q
1
=
1
f
p
1
+=
1
f
p
1
1 −
h
h
=
1
f
p = f
1 −
h
h
p = (30.0 m)
1 +
7
2
.
8
0
.
0
0
m
m
p = 37.5 m
1
−p
h
h
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section Two—Problem Workbook Solutions II Ch. 13–3
4. h = 67.4 m
h = 1.69 m
R = 12.0 m
(h > 0, q < 0)
M =−
p
q
=
h
h
q =−
p
h
h
p
1
+
q
1
=
R
2
p
1
+=
R
2
p
1
1 −
h
h
=
R
2
p =
R
2
1 −
h
h
p =
(12.
2
0m)
1 −
1
6
.
7
6
.
9
4
m
m
= (6.00 m)(0.975)
p =
Image is virtual and therefore upright.
5.85 m
1
−p
h
h
II
5. h = 32 m
f = 120 m
p = 180 m
p
1
+
q
1
=
1
f
q
1
=
1
f
−
p
1
q
1
=
(120
1
m)
−
(180
1
m)
=
0.
1
00
m
83
−
0.
1
00
m
56
=
0.
1
00
m
27
q =
M =
h
h
=−
p
q
h =−
q
p
h
h =
−(37
(
0
18
m
0
)
m
(3
)
2m)
h =
The image is inverted (h < 1)
and real (q > 0)
−66 m
3.7 × 10
2
m
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualII Ch. 13–4
6. h = 0.500 m
R = 0.500 m
p = 1.000 m
q
1
=
R
2
−
p
1
q
1
=
(0.50
2
0m)
−
(1.00
1
0m)
=
4
1
.0
m
0
−
1
1
.0
m
00
=
3
1
.0
m
0
q =
M =−
p
q
=
h
h
h =−
q
p
h
=
h =
The image is real (q > 0).
−0.166 m =−166 mm
−(0.333 m)(0.500 m)
(1.000 m)
0.333 m = 333 mm
II
7. p = 1.00 × 10
5
m
h = 1.00 m
h =−4.00 × 10
−6
m
(h < 0 because image is
inverted)
M =−
p
q
=
h
h
q =−
p
h
h
p
1
+
q
1
=
R
2
R ==
R ==
(
(
1
2.
+
00
2.
×
50
10
×
5
1
m
0
5
)
)
R = 0.800 m = 80.0 cm
2(1.00 × 10
5
m)
1 +
(4.0
(
0
1.
×
00
10
m
−6
)
m)
2p
1 −
h
h
2
p
1
−
p
h
h
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section Two—Problem Workbook Solutions II Ch. 13–5
8. h = 10.0 m
p = 18.0 m
h =−24.0 m
Image is real, so q > 0, and
h must be negative.
M =−
p
q
=
h
h
q =−
h
h
p
p
1
+
q
1
=
R
2
R ==
R ==
(1
3
+
6.
0
0
.4
m
17)
=
(
(
3
1
6
.
.
4
0
1
m
7)
)
R = 25.4 m
2(18.0 m)
1 +
1
2
0
4
.
.
0
0
m
m
2p
1 −
h
h
2
p
1
−
p
h
h
Holt Physics Solution ManualII Ch. 13–6
2. p = 553 m
R =−1.20 × 10
2
m
p
1
+
q
1
=
R
2
q
1
=
R
2
−
p
1
q
1
=
(−1.20 ×
2
10
2
m)
−
(553
1
m)
=−
0.
1
01
m
67
−
0.0
1
0
m
181
=−
0.
1
01
m
85
q =−54.1 m
M =−
p
q
=
−(
(
−
5
5
5
4
3
.1
m
m
)
)
M = 9.78 × 10
−2
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. R =−6.40 × 10
6
m
p = 3.84 × 10
8
m
h = 3.475 × 10
6
m
p
1
+
q
1
=
R
2
q
1
=
R
2
−
p
1
q
1
=
(−6.40 ×
2
10
6
m)
−
(3.84 ×
1
10
8
m)
=−
(3.13
1
×
m
10
−7
)
−
(2.60
1
×
m
10
−9
)
q =−
3.16
1
×
m
10
−7
−1
=−3.16 × 10
6
m =−3.16 × 10
3
km
M =−
p
q
=
h
h
h =−
q
p
h
h =
h = 2.86 × 10
4
m = 28.6 km
−(−3.16 × 10
6
m)(3.475 × 10
6
m)
(3.84 × 10
8
m)
Additional Practice C
Givens Solutions
3. R =−35.0 × 10
3
m
p = 1.00 × 10
5
m
p
1
+
q
1
=
R
2
q
1
=
R
2
−
p
1
q
1
=
(−35.0 ×
2
10
3
m)
−
(1.00 ×
1
10
5
m)
=−
(5.71
1
×
m
10
−5
)
−
(1.00
1
×
m
10
−5
)
q =−
6.71
1
×
m
10
−5
−1
=−1.49 × 10
4
m =−14.9 km
Section Two—Problem Workbook Solutions II Ch. 13–7
II
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
4. h = 1.4 × 10
6
m
h = 11.0 m
R =−5.50 m
M =
h
h
M =
(1.4
11
×
.0
10
m
6
m)
M =
q =−pM
p
1
+
q
1
=
R
2
p
1
1 −
M
1
=
R
2
p =
R
2
1 −
M
1
p =
−5.5
2
0m
7.9
1
×
−
1
1
0
−
6
p = 3.5 × 10
5
m = 3.5 × 10
2
km
Scale is 7.9 × 10
−6
:1
7.9 × 10
−6
5. scale factor = 1:1400
f =−20.0 × 10
−3
m
M =
14
1
00
M =−
p
q
q =−Mp
p
1
+
q
1
=
1
f
p
1
1 −
M
1
=
1
f
p = f
1 −
M
1
p = (−20.0 × 10
−3
m)(1 − 1400)
p = 28 m
Holt Physics Solution ManualII Ch. 13–8
7. h = 4.78 × 10
−3
m
h = 12.8 × 10
−2
m
f =−64.0 × 10
−2
m
M =−
p
q
=
h
h
p =−
q
h
h
p
1
+
q
1
=
1
f
+
q
1
=
1
f
q
1
−
h
h
+ 1
=
1
f
q = f
1 −
h
h
q = (−64.0 × 10
−2
m)
1 −
4
1
.
2
7
.
8
8
×
×
1
1
0
0
−
−
3
2
m
m
= (−64.0 × 10
−2
m)(0.963)
q =−61.6 × 10
−2
m =−61.6 cm
1
−
h
q
h
II
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
6. h = 1.38 m
p = 6.00 m
h = 9.00 × 10
−3
m
M =−
p
q
=
h
h
q =−
p
h
h
p
1
+
q
1
=
R
2
p
1
−
p
h
h
=
R
2
R =
R ==
(1
12
−
.0
15
m
3)
R =−7.89 × 10
−2
m =−7.89 cm
2(6.00 m)
1 −
9.00
1.
×
38
10
m
−3
m
2p
1 −
h
h
II
8. h = 0.280 m
h = 2.00 × 10
−3
m
q =−50.0 × 10
−2
m
M =
h
h
=−
p
q
p =−
q
h
h
p
1
+
q
1
=
1
f
+
q
1
=
1
f
q
1
−
h
h
+ 1
=
1
f
f =
f ==
(−50.
(
0
0.
×
99
1
3
0
)
−2
m)
f =−50.4 × 10
−2
m =−50.4 cm
(−50.0 × 10
−2
m)
1 −
(2.0
(0
0
.2
×
8
1
0
0
m
−3
)
m)
q
1 −
h
h
1
−
h
q
h
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section Two—Problem Workbook Solutions II Ch. 13–9
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section Two—Problem Workbook Solutions II Ch. 14–1
1. q
i
= 72°
θ
r
= 34°
n
i
= 1.00
n
r
= n
i
s
s
i
i
n
n
θ
θ
r
i
= (1.00)
(
(
s
s
i
i
n
n
7
3
2
4
°
°
)
)
= 1.7
Additional Practice A
Givens Solutions
2.
θ
i
= 47.9°
θ
r
= 29.0°
n
i
= 1.00
n
r
= n
i
s
s
i
i
n
n
θ
θ
r
i
= (1.00)
(
(
s
s
i
i
n
n
4
2
7
9
.
.
9
0
°
°
)
)
= 1.53
3.
θ
r
= 17°
n
i
= 1.5
n
r
= 1.33
θ
r
= 15°
n
r
= 1.5
n
i
= 1.00
glass to water:
θ
i
= sin
−1
n
n
r
i
(sin
θ
r
)
= sin
−1
1
1
.3
.5
3
(sin 17°)
=
air to glass:
θ
i
= sin
−1
n
n
r
i
(sin
θ
r
)
= sin
−1
1
1
.
.
0
5
0
(sin 15°)
= 23°
15°
4.
θ
i
= 55.0°
θ
r
= 53.8°
n
r
= 1.33
n
i
= n
r
(
(
s
s
i
i
n
n
θ
θ
r
i
)
)
= 1.33
(
(
s
s
i
i
n
n
5
5
3
5
.
.
8
0
°
°
)
)
= 1.31
5.
θ
i
= 48°
n
i
= 1.00
n
r
= 1.5
θ
i
= 3.0 × 10
1
°
n
i
= 1.5
n
r
= 1.6
θ
i
= 28°
n
i
= 1.6
n
r
= 1.7
air to glass 1:
θ
r
= sin
−1
n
n
r
i
(sin
θ
i
)
= sin
−1
1
1
.0
.5
0
(sin 48°)
=
glass 1 to glass 2:
θ
r
= sin
−1
n
n
r
i
(sin
θ
i
)
= sin
−1
1
1
.
.
5
6
(sin 3.0°)
=
glass 2 to glass 3:
θ
r
= sin
−1
n
n
r
i
(sin
θ
i
)
= sin
−1
1
1
.
.
6
7
(sin 28°)
= 26°
28°
3.0 × 10
1
°
Refraction
Problem Workbook Solutions
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualII Ch. 14–2
1. f = 8.45 m
q =−25 m
Additional Practice B
Givens Solutions
2. h = 1.50 m
q =−6.00 m
f =−8.58 m
p
1
=
1
f
−
1
q
=
−8.5
1
8m
−
−6.0
1
0m
p
1
=
−0
1
.1
m
17
+
0
1
.1
m
67
=
0
1
.0
m
50
p =
h =
−h
q
′p
= −
(1.5
(
0
−
m
6.0
)(
0
2
m
0.0
)
m)
= 5.00 m
20.0 m
3. h = 7.60 × 10
−2
m
h = 4.00 × 10
−2
m
f =−14.0 × 10
−2
m
M =
h
h
=−
p
q
q =−
p
h
h
p
1
+
q
1
=
1
f
p
1
+=
−
f
1
p
1
1 −
h
h
=
1
f
p = f
1 −
h
h
p = (−14.0 × 10
−2
m)
1 −
7
4
.
.
6
0
0
0
×
×
1
1
0
0
−
−
2
2
m
m
= (−14.0 × 10
−2
m)(0.90)
p =
q =−
p
h
h
=−
q =−6.84 × 10
−2
m =−6.84 cm
(1.3 × 10
−1
m)(4.00 × 10
−2
m)
(7.60 × 10
−2
m)
1.30 × 10
−1
m = 13.0 cm
1
−p
h
h′
p
1
+
q
1
=
1
f
p
1
=
1
f
−
q
1
p
1
=
(8.4
1
5m)
−
(−
1
25)
=
0
1
.1
m
18
+
0
1
.0
m
40
=
0
1
.1
m
58
p = 6.3 m
M =−
p
q
=
−(
6
−
.
2
3
5
m
m)
M = 4.0
Section Two—Problem Workbook Solutions II Ch. 14–3
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
4. h = 28.0 m
h = 3.50 m
f =−10.0 m
M =
h
h
=−
p
q
q =−
h
h
p
p
1
+
q
1
=
1
f
p
1
+=
1
f
p
1
1 −
h
h
=
1
f
p = f
1 −
h
h
p = (−10.0 m)
1 −
2
3
8
.5
.0
0
m
m
p = 70.0 m
1
−h
h
p
Givens Solutions
5. h = 1.40 cm
q =−19.0 cm
f = 20.0 cm
p
1
=
1
f
−
q
1
=
−20.
1
0cm
−
−19.
1
0cm
p
1
=
−0
1
.0
cm
500
+
0
1
.0
c
5
m
26
=
2.6
1
0
c
×
m
10
3
p = 385 cm =
h =−
p
q
h
=−
(385
(−
cm
19
)
.
(
0
1
c
.4
m
0
)
cm)
= 28.4 cm
3.85 m
6. h = 1.3 × 10
−3
m
h = 5.2 × 10
−3
m
f = 6.0 × 10
−2
m
M =
h
h
=−
p
q
q =−
p
h
h
p
1
+
q
1
=
1
f
p
1
+=
1
f
p
1
1 −
h
h
=
1
f
p = f
1 −
h
h
p = (6.0 × 10
−2
m)
1 −
(
(
1
5
.
.
3
2
×
×
1
1
0
0
−
−
3
3
m
m
)
)
p =
q =−
p
h
h
=
q =−0.18 m =−18 cm
−(4.5 × 10
−2
m)(5.2 × 10
−3
m)
(1.3 × 10
−3
m)
4.5 × 10
−2
m = 4.5 cm
1
−
p
h
h
Holt Physics Solution ManualII Ch. 14–4
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
7. f = 26.7 × 10
−2
m
p = 3.00 m
Image is real, so h< 0.
p
1
+
q
1
=
1
f
q
1
=
1
f
−
p
1
q
1
=
(26.7 ×
1
10
−2
m)
−
(3.0
1
0m)
=
3
1
.7
m
5
−
0
1
3
m
33
=
3
1
.4
m
2
q =
M =−
p
q
M =−
(
(
0
3
.2
.0
9
0
2
m
m
)
)
M =−9.73 × 10
−2
0.292 m = 29.2 cm
Givens Solutions
8. h = 2.25 m
p = 12.0 m
f =−5.68 m
9. h = 0.108 m
p = 4h = 0.432 m
f =−0.216 m
p
1
+
q
1
=
1
f
1
q
=
1
f
−
p
1
q
1
=
(−0.2
1
16 m)
−
(0.43
1
2m)
= −
4
1
.6
m
3
−
2
1
.3
m
1
= −
6
1
.9
m
4
q =
h
h
=−
p
q
h =−
q
p
h
h =
h = 0.0360 m = 36.0 mm
− (−0.144 m)(0.108 m)
(0.432 m)
− 0.144 m =−144 mm
1
q
=
1
f
−
p
1
=
−5.6
1
8m
−
12.
1
0m
1
q
=
−0
1
.1
m
76
−
0
1
.0
m
83
=
−0
1
.2
m
59
q =
h =−
h
q
′p
= −
(2.25
−
m
3.8
)(
6
1
m
2.0 m)
= 6.99 m
−3.86 m
Section Two—Problem Workbook Solutions II Ch. 14–5
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
10. p = 117 × 10
−3
m
M = 2.4
M =−
p
q
q =−pM =−(117 × 10
−3
m)(2.4)
q =− 0.28 m
p
1
+
q
1
=
1
f
1
f
=
(117 ×
1
10
−3
m)
−
(0.2
1
8m)
=
8
1
.5
m
5
−
1
3.
m
6
=
1
5.
m
0
f = 0.20 m = 2.0 × 10
2
mm
Givens Solutions
11. Image is real, and therefore
inverted.
h
h
= M =−64
q = 12 m
p =−
M
q
p
1
+
q
1
=
1
f
−
M
q
+
q
1
=
1
f
f =
(1 −
q
M)
f =
[1
(
−
12
(−
m
6
)
4)]
f = Image is inverted0.18 m = 18 cm
12. h =−0.55 m
h = 2.72 m
p = 5.0 m
−
p
q
=
h
h
q =−
p
h
h
p
1
+
q
1
=
1
f
1
f
=
p
1
−
p
h
h
1
f
=
p
1
1 −
h
h
f =
f ==
5.
5
0
.9
m
f = 0.85 m
5.0 m
1 −
(
(
−
2
0
.7
.5
2
5
m
m
)
)
p
1 −
h
h
Holt Physics Solution ManualII Ch. 14–6
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
13. p = 12.0 × 10
−2
m
M = 3.0
M =−
p
q
q =− Mp
p
1
+
q
1
=
1
f
p
1
−
M
1
p
=
1
f
p
1
1 −
M
1
=
1
f
f =
f =
f = 1.8 × 10
−1
m = 18 cm
(12.0 × 10
−2
m)
1 −
3
1
.0
p
1 −
M
1
14. h = 7.60 × 10
−2
m
p = 16.0 × 10
−2
m
f =−12.0 × 10
−2
m
p
1
+
q
1
=
1
f
M =−
p
q
=
h
h
q =−
p
h
h
p
1
+=
1
f
p
1
1 −
h
h
=
1
f
1 −
h
h
=
p
f
h
h
= 1 −
p
f
h =
h ==
(7.60
(
×
2.3
1
3
0
)
−2
m)
h = 3.26 × 10
−2
m = 3.26 cm
(7.60 × 10
−2
m)
1 −
(
(
−
1
1
6
2
.0
.0
×
×
1
1
0
0
−
−
2
2
m
m
)
)
h
1 −
p
f
1
−p
h
h
Section Two—Problem Workbook Solutions II Ch. 14–7
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
15. h = 48 m
f = 1.1 × 10
−1
m
p = 120 m
p
1
+
q
1
=
1
f
q
1
=
1
f
−
p
1
q
1
=
(1.1 × 1
1
0
−1
m)
−
(120
1
m)
=
1
9.
m
1
−
(8.3
1
×
m
10
−3
)
=
1
9.
m
1
q = 1.1 × 10
−1
m
M =
h
h
=−
p
q
h =−
q
p
h
h =
h = 4.4 × 10
−2
m =−4.4 cm
−(1.1 × 10
−1
m)(48 m)
(120 m)
Givens Solutions
16. f =−0.80 m
h = 0.50 × 10
−3
m
h = 0.280 m
M =
h
h
=−
p
q
q =−
p
h
h
p
1
+
q
1
=
1
f
p
1
+=
1
f
p
1
1 −
h
h
=
1
f
p = f
1 −
h
h
p = (− 0.80 m)
1 −
(0.5
(0
0
.2
×
8
1
0
0
m
−3
)
m)
p =
q =−
p
h
h
=
q =−0.80 m
−(4.5 × 10
2
m)(0.50 × 10
−3
m)
(0.280 m)
4.5 × 10
2
m
1
−p
h
h
1.
θ
c
= 46°
n
i
= 1.5
n
r
= n
i
sin
θ
c
= (1.5)(sin 46°) = 1.1
Additional Practice C
Holt Physics Solution ManualII Ch. 14–8
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. n
i
= 1.00
q
i
= 75.0°
q
r
= 23.3°
n
i
= 2.44
n
r
= 1.00
n
r
= n
i
(
(
s
s
i
i
n
n
θ
θ
r
i
)
)
= (1.00)
(
(
s
s
i
i
n
n
7
2
5
3
.
.
0
3
°
°
)
)
= 2.44
θ
c
= sin = −1
n
n
r
i
θ
c
= sin
−1
1
2
.
.
0
4
0
4
= 24.2°
Givens Solutions
3.
θ
c
= 42.1°
n
r
= 1.00
n
i
=
sin
n
r
θ
c
=
sin
1.
4
0
2
0
.1°
= 1.49
4. n
i
= 1.56
n
r
= 1.333
sin q
c
=
n
n
i
r
θ
c
= sin
−1
n
n
r
i
= sin
−1
1
1
.3
.5
3
6
3
= 58.7°
5. n
i
= 1.52
h = 0.025 mm
n
r
= 1.00
θ
c
= sin
−1
n
n
r
i
= sin
−1
1
1
.
.
0
5
0
2
=
∆x = h(tan q
c
) where tan q
c
=
n
n
r
i
∆x = h
n
n
r
i
= (0.025 mm)
1
1
.
.
0
5
0
2
= 0.0160 mm
d = 2∆x = 2(0.0160 mm) = 0.0320 mm
41.1°
Section Two — Problem Workbook Solutions II Ch. 15–1
Interference and
Diffraction
Problem Workbook Solutions
II
HRW material copyrighted under notice appearing earlier in this book.
Additional Practice A
Givens Solutions
1. d = 1.20 × 10
−6
m
l = 156.1 × 10
−9
m
m = 5; constructive
interference
For constructive interference,
d sin q = ml
sin q =
m
d
l
q = sin
−1
m
d
l
q = sin
−1
(5
(
)
1
(1
.2
5
0
6.
×
1
1
×
0
1
−
0
6
−
m
9
)
m)
q = 40.6°
2. d = 6.00 × 10
−6
m
l = 6.33 × 10
−7
m
m = 0; destructive
interference
For destructive interference,
d sin q =
m +
1
2
l
sin q =
q = sin
−1
q = sin
−1
q = 3.02°
0 +
1
2
(6.33 × 10
−7
m)
(6.00 × 10
−6
m
m +
1
2
l
d
m +
1
2
l
d
3. d = 0.80 × 10
−3
m
m = 3; destructive
interference
q = 1.6°
For destructive interference,
d sin q =
m +
1
2
l
l =
l =
l = 6.4 × 10
−6
m = 6.4 mm
(0.80 × 10
−3
m)(sin 1.6°)
3 +
1
2
d sin q
m +
1
2
Holt Physics Solution ManualII Ch. 15–2
4. d = 15.0 × 10
−6
m
m = 2; constructive
interference
q = 19.5°
For constructive interference,
d sin q = ml
l =
d s
m
in q
l =
l = 2.50 × 10
−6
m = 2.50 mm
(15.0 × 10
−6
m)[sin(19.5°)]
2
6. f = 60.0 × 10
3
Hz
c = 3.00 × 10
8
m/s
m = 4; constructive
interference
q = 52.0°
For constructive interference,
d sin q = ml =
m
f
c
d =
f s
m
in
c
q
d =
d = 2.54 × 10
4
m = 25.4 km
(4)(3.00 × 10
8
m/s)
(60.0 × 10
3
Hz)(sin 52.0°)
7. f = 137 × 10
6
Hz
c = 3.00 × 10
8
m/s
m = 2; constructive
interference
q = 60.0°
For constructive interference,
d sin q = ml =
m
f
c
d =
f s
m
in
c
q
d =
d = 5.06 m
(2)(3.00 × 10
8
m/s)
(137 × 10
6
Hz)(sin 60.0°)
m
max
=
d(sin
l
90.0°)
=
l
d
=
d
c
f
m
max
==2.31
The second-order maximum (m = 2) is the highest observable with this apparatus.
(5.06 m)(137 × 10
6
Hz)
(3.00 × 10
8
m/s)
Givens Solutions
5. l = 443 × 10
−9
m
m = 4; destructive
interference
q = 2.27°
For destructive interference,
d sin q =
m +
1
2
l
d =
d =
d = 5.03 × 10
−5
m
4 +
1
2
(443 × 10
−9
m)
(sin 2.27°)
m +
1
2
l
sin q
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section Two — Problem Workbook Solutions II Ch. 15–3
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
4. l = 40.0 × 10
−9
m
d = 150.0 × 10
−9
m
m = 2
d(sin q) = ml
q = sin
−1
m
d
l
q = sin
−1
q = 32.2°
2(40.0 × 10
−9
m)
(150.0 × 10
−9
m)
Additional Practice B
Givens Solutions
1. d =
1.00 × 10
1
2
lines/m
m = 1
q = 30.0°
c = 3.00 × 10
8
m/s
d(sin q) = ml
l =
d(si
m
n q)
l =
l =
f =
l
c
=
(
(
3
5
.
.
0
0
0
0
×
×
1
1
0
0
8
−3
m
m
/s
)
)
f = 6.00 × 10
10
Hz = 60.0 Ghz
5.00 × 10
−3
m = 5.00 mm
[sin(30.0°)]
(1.00 × 10
2
lines/m)(1)
3. l = 714 × 10
−9
m
m = 3
q = 12.0°
d(sin q) = ml
d =
(s
m
in
l
q)
d =
(3)
[
(
s
7
i
1
n
4
(
×
12
1
.0
0
°
−
)
9
]
m)
d =
or
9.71 × 10
4
lines/m
1.03 × 10
−5
m between lines
2. d = 2.0 × 10
−8
m
m = 3
q = 12°
d(sin q) = ml
l =
d(si
m
n q)
l =
l = 1.4 × 10
−9
m = 1.4 nm
(2.0 × 10
−8
m)[sin(12°)]
3
Holt Physics Solution ManualII Ch. 15–4
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
6. l = 2.2 × 10
−6
m
d =
6.4 × 10
1
4
lines/m
q = 34.0°
d(sin q) = ml
m =
d(si
l
n q)
m ==4.0
m = 4.0
[sin (34.0°)]
(6.4 × 10
4
lines/m)(2.2 × 10
−6
m)
5. f = 1.612 × 10
9
Hz
c = 3.00 × 10
8
m/s
d = 45.0 × 10
−2
m
m = 1
d(sin q) = ml =
m
f
c
q = sin
−1
m
df
c
q = sin
−1
q = 24.4°
(1)(3.00 × 10
8
m/s)
(45.0 × 10
−2
m)(1.612 × 10
9
Hz)
Givens Solutions
7. d =
25 × 10
4
1
lines/m
l = 7.5 × 10
−7
m
q = 48.6°
d(sin q) = ml
m =
d(si
l
n q)
m ==4.0
m = 4.0
[sin(48.6°)]
(25 × 10
4
lines/m)(7.5 × 10
−7
m)
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section Two—Problem Workbook Solutions II Ch. 16–1
1. q
1
= 0.085 C
r = 2.00 × 10
3
m
F
electric
= 8.64 × 10
−8
N
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
F
electric
= k
C
q
r
1
q
2
2
q
2
=
F
el
k
e
C
ctr
q
ic
1
r
2
q
2
==4.5 × 10
−10
C
(8.64 × 10
−8
N)(2.00 × 10
3
m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(0.085 C)
Additional Practice A
Givens Solutions
2. q
1
= q
q
2
= 3q
F
electric
= 2.4 × 10
−6
N
r = 3.39 m
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
F = k
C
q
r
1
q
2
2
= k
C
3
r
q
2
2
q =
3
F
k
r
C
2
=
q = 3.2 × 10
−8
C
(2.4 × 10
−6
N)(3.39 m)
2
(3)(8.99 × 10
9
N
•
m
2
/C
2
)
3. F
electric
= 1.0 N
r = 2.4 × 10
22
m
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
F = k
C
N
2
r
(q
2
e
)
2
q
e
=
F
k
r
C
2
= r
k
F
C
q
e
= (2.4 × 10
22
m)
q
e
= 2.5 × 10
17
C
1.0 N
8.99 × 10
9
N
•
m
2
/C
2
4. r = 1034 m
q
1
= 2.0 × 10
−9
C
q
2
=−2.8 × 10
−9
C
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
r
2
= 2r
F
electric
= k
C
q
r
1
q
2
2
=
F
electric
=
r
2
= 2r = (2)(1034 m) = 2068 m
q =
F
el
ec
k
t
C
ri
c
r
2
2
=
q = 4.7 × 10
−9
C
(4.7 × 10
−14
N)(2068 m)
2
8.99 × 10
9
N
•
m
2
/C
2
4.7 × 10
−14
N
(8.99 × 10
9
N
•
m
2
/C
2
)(2.0 × 10
−9
C)(2.8 × 10
−9
C)
(1034 m)
2
5. q
1
= 1.0 × 10
5
C
q
2
=−1.0 × 10
5
C
r = 7.0 × 10
11
m
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
F = k
C
q
r
1
q
2
2
F = (8.99 × 10
9
N
•
m
2
/C
2
)
(
(
7
1
.0
.0
×
×
1
1
0
0
1
5
1
C
m
)
)
2
2
F = 1.8 × 10
−4
N
Electric Forces
and Fields
Problem Workbook Solutions
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualII Ch. 16–2
6. N = 2 000 744
q
p
= 1.60 × 10
−19
C
r = 1.00 × 10
3
m
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
q =
N
2
q
p
==
F
electric
= k
C
q
r
2
2
F
electric
= (8.99 × 10
9
N
•
m
2
/C
2
)
(
(
1
1
.6
.0
0
0
×
×
1
1
0
0
−
3
13
m
C
)
)
2
2
F
electric
= 2.30 × 10
−22
N
1.60 × 10
−13
C
(2 000 744)(1.60 × 10
−19
C)
2
Givens Solutions
7. N
1
= 4.00 × 10
3
N
2
= 3.20 × 10
5
q = 1.60 × 10
−19
C
r = 1.00 × 10
3
m
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
8. F
electric
= 2.0 × 10
−28
N
N = 111
q
p
= 1.60 × 10
−19
C
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
9. q = 1.00 C
F
electric
= 4.48 m × 10
4
N
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
r =
k
C
F
el
q
ec
2
tr
ic
=
= 448 m
(8.99 × 10
9
N
•
m
2
/C
2
)(1.0 C)
2
4.48 × 10
4
N
10. F
electric
= 1.18 × 10
−11
N
q
1
= 5.00 × 10
−9
C
q
2
=−2.50 × 10
−9
C
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
F
electric
= k
C
q
r
1
q
2
2
r =
F
k
el
C
ec
q
t
2
r
ic
=
r =
L = r cos q = (97.6 m)cos 45°= 69.0 m
97.6 m
(8.99 × 10
9
N
•
m
2
/C
2
)(5.00 × 10
−9
C)(2.50 × 10
−9
C)
1.18 × 10
−11
N
F
electric
=
k
C
r
q
2
1
q
2
=
k
C
N
r
1
N
2
2
q
2
F
electric
=
F
electric
=
F
electric
= k
C
N
2
r
2
2
q
2
=
F
electric
= 2.36 × 10
−23
N
(8.99 × 10
9
N
•
m
2
/C
2
)(3.20 × 10
5
)
2
(1.60 × 10
−19
C)
2
(1.00 × 10
3
m)
2
2.95 × 10
−25
N
(8.99 × 10
9
N
•
m
2
/C
2
)(4.00 × 10
3
)(3.20 × 10
5
)(1.60 × 10
−19
C)
2
(1.00 × 10
3
m)
2
F
electric
= k
C
q
r
2
2
= k
C
N
r
2
q
2
p
2
r =
k
F
C
e
N
le
c
2
t
q
ri
p
c
2
=
r = 1.2 × 10
2
m
(8.99 × 10
9
N
•
m
2
/C
2
)(111)
2
(1.60 × 10
−19
C)
2
2.0 × 10
−28
N
Section Two—Problem Workbook Solutions II Ch. 16–3
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. q
1
= 2.0 × 10
−9
C
q
2
= 3.0 × 10
−9
C
q
3
= 4.0 × 10
−9
C
q
4
= 5.5 × 10
−9
C
r
1,2
= 5.00 × 10
2
m
r
1,3
= 1.00 × 10
3
m
r
1,4
= 1.747 × 10
3
m
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
3. w = 7.00 × 10
−2
m
L = 2.48 × 10
−1
m
q = 1.0 × 10
−9
C
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
F = k
C
q
r
1
q
2
2
F
x
= F
1
+ F
2
(cos q) = F
1
+ F
2
F
x
= k
C
q
2
L
1
2
+
(w
2
+
L
L
2
)
3/2
F
x
= k
C
q
2
(2.48 × 1
1
0
−1
m)
2
+
F
x
= (8.99 × 10
9
N
•
m
2
/C
2
)(1.0 × 10
−9
C)
2
(30.8/m
2
) = 2.8 × 10
−7
N
F
y
= F
3
+ F
2
(sin q) = F
3
+ F
2
F
y
= k
C
q
2
w
1
2
+
(w
2
+
w
L
2
)
3/2
F
y
= k
C
q
2
(7.00 × 1
1
0
−2
m)
2
+
F
y
= (8.99 × 10
9
N
•
m
2
/C
2
)(1.0 × 10
−9
C)
2
(2.00 × 10
2
/m
2
) = 1.8 × 10
−6
N
F
net
=
F
x
2
+
F
y
2
=
(2
.8
×
1
0
−
7
N
)
2
+
(
1.
8
×
1
0
−
6
N
)
2
F
net
= 1.8 × 10
−6
N
q = tan
−1
F
F
x
y
= tan
−1
1
2
.
.
8
8
×
×
1
1
0
0
−
−
6
7
N
N
= 81°
F
net
= 1.8 × 10
−6
N, 81° above the positive x-axis
7.00 × 10
−2
m
[(7.00 × 10
−2
m)
2
+ (2.48 × 10
−1
m)
2
]
3/2
w
w
2
+
L
2
2.48 × 10
−1
m
[(7.00 × 10
−2
m)
2
+ (2.48 × 10
−1
m)
2
]
3/2
L
w
2
+
L
2
1. q
1
= 2.80 × 10
−3
C
q
2
=−6.40 × 10
−3
C
q
3
= 4.80 × 10
−2
C
r
1,3
= 9740 m
r
1,2
= 892 m
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
F = k
C
q
r
1
q
2
2
F
1,2
==2.02 × 10
−1
N
F
1,3
==1.27 × 10
−2
N
F
1,tot
= F
1,2
+ F
1,3
=−(2.02 × 10
−1
N) + (1.27 × 10
−2
N) =−0.189 N
F
1,tot
= 0.189 N downward
(8.99 × 10
9
N
•
m
2
/C
2
)(2.80 × 10
−3
C)(4.80 × 10
−2
C)
(9740 m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(2.80 × 10
−3
C)(6.40 × 10
−3
C)
(892 m)
2
Additional Practice B
Givens Solutions
F = k
C
q
r
1
q
2
2
F
1,2
==2.2 × 10
−13
N
F
1,3
==7.2 × 10
−14
N
F
1,4
==3.2 × 10
−14
N
F
1,tot
= F
1,2
+ F
1,3
+ F
1,4
= (2.2 × 10
−13
N) + (7.2 × 10
−14
N) + (3.2 × 10
−14
N)
F
1,tot
= 3.2 × 10
−13
N down the rope
(8.99 × 10
9
N
•
m
2
/C
2
)(2.0 × 10
−9
C)(5.5 × 10
−9
C)
(1.747 × 10
3
m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(2.0 × 10
−9
C)(4.0 × 10
−9
C)
(1.00 × 10
3
m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(2.0 × 10
−9
C)(3.0 × 10
−9
C)
(5.00 × 10
2
m)
2
Holt Physics Solution ManualII Ch. 16–4
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
4. L = 10.7 m
w = 8.7 m
q
1
=−1.2 × 10
−8
C
q
2
= 5.6 × 10
−9
C
q
3
= 2.8 × 10
−9
C
q
4
= 8.4 × 10
−9
C
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
5. d = 1.2 × 10
3
m
q
1
= 1.6 × 10
−2
C
q
2
= 2.4 × 10
−3
C
q
3
=−3.2 × 10
−3
C
q
4
=−4.0 × 10
−3
C
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
∆x =∆y == =8.5 × 10
2
m
F =
k
C
r
q
2
1
q
2
F
x
=−F
2
+ F
3
(cos 45°) = k
C
q
1
−
∆
q
x
2
2
+
q
3
(co
d
s
2
45°)
F
x
= (8.99 × 10
9
N
•
m
2
/C
2
)(1.6 × 10
−2
C)
−
(8
2
.
.
5
4
×
×
1
1
0
0
2
−3
m
C
)
2
+
F
x
=−0.24 N
F
y
=−F
4
− F
3
(sin 45°) = k
C
q
1
∆
q
y
4
2
+
q
3
(si
d
n
2
45°)
F
y
=−(8.99 × 10
9
N
•
m
2
/C
2
)(1.60 × 10
−2
C)
(8
4
.
.
5
0
×
×
1
1
0
0
2
−3
m
C
)
2
+
F
y
=−1.0 N
F
net
=
F
x
2
+
F
y
2
=
(0
.2
4
N
)
2
+
(
1.
0
N
)
2
= 1.0 N
q = tan
−1
F
F
x
y
= tan
−1
(
(
0
1
.
.
2
0
4
N
N
)
)
= 77°
F
net
= 1.0 N, 77° below the negative x-axis
(3.2 × 10
−3
C)(sin 45°)
(1.2 × 10
3
m)
2
(3.2 × 10
−3
C)(cos 45°)
(1.2 × 10
3
m)
2
1.2 × 10
3
m
2
d
2
Givens Solutions
F = k
C
q
r
1
q
2
2
F
x
= F
4
+ F
3
(cos q)
F
y
= F
2
+ F
3
(sin q)
F
x
= k
C
q
1
L
q
4
2
+
(L
2
+
q
3
w
L
2
)
3/2
F
x
= (8.99 × 10
9
N
•
m
2
/C
2
)(1.2 × 10
−8
C)
(8.
(
4
10
×
.7
10
m
−9
)
2
C)
+
F
x
= 9.1 × 10
−9
N
F
y
= k
C
q
1
w
q
2
2
+
(L
2
+
q
3
w
w
2
)
3/2
F
y
= (8.99 × 10
9
N
•
m
2
/C
2
)(1.2 × 10
−8
C)
(5.6
(8
×
.7
1
m
0
−
)
9
2
C)
+
F
y
= 9.0 × 10
−9
N
F
net
=
F
x
2
+
F
y
2
=
(9
.1
×
1
0
−
9
N
)
2
+
(
9.
0
×
1
0
−
9
N
)
2
= 1.28 × 10
−8
N
q = tan
−1
F
F
x
y
= tan
−1
9
9
.
.
1
0
×
×
1
1
0
0
−
−
9
9
N
N
)
= 45°
F
net
= 1.28 × 10
−8
N, 45° above the positive x-axis
(2.8 × 10
−9
C)(8.7 m)
[(10.7 m)
2
+ (8.7 m)
2
]
3/2
(2.8 × 10
−9
C)(10.7 m)
[(10.7 m)
2
+ (8.7 m)
2
]
3/2
Section Two—Problem Workbook Solutions II Ch. 16–5
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
1. q
1
= 2.5 × 10
−9
C
q
3
= 1.0 × 10
−9
C
r
2,1
= 5.33 m
r
3,1
= 1.90 m
r
3,2
= r
2,1
− r
3,1
= 5.33 m − 1.90 m = 3.43 m
F
3,1
= F
3,2
= k
C
(
q
r
3
3
,
q
1
)
1
2
= k
C
(
q
r
3
3
,
q
2
)
2
2
q
2
= q
1
r
r
3
3
,
,
1
2
2
q
2
= (2.50 × 10
−9
C)
3
1
.
.
4
9
3
0
m
m
2
= 8.15 × 10
−9
C
6. d =
228.930
3
× 10
3
m
=
7.631 × 10
4
m
q
1
= 8.8 × 10
−9
C
q
2
=−2.4 × 10
−9
C
q
3
= 4.0 × 10
−9
C
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
q = 60.0°
F =
k
C
r
q
2
1
q
2
F
x
= F
2
− F
3
(cos 60.0°)
F
y
= F
3
(sin 60.0°)
F
x
= k
C
q
1
d
q
2
2
−
q
3
(co
d
s
2
60.0°)
F
x
= (8.99 × 10
9
N
•
m
2
/C
2
)(8.8 × 10
−9
C)
(7.
2
6
.
3
4
1
×
×
1
1
0
0
−
4
9
m
C
)
2
−
F
x
= 5.5 × 10
−18
N
F
y
=−
k
C
q
1
q
3
(
r
si
2
n 60.0°)
F
y
=−
F
y
=−4.7 × 10
−17
N
F
net
=
F
x
2
+
F
y
2
=
(5
.5
×
1
0
−
18
N
)
2
+
(
4.
7
×
1
0
−
17
N
)
2
= 4.7 × 10
−17
N
q = tan
−1
F
F
x
y
= tan
−1
4
5
.
.
7
5
×
×
1
1
0
0
−
−
1
1
7
8
N
N
= 83°
F
net
= 4.7 × 10
−18
N, 83° below the positive x-axis
(8.99 × 10
9
N
•
m
2
/C
2
)(8.8 × 10
−9
C)(4.0 × 10
−9
C)(sin 60.0°)
(7.631 × 10
4
m)
2
(4.0 × 10
−9
C)(cos 60.0°)
(7.631 × 10
4
m)
2
Additional Practice C
2. q
1
= 7.5 × 10
−2
C
q
3
= 1.0 × 10
−4
C
r
2,1
= 6.00 × 10
2
km
r
3,1
= 24 km
r
3,2
= r
2,1
− r
3,1
= 6.00 × 10
2
km − 24 km = 576 km
F
3,1
= F
3,2
= k
C
(
q
r
3
3
,
q
1
)
1
2
= k
C
(
q
r
3
3
,
q
2
)
2
2
q
2
= q
1
=
r
r
3
3
,
,
1
2
2
q
2
= (7.5 × 10
−2
C)
5
2
7
4
6
k
k
m
m
2
= 43 C
Holt Physics Solution ManualII Ch. 16–6
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
3. m
E
= 6.0 × 10
24
kg
m
m
= 7.3 × 10
22
kg
G = 6.673 × 10
−11
N
•
m
2
/kg
2
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
F
g
= F
electric
Gm
r
E
2
m
m
=
k
C
r
2
q
2
q =
G
m
k
E
C
m
m
=
q = 5.7 × 10
13
C
(6.673 × 10
−11
N
•
m
2
/kg
2
)(6.0 × 10
24
kg)(7.3 × 10
22
kg)
8.99 × 10
9
N
•
m
2
/C
2
4. m = 17.23 kg
r = 0.800 m
F
net
= 167.6 N
g = 9.81 m/s
2
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
F
net
= F
g
− F
electric
F
net
= mg −
k
C
r
2
q
2
q =
q =
q = 1.0 × 10
−5
C
(0.800 m)
2
[(17.23 kg)(9.81 m/s
2
) − (167.6 N)]
8.99 × 10
9
N
•
m
2
/C
2
r
2
(mg − F
net
)
k
C
5. m
1
= 9.00 kg
m
2
= 8.00 kg
r = 1.00 m
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
g = 9.81 m/s
2
F
g,1
= F
g,2
+ F
electric
g(m
1
− m
2
) =
k
C
r
2
q
2
q =
gr
2
(
m
k
1
C
−
m
2
)
=
q = 3.30 × 10
−5
C
(9.81 m/s
2
)(1.00 m)
2
(9.00 kg − 8.00 kg)
8.99 × 10
9
N
•
m
2
/C
2
6. m = 9.2 × 10
4
kg
l
1
= 1.00 m
g = 9.81 m/s
2
l
2
= 8.00 m
r = 2.5 m
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
t
1
= t
2
mgl
1
=
k
C
r
q
2
2
l
2
q =
r
2
k
m
C
l
g
2
l
1
q =
= 8.9 × 10
−3
C
(2.5 m)
2
(9.2 × 10
4
kg)(9.81 m/s
2
)(1.00 m)
(8.99 × 10
9
N
•
m
2
/C
2
)(8.00 m)
Givens Solutions
7. q
1
= 2.0 C
q
2
= 6.0 C
q
3
= 4.0 C
L = 2.5 × 10
9
m
F
net
= 0 = F
1
+ F
2
k
C
q
x
1
q
2
3
=
(
k
L
C
−
q
2
x
q
)
3
2
x
q
2
1
=
(L
q
−
2
x)
2
(L − x)
q
1
= x
q
2
L
x
−
x
x
=
q
q
2
1
L
x
=
q
q
2
1
+ 1
x == =9.3 × 10
8
m
2.5 × 10
9
m
6
2
.
.
0
0
C
C
+ 1
L
q
q
2
1
+ 1
Section Two—Problem Workbook Solutions II Ch. 16–7
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
8. q
1
= 55 × 10
−6
C
q
2
= 137 × 10
−6
C
q
3
= 14 × 10
−6
C
L = 87 m
F
net
= 0 = F
1
+ F
2
k
C
q
x
1
q
2
3
=
(
k
L
C
−
q
2
x
q
)
3
2
x
q
2
1
=
(L
q
−
2
x)
2
(L − x)
q
1
= x
q
2
L
x
−
x
x
=
q
q
2
1
L
x
=
q
q
2
1
+ 1
x == =34 m
87 m
1
5
3
5
7
×
×
1
1
0
0
−
−
6
6
C
C
+ 1
L
q
q
2
1
+ 1
9. F = 1.00 × 10
8
N
q
1
= 1.80 × 10
4
C
q
2
= 6.25 × 10
4
C
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
F =
k
C
r
q
2
1
q
2
r =
k
C
q
F
1
q
2
r =
r = 3.18 × 10
5
m
(8.99 × 10
9
N
•
m
2
/C
2
)(1.80 × 10
4
C)(6.25 × 10
4
C)
1.00 × 10
8
N
10. m = 5.00 kg
q = 4.00 × 10
−2
C
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
g = 9.81 m/s
2
F
g
= F
electric
mg =
k
C
h
q
2
2
h =
k
m
C
q
g
2
h =
= 542 m
(8.99 × 10
9
N
•
m
2
/C
2
)(4.00 × 10
−2
C)
2
(5.00 kg)(9.81 m/s
2
)
11. m = 1.0 × 10
−19
kg
r = 1.0 m
q = 1.60 × 10
−19
C
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
F
res
= F
electric
=
k
C
r
q
2
2
F
res
=
F
res
= 2.3 × 10
−28
N
(8.99 × 10
9
N
•
m
2
/C
2
)(1.60 × 10
−19
C)
2
(1.0 m)
2
12. m = 5.0 × 10
−6
kg
q = 2.0 × 10
−15
C
r = 1.00 m
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
G = 6.673 × 10
−11
N
•
m
2
/kg
2
F
net
= F
electric
+ F
g
F
electric
=
k
C
r
q
2
2
=
F
g
=
G
r
m
2
2
=
F
net
= 3.6 × 10
−20
N + 1.7 × 10
−21
N = 3.8 × 10
−20
N
(6.673 × 10
−11
N
•
m
2
/kg
2
)(5.0 × 10
−6
kg)
2
(1.00 m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(2.0 × 10
−15
C)
2
(1.00 m)
2
Holt Physics Solution ManualII Ch. 16–8
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
13. m = 2.00 × 10
−2
kg
q
1
= 2.0 × 10
−6
C
q
2
=−8.0 × 10
−6
C
r = 1.7 m
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
g = 9.81 m/s
2
F
electric
= F
friction
k
C
r
q
2
1
q
2
= m
k
mg
m
k
=
k
m
C
q
g
1
r
q
2
2
m
k
==0.25
(8.99 × 10
9
N
•
m
2
/C
2
)(2.0 × 10
−6
C)(8.0 × 10
−6
C)
(2.00 × 10
−2
kg)(9.81 m/s
2
)(1.7 m)
2
1. r = 3.72 m
E = 0.145 N/C
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
q = 60.0°
Additional Practice D
2. ∆y = 190 m
q
1
= 1.2 × 10
−8
C
∆x = 120 m
E
x
= 1.60 × 10
−2
N/C
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
E =
k
r
C
2
q
E
x
= E
1
+ E
2
(cos q) =
k
∆
C
x
q
2
1
+
q
2
=
E
x
−
k
∆
C
x
q
2
1
(∆x
2
k
+
C
∆
∆
x
y
2
)
3/2
E
x
−
k
∆
C
x
q
2
1
=
1.60 × 10
−2
N/C −
= 8.5 × 10
−3
N/C
(∆x
2
k
+
C
∆
∆
x
y
2
)
3/2
=
= 1.0 × 10
−5
C
2
/N
q
2
= (8.5 × 10
−3
N/C)(1.0 × 10
−5
C
2
/N) = 8.5 × 10
−8
C
[(120 m)
2
+ (190 m)
2
]
3/2
(8.99 × 10
9
N
•
m
2
/C
2
)(120 m)
(8.99 × 10
9
N
•
m
2
/C
2
)(1.2 × 10
−8
C)
(120 m)
2
k
C
q
2
(∆x)
(∆x
2
+∆y
2
)
∆
x
2
+
∆
y
2
E =
k
r
C
2
q
E
x
=
k
r
C
2
q
(cos 60.0°) −
k
r
C
2
q
(cos 60.0°) = 0 N/C
Because E
x
= 0 N/C, the electric field points directly upward.
E
y
=
2k
C
q(s
r
in
2
60.0°)
q =
2k
C
(s
E
in
y
r
6
2
0.0°)
==1.29 × 10
−10
C
(0.145 N/C)(3.72 m)
2
(2)(8.99 × 10
9
N
•
m
2
/C
2
)(sin 60.0°)
3. q
1
= 1.80 × 10
−5
C
q
2
=−1.20 × 10
−5
C
E
net
= 22.3 N/C toward q
2
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
E
net
=
k
r
C
2
(q
1
+ q
2
) r
2
=
E
k
n
C
et
(q
1
+ q
2
)
r =
k
C
(q
E
1
n
e
+
t
q
2
)
r =
r = 1.10 × 10
2
m
(8.99 × 10
9
N
•
m
2
/C
2
)[(1.80 × 10
−5
C) + (1.20 × 10
−5
C)]
22.3 N/C toward q
2
Section Two—Problem Workbook Solutions II Ch. 16–9
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
4. d = 86.5 m
q
1
= 4.8 × 10
−9
C
q
2
= 1.6 × 10
−8
C
5. q = 3.6 × 10
−6
C
L = 960 m
w = 750 m
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
E =
k
r
C
2
q
E
y
= E
1
+ E
2
(sin q) =
k
w
C
2
q
+
E
y
= k
C
q
w
1
2
+
(w
2
+
w
L
2
)
3/2
E
y
= (8.99 × 10
9
N
•
m
2
/C
2
)(3.6 × 10
−6
C)
(750
1
m)
2
+
E
y
= 7.1 × 10
−2
N/C
E
x
= E
3
+ E
2
(cos q) =
k
L
C
2
q
+
E
x
= k
C
q
L
1
2
+
(w
2
+
L
L
2
)
3/2
E
x
= (8.99 × 10
9
N
•
m
2
/C
2
)(3.6 × 10
−6
C)
(960
1
m)
2
+
E
x
= 5.2 × 10
−2
N/C
E
net
=
E
y
2
+
E
x
2
=
(7
.1
×
1
0
−
2
N
/C
)
2
+
(
5.
2
×
1
0
−
2
N
/C
)
2
= 8.8 × 10
−2
N/C
q = tan
−1
E
E
y
x
= tan
−1
7
5
.
.
1
2
×
×
1
1
0
0
−
−
2
2
N
N
/
/
C
C
= 54°
E
net
= 8.8 × 10
−2
N/C, 54° above the horizontal
960 m
[(750 m)
2
+ (960 m)
2
]
3/2
k
C
qL
w
2
+
L
2
(w
2
+ L
2
)
750 m
[(750 m)
2
+ (960 m)
2
]
3/2
k
C
qw
w
2
+
L
2
(w
2
+ L
2
)
E
net
= E
1
+ E
2
= 0
E
1
= E
2
x
q
1
2
=
(d −
q
2
x)
2
(d − x)
q
1
= x
q
2
x
q
1
+
q
2
= d
q
1
x ==
x = 3.0 × 10
1
m
(86.5 m)
4.
8
×
1
0
−
9
C
(4
.8
×
1
0
−
9
C
)
+
(1
.6
×
1
0
−
8
C
)
d
q
1
q
1
+
q
2
Holt Physics Solution ManualII Ch. 16–10
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
6. w = 218 m
h = 50.0 m
q = 6.4 × 10
−9
C
k
C
= 8.99 × 10
9
N
•
m
2
/C
2
q
1
= q
2
= q
q
3
= 3q
q
4
= 2q
r == =112 m
q = tan
−1
w
h
= tan
−1
5
2
0
1
.
8
0
m
m
= 12.9°
The electric fields of charges on opposite corners of the rectangle cancel to give 2q
on the lower left corner and q on the lower right corner.
E =
k
r
C
2
q
E
x
=
k
C
r
2
2q
−
k
r
C
2
q
(cos q) =
k
C
q(
r
c
2
os q)
E
x
==4.5 × 10
−3
N/C
E
y
=
k
C
r
2
2q
+
k
r
C
2
q
(sin q) =
3k
C
q
r
(
2
sin q)
E
y
==3.1 × 10
−3
N/C
E
net
=
E
x
2
+
E
y
2
=
(4
.5
×
1
0
−
3
N
/C
)
2
+
(
3.
1
×
1
0
−
3
N
/C
)
2
E
net
= 5.5 × 10
−3
N/C
q = tan
−1
E
E
x
y
= tan
−1
3
4
.
.
1
5
×
×
1
1
0
0
−
−
3
3
N
N
/
/
C
C
= 35°
E
net
= 5.5 × 10
−3
N/C, 35° above the positive x-axis
(3)(8.99 × 10
9
N
•
m
2
/C
2
)(6.4 × 10
−9
C)(sin 12.9°)
(112 m)
2
(8.99 × 10
9
N
•
m
2
/C
2
)(6.4 × 10
−9
C)(cos 12.9°)
(112 m)
2
(5
0.
0
m
)
2
+
(
21
8
m
)
2
2
h
2
+
w
2
2
Givens Solutions
Section Two—Problem Workbook Solutions II Ch. 17–1
II
HRW material copyrighted under notice appearing earlier in this book.
1. r = 4.8 × 10
−4
m
q = 2.9 × 10
−9
C
∆V = k
C
q
r
= (8.99 × 10
9
N
•
m
2
/C
2
)
2
2
.
.
8
9
×
×
1
1
0
0
−
−
4
9
m
C
= 5.4 × 10
4
V
Additional Practice A
Givens Solutions
2. q =−1.6 × 10
−19
C
∆PE
electric
= 3.3 × 10
−15
J
d = 3.5 cm
∆PE
electric
=−qEd
Rearrange to solve for E.
E =
∆PE
−
e
q
l
d
ectric
= =
5.9 × 10
5
N
C
3.3 × 10
−15
J
−(−1.6 × 10
−19
C)(0.035 m)
3. ∆PE
electric
= 3.1 × 10
−12
J
d = 4.7 cm
∆V =−73 V
∆PE
electric
= 3.1 × 10
−12
J
d = 4.7 cm
∆V =−73 V
a. ∆V = −Ed
Rearrange to solve for E.
E = −
∆
d
V
=
4.7
−
×
7
1
3
0
V
−2
m
=
b. ∆V =
∆PE
q
electric
Rearrange to solve for q.
q =
∆PE
∆
e
V
lectric
=
3.1
−
×
7
1
3
0
V
−12
J
=−4.2 × 10
−14
C
1.6 × 10
3
N
C
4. d = 9.35 m
∆PE
electric
= 3.17 × 10
−10
J
E = 1.25 × 10
5
N/C
d = 9.35 m
∆PE
electric
= 3.17 × 10
−10
J
E = 1.25 × 10
5
N/C
a. ∆PE
electric
= −qEd
Rearrange to solve for q.
q = −
∆PE
E
e
d
lectric
= −
q =
b. ∆PE
electric
= −qEd
Rearrange to solve for q.
q = −
∆PE
E
e
d
lectric
= −
q = −2.71 × 10
−16
C
∆V =
∆PE
q
electric
=
−
3
2
.
.
1
7
7
1
×
×
1
1
0
0
−
−
1
1
0
6
J
C
=−1.17 × 10
6
V
3.17 × 10
−10
J
(1.25 × 10
5
N/C)(9.35 m)
−2.71 × 10
−16
C
3.17 × 10
−10
J
(1.25 × 10
5
N/C)(9.35 m)
Electrical Energy
and Current
Problem Workbook Solutions
Holt Physics Solution ManualII Ch. 17–2
II
HRW material copyrighted under notice appearing earlier in this book.
5. E = 1.5 × 10
2
N/C
d = 439 m
∆PE
electric
=−3.7 × 10
−8
J
E = 1.5 × 10
2
N/C
d = 439 m
∆PE
electric
=−3.7 × 10
−8
J
E = 1.5 × 10
2
N/C
d = 439 m
∆PE
electric
=−3.7 × 10
−8
J
a. q =−
∆PE
E
e
d
lectric
=−
q =
b. ∆V =−Ed =−(1.5 × 10
2
N/C)(439 m)
∆V =
c. Use the value for q found in part a.
V =
∆PE
q
electric
=
5
−
.
3
6
.7
×
×
10
1
−
0
1
−
3
8
C
J
= −6.6 × 10
4
V
−6.6 × 10
4
V
5.6 × 10
−13
C
–3.7 × 10
−8
J
(1.5 × 10
2
N/C)(439 m)
Givens Solutions
6. E = 6.5 × 10
2
N/C
d = 0.077 cm
∆V =−Ed =−(6.5 × 10
2
N/C)(7.7 × 10
−4
m) = −5.0 × 10
−1
V
The absolute value gives the magnitude of the potential difference.
−5.0 × 10
−1
V
= 5.0 × 10
−1
V
7. q = 1.6 × 10
−19
C
E = 383 N/C
d = 3.75 m
q = 1.6 × 10
−19
C
E = 383 N/C
d = 3.75 m
a. ∆V =−Ed =−(383 N/C)(3.75 m) =−1.44 × 10
3
V
−1.44 × 10
3
V
=
b. ∆V =−Ed =−(383 N/C)(3.75 m) =−1.44 × 10
3
V
∆V =
∆PE
q
electric
Rearrange to solve for ∆PE
electric
.
∆PE
electric
=∆Vq = (−1.44 × 10
3
V) × (1.6 × 10
−19
C)
∆PE
electric
=−2.3 × 10
−16
J
1.44 × 10
3
V
8. q =−4.8 × 10
−19
C
d =−0.63 cm
E = 279 V/m
q =−4.8 × 10
−19
C
d =−0.63 cm
E = 279 V/m
a. V =
N
C
•
m
; Rearrange to get
m
V
=
N
C
279 V/m = 279 N/C
∆PE
electric
=−qEd = (−4.8 × 10
−19
C)(279 N/C)(−6.3 × 10
−3
m)
∆PE
electric
=
b. V =
N
C
•
m
; Rearrange to get
m
V
=
N
C
279 V/m = 279 N/C
∆PE
electric
=−qEd = (−4.8 × 10
−19
C)(279 N/C)(−6.3 × 10
−3
m)
∆PE
electric
= −8.4 × 10
−19
J
Find the electric potential associated with a charged particle.
V =
PE
e
q
lectric
=
−
−
4
8
.
.
8
4
×
×
1
1
0
0
−
−
1
1
9
9
C
J
= 1.8 V
−8.4 × 10
−19
J
Section Two—Problem Workbook Solutions II Ch. 17–3
II
HRW material copyrighted under notice appearing earlier in this book.
Givens Solutions
1. ∆V = 3.00 × 10
2
V
PE
electric
= 17.1 kJ
PE
electric
=
1
2
C(∆V )
2
C =
2P
(∆
E
V
ele
)
ct
2
ric
C =
(
2
3
(
.
1
0
7
0
.1
×
×
10
1
2
0
3
V
J
)
)
2
C = 3.80 × 10
−1
F
2. PE
electric
= 1450 J
∆V = 1.0 × 10
4
V
PE
electric
=
1
2
C(∆V )
2
C =
2P
(∆
E
V
ele
)
ct
2
ric
C =
(1.
2
0
(
×
14
1
5
0
0
4
J
V
)
)
2
C = 2.9 × 10
−5
F
3. E
max
= 3.0 × 10
6
V/m
d = 0.2 × 10
−3
m
A = 6.7 × 10
3
m
2
e
0
= 8.85 × 10
−12
C
2
/N
•
m
2
∆V
max
= E
max
d
∆V
max
=
Q
C
max
=
E
max
d =
Q
max
= E
max
e
0
A
Q
max
= (3.0 × 10
6
V/m)(8.85 × 10
−12
C
2
/N
•
m
2
)(6.7 × 10
3
m
2
)
Q
max
= 0.18 C
Q
max
e
0
d
A
Q
max
e
0
d
A
4. r = 3.1 m
d = 1.0 × 10
−3
m
E
max
= 3.0 × 10
6
V/m
e
0
= 8.85 × 10
−12
C
2
/N
•
m
2
Q
max
= C∆V
max
= CE
max
d
C =
e
0
d
A
Q
max
= e
0
AE
max
= e
0
pr
2
E
max
Q
max
= (8.85 × 10
−12
C
2
/N
•
m
2
)(p)(3.1 m)
2
(3.0 × 10
6
V/m)
Q
max
= 8.0 × 10
−4
C = 0.80 mC
Additional Practice B
5. P = 5.0 × 10
15
W
∆t = 1.0 × 10
−12
s
C = 0.22 F
PE
electric
=
1
2
C(∆V)
2
PE
electric
= P∆t
P∆t =
1
2
C(∆V )
2
∆V =
2P
C
∆
t
∆V =
∆V = 210 V
2(5.0 × 10
15
W)(1.0 × 10
−12
s)
(0.22 F)
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualII Ch. 17–4
6. A = 2.32 × 10
5
m
2
d = 1.5 × 10
−2
m
Q = 0.64 × 10
−3
C
e
0
= 8.85 × 10
−12
C
2
/N
•
m
2
PE
electric
=
1
2
Q
C
2
C =
e
0
d
A
PE
electric
=
1
2
Q
e
0
2
A
d
PE
electric
=
PE
electric
= 1.5 × 10
−3
J
(0.64 × 10
−3
C)
2
(1.5 × 10
−2
m)
(8.85 × 10
−12
C
2
/N
•
m
2
)(2.32 × 10
5
m
2
)
1
2
Givens Solutions
7. r = 18.0 m
∆V = 575 V
PE
electric
= 3.31 J
PE
electric
=
1
2
C(∆V)
2
C =
2 P
(∆
E
V
ele
)
c
2
tric
=
(
2
5
(
7
3
5
.3
V
1
)
J
2
)
C =
d =
e
0
C
A
=
e
0
C
πr
2
d =
d = 4.5 × 10
−4
m = 0.45 mm
(8.85 × 10
−12
C2/N
•
m2)(π)(18.0 m)
2
(2.00 × 10
−5
F)
2.00 × 10
−5
F
8. d
i
= 5.00 × 10
−3
m
d
f
= 0.30 × 10
−3
m
e
0
= 8.85 × 10
−12
C
2
/N
•
m
2
A = 1.20 × 10
−4
m
2
∆C = C
f
− C
i
=
e
d
0
A
f
−
e
d
0
A
i
∆C = e
0
A
d
1
f
−
d
1
i
∆C =
8.85 × 10
−12
N
C
•
m
2
2
(1.20 × 10
−4
m
2
)
0.30 ×
1
10
−3
m
−
5.00 ×
1
10
−3
m
∆C = 3.3 × 10
−12
F =−3.3 pF
9. A = 98 × 10
6
m
2
C = 0.20 F
e
0
= 8.85 × 10
−12
C
2
/N
•
m
2
C =
e
0
d
A
d =
e
0
C
A
d =
d = 4.3 × 10
−3
m = 4.3 mm
(8.85 × 10
−12
C
2
/N
•
m
2
)(98 × 10
6
m
2
)
(0.20 F)
Section Two—Problem Workbook Solutions II Ch. 17–5
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens Solutions
11. A = 44 m
2
e
0
= 8.85 × 10
−12
C
2
/N•m
2
Q = 2.5 × 10
−6
C
∆V = 30.0 V
a. C =
∆
Q
V
C =
(2.5
(3
×
0.
1
0
0
V
−6
)
C)
C =
b. C =
e
0
d
A
d =
e
0
C
A
d =
d =
c. PE
electric
=
1
2
Q∆V
PE
electric
=
1
2
(2.5 × 10
−6
C)(30.0 V)
PE
electric
= 3.8 × 10
−5
J
4.7 × 10
−3
m
(8.85 × 10
−12
C
2
/N
•
m
2
)(44 m
2
)
(8.3 × 10
−8
F)
8.3 × 10
−8
F = 83 nF
10. A = 7.0 m × 12.0 m
d = 1.0 × 10
−3
m
e
0
= 8.85 × 10
−12
C
2
/N
•
m
2
PE
electric
= 1.0 J
a. C =
e
0
d
A
C =
C =
b. PE
electric
=
1
2
C(∆V )
2
∆V =
2P
E
C
el
ec
tr
ic
∆V =
(7
.4
2
(
×
1.
1
0
0
J
−
)
7
F
)
∆V = 1.6 × 10
3
V = 1.6 kV
7.4 × 10
−7
F = 0.74 mF
(8.85 × 10
−12
C
2
/N•m
2
)(7.0 m)(12.0 m)
(1.0 × 10
−3
m)
1. I = 3.00 × 10
2
A
∆t = 2.4 min
∆Q = I∆t
∆Q = (3.00 × 10
2
A)(2.4 min)
1
6
m
0
i
s
n
∆Q = 4.3 × 10
4
C
Additional Practice C
Holt Physics Solution ManualII Ch. 17–6
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. ∆t = 7 min, 29 s
I = 0.22 A
∆Q = I∆t
∆Q = (0.22 A)
(7 min)
1
6
m
0
i
s
n
+ 29 s
= (0.22 A)(449 s)
∆Q = 99 C
3. ∆t = 3.3 × 10
−6
s
I = 0.88 A
q = e = 1.60 × 10
−19
elec
C
tron
∆Q = I∆t = nq
n =
I∆
q
t
n =
n = 1.8 × 10
13
electrons
(0.88 A)(3.3 × 10
−6
s)
(1.60 × 10
−19
C/electron)
4. ∆t = 3.00 h
∆Q = 1.51 × 10
4
C
I =
∆
∆
Q
t
I =
I = 1.40 A
(1.51 × 10
4
C)
(3.00 h)
3.60
1
×
h
10
3
s
5. ∆Q = 1.8 × 10
5
C
∆t = 6.0 min
I =
∆
∆
Q
t
I =
I = 5.0 × 10
2
A
(1.8 × 10
5
C)
(6.0 min)
1
6
m
0
i
s
n
Givens Solutions
6. I = 13.6 A
Q = 4.40 × 10
5
C
∆t =
∆
I
Q
∆t =
(4.4
(1
0
3
×
.6
1
A
0
5
)
C)
∆t = 3.24 × 10
4
s = 9.00 h
1. ∆V = 440 V
I = 0.80 A
R =
∆
I
V
R =
(
(
0
4
.
4
8
0
0
V
A
)
)
R = 5.5 × 10
2
Ω
Additional Practice D
Section Two—Problem Workbook Solutions II Ch. 17–7
II
Givens Solutions
HRW material copyrighted under notice appearing earlier in this book.
2. ∆V = 9.60 V
I = 1.50 A
R =
∆
I
V
R =
(
(
9
1
.
.
6
5
0
0
V
A)
)
R = 6.40 Ω
3. ∆V = 312 V
∆Q = 2.8 × 10
5
C
∆t = 1.00 h
I =
∆
∆
Q
t
R =
∆
I
V
==
∆
∆
V
Q
∆t
R =
R = 4.0 Ω
(312 V)(1.00 h)
3.60
1
×
h
10
3
s
(2.8 × 10
5
C)
∆V
∆
∆
Q
t
4. I = 3.8 A
R = 0.64 Ω
∆V = IR
∆V = (3.8 A)(0.64 Ω)
∆V = 2.4 V
5. R = 0.30 Ω
I = 2.4 × 10
3
A
∆V = IR = (2.4 × 10
3
A)(0.30 Ω) = 7.2 × 10
2
V
6. ∆V = 3.0 V
R = 16 Ω
I =
∆
R
V
I =
(
(
3
1
.
6
0
Ω
V
)
)
I = 0.19 A
7. ∆V = 6.00 × 10
2
V
R = 4.4 Ω
I =
∆
R
V
==1.4 × 10
2
A
(6.00 × 10
2
V)
(4.4 Ω)
1. P = 12 × 10
3
W
R = 2.5 × 10
2
Ω
P = I
2
R
I =
R
P
I =
(
(
2
1
.
2
5
×
×
1
1
0
0
3
2
W
Ω
)
)
I = 6.9 A
Additional Practice E
Holt Physics Solution ManualII Ch. 17–8
II
Givens Solutions
HRW material copyrighted under notice appearing earlier in this book.
2. P = 33.6 × 10
3
W
∆V = 4.40 × 10
2
V
P = I∆V
I =
∆
P
V
I =
(
(
3
4
3
.4
.6
0
×
×
1
1
0
0
3
2
W
V)
)
I = 76.4 A
3. P = 850 W
V = 12.0 V
P = I∆V
I =
∆
P
V
I =
8
1
5
2
0
.0
W
V
I = 70.8 A
4. P =
4
1
.
.
2
1
×
×
1
1
0
0
1
3
0
h
J
R = 40.0 Ω
P =
(∆V
R
)
2
∆V =
P
R
∆V =
4
1
.
.
2
1
×
×
1
1
0
0
1
3
0
h
J
36
1
0
h
0
s
(
40
.0
Ω
)
∆V = 6.5 × 10
2
V
5. P = 6.0 × 10
13
W
∆V = 8.0 × 10
6
V
P =
(∆
R
V )
2
R =
(∆
P
V )
2
R =
(
(
6
8
.
.
0
0
×
×
1
1
0
0
1
6
3
V
W
)
2
)
R = 1.1 Ω
6. I = 6.40 × 10
3
A
∆V = 4.70 × 10
3
V
P = I∆V
P = (6.40 × 10
3
A)(4.70 × 10
3
V)
P = 3.01 × 10
7
W = 30.1 MW
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Section Two—Problem Workbook Solutions II Ch. 17–9
Givens Solutions
1. q
1
=−12.0 × 10
−9
C
q
2
=−68.0 × 10
−9
C
V =−25.3 V
r
1
= 16.0 m
r
2
= d − r
1
k
C
= 8.99 × 10
9
N
C
•
m
2
2
V = k
C
q
r
1
1
+
q
r
2
2
= k
C
q
r
1
1
+
(d
q
−
2
r
1
)
k
V
C
−
q
r
1
1
+
(d
q
−
2
r
1
)
d =+r
1
d =+16.0 m
d = 33.0 m + 16.0 m = 49.0 m
−68.0 × 10
−9
C
8.99 ×
−
1
2
0
5
9
.3
N
V
•
m
2
/C
2
−
(−12.
1
0
6
×
.0
1
m
0
−9
C)
q
2
k
V
C
−
q
r
1
1
Additional Practice F
2. q
1
= 18.0 × 10
−9
C
q
2
= 92.0 × 10
−9
C
V = 53.3 V
r
1
= d − r
2
d = 97.5 m
k
C
= 8.99 × 10
9
N
C
•
m
2
2
V = k
C
q
r
= k
C
q
r
1
1
+
q
r
2
2
V = k
C
d −
q
1
r
2
+
q
r
2
2
k
V
C
=
(q
1
r
(
2
d
+
−
q
r
2
2
d
)(
−
r
2
q
)
2
r
2
)
−
k
V
C
r
2
2
+
k
V
C
dr
2
= (q
1
− q
2
)r
2
+ q
2
d
k
V
C
r
2
2
+
q
1
− q
2
−
V
k
C
d
r
2
+ q
2
d = 0
Solve using the quadratic formula:
r
2
=
q
1
− q
2
−
V
k
C
d
= 18.0 × 10
−9
C − 92.0 × 10
−9
C −
q
1
− q
2
−
V
k
C
d
=−652 × 10
−9
C
4V
k
q
C
2
d
==2.13 × 10
−13
C
2
2
k
V
C
==11.9 × 10
−9
m
C
r
2
=
r
2
=
652
11
±
.9
460
m
−(−652 × 10
−9
C) ±
(−
65
2
×
1
0
−
9
C
)
2
−
(
2.
13
×
1
0
−
13
C
2
)
(11.9 × 10
−9
C/m)
2(53.3 V )
(8.99 × 10
9
N
•
m
2
/C
2
)
4(53.3 V)(92.0 × 10
−9
C)(97.5 m)
(8.99 × 10
9
N
•
m
2
/C
2
)
(53.3 V)(97.5 m)
8.99 × 10
9
N
C
•
m
2
2
−
q
1
− q
2
−
V
k
C
d
±
q
1
−
q
2
−
V
k
C
d
2
−
4V
k
q
C
2
d
2
k
V
C
Holt Physics Solution ManualII Ch. 17–10
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
3. V = 1.0 × 10
6
V
r = 12 × 10
−2
m
k
C
= 8.99 × 10
9
N
C
•
m
2
2
V = k
C
q
r
q =
V
k
C
r
q =
q = 1.3 × 10
−5
C
(1.0 × 10
6
V)(12 × 10
−2
m)
8.99 × 10
9
N
C
•
m
2
2
4. M
E
= 5.98 × 10
24
kg
G = 6.673 × 10
−11
N
k
•
g
m
2
2
k
C
= 8.99 × 10
9
N
C
•
m
2
2
m = 1.0 kg
q = 1.0 C
mV
gravity
= qV
electric
mM
r
E
G
=
qQ
r
E
k
C
Q
E
=
m
q
M
k
C
E
G
Q
E
=
Q
E
= 4.44 × 10
4
C
(1.0 kg)(5.98 × 10
24
kg)
6.673 × 10
−11
N
k
•
g
m
2
2
(1.0 C)
8.99 × 10
9
N
C
•
m
2
2
Givens Solutions
Of the two roots, the one that yields the correct answer is
r
2
=
(652
11
−
.9
460)
m
r
2
= 16.1 m
5. m
sun
= 1.97 × 10
30
kg
m
H
= mass of hydrogen
atom = 1.67 × 10
−27
kg
q
1
= charge of proton
=+1.60 × 10
−19
C
q
2
= charge of electron
=−1.60 × 10
−19
C
r
1
= 1.1 × 10
11
m
r
2
= 1.5 × 10
11
m − 1.1 ×
10
11
m = 4.0 × 10
10
m
k
C
= 8.99 × 10
9
N
C
•
m
2
2
a. Q
+
= charge of proton cloud = (number of protons)q
1
=
m
m
su
H
n
q
1
Q
+
=
Q
+
=
Q
−
= charge of electron cloud =
m
m
sun
H
q
2
Q
−
=
b. V = k
C
q
r
= k
C
Q
r
1
+
+
Q
r
2
−
V =
8.99 × 10
9
N
C
•
m
2
2
1
1
.
.
8
1
9
×
×
1
1
0
0
1
3
1
8
m
C
−
1
4
.
.
8
0
9
×
×
1
1
0
0
1
3
0
8
m
C
V =−2.7 × 10
37
V
−1.89 × 10
38
C
1.89 × 10
38
C
(1.97 × 10
30
kg)(1.60 × 10
−19
C)
(1.67 × 10
−27
kg)
Section Two—Problem Workbook Solutions II Ch. 17–11
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Givens SolutionsGivens Solutions
6. r = r
1
= r
2
= r
3
= r
4
=
2
x
2
+
2
y
2
x = 292 m
y = 276 m
q = 64 × 10
−9
C
q
1
= 1.0q
q
2
=−3.0q
q
3
= 2.5q
q
4
= 4.0q
k
C
= 8.99 × 10
9
N
C
•
m
2
2
V = k
C
q
r
= k
C
q
r
1
1
+
q
r
2
2
+
q
r
3
3
+
q
r
4
4
V =
V =
V = 13 V
8.99 × 10
9
N
C
•
m
2
2
(64 × 10
−9
C)(4.5)
2
92
2
m
2
+
27
6
2
m
2
k
C
q(1.0 − 3.0 + 2.5 + 4.0)
2
x
2
+
2
y
2
7. q
1
= q
2
= q
3
= q
= 7.2 × 10
−2
C
l
= 1.6 × 10
7
m
r
1
= r
2
=
2
l
r
3
=
l
2
−
2
l
2
k
C
= 8.99 × 10
9
N
C
•
m
2
2
V = k
C
q
r
= k
C
q
r
1
1
+
q
r
2
2
+
q
r
3
3
V = k
C
++
=
2 + 2 +
V =
4 +
V = 2.1 × 10
2
V
1
3
4
8.99 × 10
9
N
C
•
m
2
2
(0.072 C)
(1.6 × 10
7
m)
1
1
−
1
2
2
k
C
q
l
q
l
2
−
2
l
2
q
2
l
q
2
l
8. q
1
= q
2
= q
3
= q
= 25.0 × 10
−
9
C
r
1
= r
2
=
l
r
3
=
l
2
+
l
2
l
= 184 m
k
C
= 8.99 × 10
9
N
C
•
m
2
2
V = k
C
q
r
= k
C
q
r
1
1
+
q
r
2
2
+
q
r
3
3
V = k
C
q
++
=
1 + 1 +
V = (2.707)
V = 3.31 V
8.99 × 10
9
N
C
•
m
2
2
(25.0 × 10
−9
C)
(184 m)
1
2
k
C
q
l
1
l
2
+
l
2
1
l
1
l
4. ∆V = 110 V
R = 80.0 Ω (for maximum
power)
∆t = 24 h
cost of energy =
$0.086/kW
•
h
P =
(∆
R
V)
2
total cost of electricity = P∆t(cost of energy)
total cost =
(∆V
R
)
2
(∆t)
(cost of energy)
total cost =
(11
(
0
8
V
0.
)
0
2
(
Ω
2
)
4h)
1
$0
k
.
W
08
•
6
h
1
1
00
k
0
W
W
total cost = $0.31
5. 15.5 percent of solar energy
converted to electricity
cost of energy =
$0.080/kW
•
h
purchase power = $1000.00
(0.155)E
solar
=
p
c
u
o
r
s
c
t
h
o
a
f
se
en
p
e
o
r
w
gy
er
E
solar
=
E
solar
= 8.1 × 10
4
kW
•
h = 2.9 × 10
11
J
($1000.00)
(0.155)($0.080/kW
•
h)
Holt Physics Solution ManualII Ch. 17–12
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. P = 8.8 × 10
6
kW
total cost = $1.0 × 10
6
cost of energy =
$0.081/kW
•
h
total cost of electricity = P∆t (cost of energy)
∆t =
∆t =
∆t = 1.4 h
$1.0 × 10
6
(8.8 × 10
6
kW)($0.081/kW
•
h)
total cost of electricity
P(cost of energy)
2. P = 104 kW
cost of energy =
$0.120/kW
•
h
purchase power = $18 000
energy that can be purchased =
p
c
u
o
r
s
c
t
h
o
a
f
se
en
p
e
o
r
w
gy
er
= P∆t
∆t =
(c
p
o
u
st
rc
o
h
f
a
e
s
n
e
e
p
rg
o
y
w
)
e
(
r
P)
∆t =
∆t = 1.4 × 10
3
h = 6.0 × 10
1
days
$18 000
($0.120/kW
•
h)(104 kW)
3. ∆t = 1.0 × 10
4
h
cost of energy =
$0.086/kW
•
h
total cost = $23
total cost of electricity = P∆t (cost of energy)
P =
P =
P = 2.7 × 10
−2
kW
$23
(1.0 × 10
4
h)($0.086 kW
•
h)
total cost of electricity
∆t(cost of energy)
Givens Solutions
Additional Practice G
Section Two—Problem Workbook Solutions
II Ch. 18–1
Circuits and
Circuit Elements
Problem Workbook Solutions
II
1. R = 160 kΩ
R
1
= 2.0R
R
2
= 3.0R
R
3
= 7.5R
R
eq
= R
1
+ R
2
+ R
3
= 2.0R + 3.0R + 7.5R = 12.5R
R
eq
= (12.5)(160 kΩ) = 2.0 × 10
3
kΩ
Additional Practice A
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. R = 5.0 × 10
8
Ω
R
1
=
1
3
R
R
2
=
2
7
R
R
3
=
1
5
R
R
eq
= R
1
+ R
2
+ R
3
=
1
3
R +
2
7
R +
1
5
R
R
eq
=
35 +
1
3
0
0
5
+ 21
R =
1
8
0
6
5
R =
1
8
0
6
5
(5.0 × 10
8
Ω) = 4.1 × 10
8
Ω
3. R
1
= 16 kΩ
R
2
= 22 kΩ
R
3
= 32 kΩ
R
eq
= 82 kΩ
R
4
= R
eq
− R
1
− R
2
− R
3
= 82 kΩ−16 kΩ−22 kΩ−32 kΩ= 12 kΩ
4. R
1
= 3.0 kΩ
R
2
= 4.0 kΩ
R
3
= 5.0 kΩ
P = (0.0100)(3.2 MW) =
0.032 MW
R
eq
= R
1
+ R
2
+ R
3
= 3.0 kΩ+4.0 kΩ+5.0 kΩ=12.0 kΩ
P =
(∆V
R
)
2
∆V =
P
R
eq
=
(3
.2
×
1
0
4
W
)(
1.
20
×
1
0
4
Ω
)
= 2.0 × 10
4
V
5. R
1
= 4.5 Ω
R
2
= 4.0 Ω
R
3
= 16.0 Ω
R
12
= R
1
+ R
2
= 4.5 Ω+4.0 Ω=
R
13
= R
1
+ R
3
= 4.5 Ω+16.0 Ω=
R
23
= R
2
+ R
3
= 4.0 Ω+16.0 Ω= 20.0 Ω
20.5 Ω
8.5 Ω
6. R
1
= 2.20 × 10
2
Ω
∆V
i
= 1.20 × 10
2
V
∆V
f
= 138 V
Because the current is unchanged, the following relationship can be written.
R
V
1
i
=
R
1
V
+
f
R
2
R
2
=
V
f
R
1
V
−
i
V
i
R
1
=
R
2
==
40
1
0
2
0
0
V
V
•
Ω
= 33 Ω
30 400 V
•
Ω−26 400 V
•
Ω
120 V
(138 V)(220 Ω) − (120 V)(220 Ω)
120 V
Holt Physics Solution Manual
II
7. R
1
= 3.6 × 10
−5
Ω
R
2
= 8.4 × 10
−6
Ω
I = 280 A
R
eq
= R
1
+ R
2
= 3.6 × 10
−5
Ω+8.4 × 10
−6
Ω=4.4 × 10
−5
Ω
P = I
2
R
eq
= (280 A)
2
(4.4 × 10
−5
Ω) = 3.4 W
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
II Ch. 18–2
1. R
1
= 1.8 Ω
R
2
= 5.0 Ω
R
3
= 32 Ω
R
eq
=
R
1
1
+
R
1
2
+
R
1
3
−1
=
1.8
1
Ω
+
5.0
1
Ω
+
32
1
Ω
−1
R
eq
=
0.55
Ω
1
+ 0.20
Ω
1
+ 0.031
Ω
1
−1
=
0.78
Ω
1
−1
= 1.3 Ω
Additional Practice B
2. R = 450 Ω
R
1
= R
R
2
= 2.0R
R
3
= 0.50R
R
eq
=
R
1
1
+
R
1
2
+
R
1
3
−1
=
450
1
Ω
+
900
1
Ω
+
220
1
Ω
−1
R
eq
=
0.0022
Ω
1
+ 0.0011
Ω
1
+ 0.0045
Ω
1
−1
=
0.0078
Ω
1
−1
= 1.3 × 10
2
Ω
3. R
1
= 2.48 × 10
−2
Ω
R
eq
= 6.00 × 10
−3
Ω
R
2
=
R
1
eq
−
R
2
1
−1
=
6.00 ×
1
10
−3
Ω
−
2.48 ×
2
10
−2
Ω
−1
R
2
=
167
Ω
1
− 80.6
Ω
1
−1
=
86
Ω
1
−1
= 0.012 Ω
4. R
1
= R
R
2
= 3R
R
3
= 7R
R
4
= 11R
R
eq
= 6.38 × 10
−2
Ω
R
eq
=
R
1
1
+
R
1
2
+
R
1
3
+
R
1
4
−1
=
R
1
+
3
1
R
+
7
1
R
+
11
1
R
−1
R
eq
=
231 + 7
2
7
31
+
R
33 + 21
−1
=
2
3
3
6
1
2
R
−1
=
1.
R
57
−1
R = 1.57R
eq
= 1.57(6.38 × 10
−2
Ω) = 0.100 Ω
5. ratio = 1.22 × 10
−2
Ω/m
l
= 1813 km
R
1
=
1
2
R
R
2
=
1
4
R
R
3
=
1
5
R
R
4
=
2
1
0
R
a. R = (ratio)(
l
)
= (1.22 × 10
−2
Ω/m)(1.813 × 10
6
m) =
b. R
eq
=
R
1
1
+
R
1
2
+
R
1
3
+
R
1
4
−1
=
R
2
+
R
4
+
R
5
+
2
R
0
−1
R
eq
=
3
R
1
−1
=
1.00 ×
3
1
1
0
10
Ω
−1
= 3.23 × 10
8
Ω
2.21 × 10
4
Ω
6. ∆V = 14.4 V
P = 225 W
P =
(∆
R
V)
2
R =
(∆
P
V)
2
=
(1
2
4
2
.
5
4
W
V)
2
=
R
eq
=
R
4
−1
=
R
4
=
0.92
4
2 Ω
= 0.230 Ω
I =
R
∆
e
V
q
=
0
1
.2
4
3
.4
0
V
Ω
= 62.6 A
0.922 Ω
Section Two—Problem Workbook Solutions
II Ch. 18–3
II
7. L = 3.22 × 10
5
km
l
= 1.00 × 10
3
km
ratio = 1.0 × 10
−2
Ω/m
∆V = 1.50 V
R
eq
= N
R
1
where N = and R = (ratio)
l
R
eq
=
−1
=
−1
= 31 Ω
I =
R
∆
e
V
q
=
1
3
.5
1
0
Ω
V
= 0.048 A
3.22 × 10
8
m
(1.0 × 10
−2
Ω/m)(1.00 × 10
6
m)
2
L
(ratio)
l
2
L
l
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. R
1
= 6.60 × 10
2
Ω
R
2
= 2.40 × 10
2
Ω
R
3
= 2.00 × 10
2
Ω
R
4
= 2.00 × 10
2
Ω
R
12
= R
1
+ R
2
= 660 Ω+240 Ω=900 Ω
R
123
=
R
1
12
+
R
1
3
−1
=
900
1
Ω
+
200
1
Ω
−1
R
123
=
0.00111
Ω
1
+ 0.00500
Ω
1
−1
=
0.00611
Ω
1
−1
= 164 Ω
R
eq
= R
123
+ R
4
= 164 Ω+200 Ω= 364 Ω
Additional Practice C
3. R
1
= 2.5 Ω
R
2
= 3.5 Ω
R
3
= 3.0 Ω
R
4
= 4.0 Ω
R
5
= 1.0 Ω
∆V = 12 V
R
12
= R
1
+ R
2
= 2.5 Ω+3.5 Ω=6.0 Ω
R
123
=
R
1
12
+
R
1
3
−1
=
6.0
1
Ω
+
3.0
1
Ω
−1
R
123
=
0.17
Ω
1
+ 0.33
Ω
1
−1
=
0.50
Ω
1
−1
= 2.0 Ω
R
45
=
R
1
4
+
R
1
5
−1
=
4.0
1
Ω
+
1.0
1
Ω
−1
R
45
=
0.25
Ω
1
+ 1.0
Ω
1
−1
=
1.2
Ω
1
−1
= 0.83 Ω
R
eq
= R
123
+ R
45
= 2.0 Ω+0.83 Ω=
I =
∆
R
V
=
2
1
.
2
8
V
Ω
= 4.3 A
2.8 Ω
2. ∆V = 24 V
R
1
= 2.0 Ω
R
2
= 4.0 Ω
R
3
= 6.0 Ω
R
4
= 3.0 Ω
R
12
= R
1
+ R
2
= 2.0 Ω+4.0 Ω=6.0 Ω
R
34
=
R
1
3
+
R
1
4
−1
=
6.0
1
Ω
+
3.0
1
Ω
−1
R
34
=
0.17
Ω
1
+ 0.33
Ω
1
−1
=
0.50
Ω
1
−1
= 2.0 Ω
R
eq
=
R
1
12
+
R
1
34
−1
=
6.0
1
Ω
+
2.0
1
Ω
−1
R
eq
=
0.17
Ω
1
+ 0.50
Ω
1
−1
=
0.67
Ω
1
−1
= 1.5 Ω
I =
R
∆
e
V
q
=
1
2
.
4
5
V
V
= 16 A
Holt Physics Solutions ManualII Ch. 18–4
II
4. ∆V = 1.00 × 10
3
V
R
1
= 1.5 Ω
R
2
= 3.0 Ω
R
3
= 1.0 Ω
R
12
=
R
1
1
+
R
1
2
−1
=
1.5
1
Ω
+
3.0
1
Ω
−1
R
12
=
0.67
Ω
1
+ 0.33
Ω
1
−1
=
1.00
Ω
1
−1
= 1.00 Ω
R
eq
= R
12
+ R
3
= 1.00 Ω+1.0 Ω=
P =
(∆
R
V
eq
)
2
=
(1.00
2
×
.0
1
Ω
0
3
V)
2
= 5.0 × 10
5
W
2.0 Ω
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
5. ∆V = 2.00 × 10
3
V
I = 1.0 × 10
−8
A
R
1
= r
R
2
= 3r
R
3
= 2r
R
4
= 4r
R
eq
=
∆
I
V
=
2
1
.
.
0
0
0
×
×
1
1
0
0
−
3
8
A
V
=
R
12
= R
1
+ R
2
= r + 3r = 4r
R
34
= R
3
+ R
4
= 2r + 4r = 6r
R
eq
=
R
1
12
+
R
1
34
−1
=
4
1
r
+
6
1
r
−1
R
eq
=
3
1
+
2r
2
−1
=
1
5
2r
−1
=
1
5
2
r
r =
1
5
2
R
eq
=
1
5
2
(2.0 × 10
11
Ω) = 8.3 × 10
10
Ω
2.0 × 10
11
Ω
1. R = 8.1 × 10
−2
Ω
R
eq
= 0.123 Ω
∆V = 220 V
R
12
= R
45
= 0.16 Ω
R
12345
= 0.042 Ω
a. I =
R
∆
e
V
q
=
0
2
.1
2
2
0
3
V
Ω
= 1800 A
∆V
12345
= IR
12345
= (1800 A)(0.042 Ω) = 76 V
∆V
3
=∆V
12345
=
I
3
=
∆
R
V
3
3
=
8.1 ×
76
10
V
−2
Ω
= 9.4 × 10
2
A
76 V
Additional Practice D
6. P = 6.0 × 10
5
W
∆V = 220 V
R =
(∆
P
V)
2
=
6.
(
0
22
×
0
1
V
0
5
)
2
W
=
R
12
= R
45
= 2R = 2(0.081 Ω) = 0.16 Ω
R
12345
=
R
1
12
+
R
1
3
+
R
1
45
−1
=
0.1
1
6 Ω
+
0.08
1
1 Ω
+
0.1
1
6 Ω
−1
R
12345
=
6.2
Ω
1
+ 12
Ω
1
+ 6.2
Ω
1
−1
=
24
Ω
1
−1
= 0.042 Ω
R
eq
= R
12345
+ R
6
= 0.042 Ω+0.081 Ω=0.123 Ω
P =
(∆
R
V
eq
)
2
=
(
0
2
.
2
1
0
23
V
Ω
)
2
= 3.9 × 10
5
W
8.1 × 10
−2
Ω
Section Two—Problem Workbook Solutions
II Ch. 18–5
II
b. ∆V
12
=∆V
12345
= 76 V
I
12
=
∆
R
V
12
12
=
0
7
.1
6
6
V
Ω
= 4.8 × 10
2
A
I
2
= I
12
=
∆V
2
= I
2
R
2
= (4.8 × 10
2
A)(8.1 × 10
−2
Ω) =
c. Same as part b:
I
4
=
∆V
4
= 39 V
4.8 × 10
2
A
39 V
4.8 × 10
2
A
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. ∆V = 12 V
R
1
= 2.5 Ω
R
3
= 3.0 Ω
R
4
= 4.0 Ω
R
5
= 1.0 Ω
R
12
= 6.0 Ω
R
123
= 2.0 Ω
R
45
= 0.83 Ω
R
eq
= 2.8 Ω
I = 4.3 A
a. ∆V
45
= IR
45
= (4.3 A)(0.83 Ω) = 3.6 V
∆V
5
=∆V
45
=
I
5
=
∆
R
V
5
5
=
1
3
.
.
0
6
Ω
V
=
b. ∆V
123
= IR
123
= (4.3 A)(2.0 Ω) = 8.6 V
∆V
12
=∆V
123
= 8.6 V
I
1
= I
12
=
∆
R
V
1
1
2
2
=
6
8
.
.
0
6
Ω
V
=
∆V
1
= I
1
R
1
= (1.4 A)(2.5 Ω) =
c. I
45
= I = 4.3 A
∆V
45
= I
45
R
45
= (4.3 A)(0.83 Ω) = 3.6 V
V
4
=∆V
45
=
I
4
=
∆
R
V
4
4
=
4
3
.
.
0
6
Ω
V
=
d. ∆V
3
=∆V
123
=
I
3
=
∆
R
V
3
3
=
3
8
.
.
0
6
Ω
V
= 2.9 A
8.6 V
0.90 V
3.6 V
3.5 V
1.4 A
3.1 A
3.6 V
II
3. R
1
= 15 Ω
R
2
= 3.0 Ω
R
3
= 2.0 Ω
R
4
= 5.0 Ω
R
5
= 7.0 Ω
R
6
= 3.0 Ω
R
7
= 3.0 × 10
1
Ω
∆V = 2.00 × 10
3
V
R
23
= R
2
+ R
3
= 3.0 Ω+2.0 Ω=5.0 Ω
R
234
=
R
1
23
+
R
1
4
−1
=
5.0
1
Ω
+
5.0
1
Ω
−1
R
234
=
0.40
Ω
1
−1
= 2.5 Ω
R
56
= R
5
+ R
6
= 7.0 Ω+3.0 Ω=10.0 Ω
R
567
=
R
1
56
+
R
1
7
−1
=
10.
1
0 Ω
+
30
1
Ω
−1
R
567
=
0.100
Ω
1
+ 0.033
Ω
1
−1
=
0.133
Ω
1
−1
= 7.52 Ω
R
eq
= R
1
+ R
234
+ R
567
= 15 Ω+2.5 Ω+7.52 Ω=25 Ω
a. I =
R
∆
e
V
q
=
2.00
2
×
5 Ω
10
3
V
= 80 A
∆V
234
= IR
234
= (80 A)(2.5 Ω) = 2.0 × 10
2
V
∆V
4
=∆V
234
=
I
4
=
∆
R
V
4
4
=
2
5
0
.0
0
Ω
V
=
b. ∆V
23
=∆V
234
= 200 V
I
23
=
∆
R
V
23
23
=
2
5
0
.0
0
Ω
V
= 40 A
I
3
= I
23
=
∆V
3
= I
3
R
3
= (40 A)(2.0 Ω) =
c. I
567
= I = 80 A
V
567
= I
567
R
567
= (80 A)(7.52 Ω) = 600 V
∆V
56
=∆V
567
= 600 V
I
56
=
∆
R
V
56
56
=
1
6
0
0
.
0
0
V
Ω
= 60 A
I
5
= I
56
=
∆V
5
= I
5
R
5
= (60 A)(7.0 Ω) =
d. ∆V
7
=∆V
567
=
I
7
=
∆
R
V
7
7
=
6
3
0
0
0
Ω
V
= 2.0 × 10
1
A
6.0 × 10
2
V
4.2 × 10
2
V
6.0 × 10
1
A
8.0 × 10
1
V
4.0 × 10
1
A
4.0 × 10
1
A
2.0 × 10
2
V
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solutions ManualII Ch. 18–6
Magnetism
Problem Workbook Solutions
II
1. B = 45 T
v = 7.5 × 10
6
m/s
q = e = 1.60 × 10
−19
C
m
e
= 9.109 × 10
−31
kg
F
magnetic
= qvB
F
magnetic
= (1.60 × 10
−19
C)(7.5 × 10
6
m/s)(45 T)
F
magnetic
= 5.4 × 10
−11
N
Additional Practice A
Givens Solutions
Copyright © Holt, Rinehart and Winston. All rights reserved.
2. q = 12 × 10
−9
C
v = 450 km/h
B = 2.4 T
F
magnetic
= qvB
F
magnetic
= (12 × 10
−9
C)(450 km/h)
36
1
0
h
0 s
1
1
0
k
3
m
m
(2.4 T)
F
magnetic
=
3.6 × 10
−6
N
3. v = 350 km/h
q = 3.6 × 10
−8
C
B = 7.0 × 10
−5
T
q = 30.0°
F
magnetic
= qvB = q[v (sin q)]B
F
magnetic
= (3.6 × 10
−8
C)(350 km/h)
36
1
0
h
0s
1
1
0
k
3
m
m
(sin 30.0°)(7.0 × 10
−5
T)
F
magnetic
= 1.2 × 10
−10
N
4. v = 2.60 × 10
2
km/h
F
magnetic
= 3.0 × 10
−17
N
q = 1.60 × 10
−19
C
F
magnetic
= qvB
B =
F
ma
q
g
v
netic
B =
B = 2.6 T
(3.0 × 10
−17
N)
(1.60 × 10
−19
C)(2.60 × 10
2
km/h)
36
1
0
h
0 s
1
1
0
k
3
m
m
Section Two—Problem Workbook Solutions II Ch. 19–1
II
5. q = 1.60 × 10
−19
C
v = 60.0 km/h
F
magnetic
= 2.0 × 10
−22
N
F
magnetic
= qvB
B =
F
ma
q
g
v
netic
B =
B = 7.5 × 10
−5
T
(2.0 × 10
−22
N)
(1.60 × 10
−19
C)(60.0 km/h)
36
1
0
h
0 s
1
1
0
k
3
m
m
Givens Solutions
Copyright © Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualII Ch. 19–2
6. q = 88 × 10
−9
C
B = 0.32 T
F
magnetic
= 1.25 × 10
−6
N
F
magnetic
= qvB
v =
F
m
q
ag
B
netic
v =
v = 44 m/s = 160 km/h
(1.25 × 10
−6
N)
(88 × 10
−9
C)(0.32 T)
7. q = 1.60 × 10
−19
C
B = 6.4 T
F
magnetic
= 2.76 × 10
−16
N
∆x = 4.0 × 10
3
m
v
i
= 0 m/s
v
f
= 270 m/s
a. F
magnetic
= qvB
v =
F
m
q
ag
B
netic
v =
v =
b. ∆x =
(v
f
2
+ v
i
)
∆t
∆t =
(v
f
2∆
+
x
v
i
)
∆t =
(2
2
7
(
0
4.
m
0
/
×
s
1
+
0
0
3
m
m
/
)
s)
∆t = 3.0 × 10
1
s
2.7 × 10
2
m/s = 9.7 × 10
2
km/h
(2.76 × 10
−16
N)
(1.60 × 10
−19
C)(6.4 T)
8. B = 0.600 T
q = 1.60 × 10
−19
C
v = 2.00 × 10
5
m/s
m
1
= 9.98 × 10
−27
kg
m
2
= 11.6 × 10
−27
kg
a. F
magnetic
= qvB
F
magnetic
= (1.60 × 10
−19
C)(2.00 × 10
5
m/s)(0.600 T)
F
magnetic
=
b. F
c,1
=
m
r
1
1
v
2
= F
magnetic
F
c,2
=
m
r
2
2
v
2
= F
magnetic
r
1
=
F
m
m
a
1
g
v
ne
2
tic
r
2
=
F
m
m
a
2
g
v
ne
2
tic
1.92 × 10
−14
N
Section Two—Problem Workbook Solutions II Ch. 19–3
II
r
1
=
r
1
= 2.08 × 10
−2
m
r
2
=
r
2
= 2.42 × 10
−2
m
r
2
− r
1
= 3.40 × 10
−3
m = 3.4 mm
(11.6 × 10
−27
kg)(2.00 × 10
5
m/s)
2
(1.92 × 10
−14
N)
(9.98 × 10
−27
kg)(2.00 × 10
5
m/s)
2
(1.92 × 10
−14
N)
Givens Solutions
Copyright © Holt, Rinehart and Winston. All rights reserved.
1. B = 22.5 T
l
= 12 × 10
−2
m
I = 8.4 × 10
−2
A
F
magnetic
= BI
l
F
magnetic
= (22.5 T)(8.4 × 10
−2
A)(12 × 10
−2
m)
F
magnetic
= 0.23 N
Additional Practice B
2.
l
= 1066 m
F
magnetic
= 6.3 × 10
−2
N
I = 0.80 A
F
magnetic
= BI
l
B =
B =
(0
(
.
6
8
.
0
3
A
×
)
1
(1
0
0
−
6
2
6
N
m
)
)
B = 7.4 × 10
−5
T
F
magnetic
I
l
3.
l
= 5376 m
F
magnetic
= 3.1 N
I = 12 A
q = 38°
F
magnetic
= BI
l
= [B(sin q)]I
l
B =
B =
B = 7.8 × 10
−5
T
(3.1 N)
(12 A)(5376 m)(sin 38.0°)
F
magnetic
I
l
(sin q)
4.
l
= 21.0 × 10
3
m
B = 6.40 × 10
−7
T
F
magnetic
= 1.80 × 10
−2
N
F
magnetic
= BI
l
I =
I =
I = 1.34 A
(1.80 × 10
−2
N)
(6.40 × 10
−7
T)(21.0 × 10
3
m)
F
magnetic
B
l
Holt Physics Solution ManualII Ch. 19–4
II
5. B = 2.5 × 10
−4
T
l
= 4.5 × 10
−2
m
F
magnetic
= 3.6 × 10
−7
N
F
magnetic
= BI
l
I =
I =
I = 3.2 10
–2
A
(3.6 × 10
−7
N)
(2.5 × 10
−4
T)(4.5 × 10
−2
m)
F
magnetic
B
l
Givens Solutions
Copyright © Holt, Rinehart and Winston. All rights reserved.
6. F
magnetic
= 5.0 × 10
5
N
B = 3.8 T
I = 2.00 × 10
2
A
F
magnetic
= BI
l
l
=
F
ma
B
g
I
netic
l
=
l
= 6.6 × 10
2
m
(5.0 × 10
5
N)
(3.8 T)(2.00 × 10
2
A)
7. F
magnetic
= 16.1 N
B = 6.4 × 10
−5
T
I = 2.8 A
F
magnetic
= BI
l
l
=
F
ma
B
g
I
netic
l
=
l
= 9.0 × 10
4
m
(16.1 N)
(6.4 × 10
−5
T)(2.8 A)
8. B = 0.040 T
I = 0.10 A
q = 45°
l
= 55 cm 0.55 m
F
magnetic
= BI
l
= [B(sin q)]I
l
F
magnetic
= (0.040 T)(sin 45°)(0.10 A)(0.55 m)
F
magnetic
= 1.6 × 10
−3
Ν
9. B = 38 T
l
= 2.0 m
m = 75 kg
g = 9.81 m/s
2
F
magnetic
= BI
l
F
g
= mg
F
magnetic
= F
g
BI
l
= mg
I =
I =
(75
(3
k
8
g
T
)(
)
9
(
.
2
8
.
1
0
m
m
/
)
s
2
)
I = 9.7 A
mg
B
l
II
10.
l
= 478 × 10
3
m
F
magnetic
= 0.40 N
B = 7.50 × 10
−5
T
F
magnetic
= BI
l
I =
I =
I = 1.1 × 10
−2
A
(0.40 N)
(7.50 × 10
−5
T)(478 × 10
3
m)
F
magnetic
B
l
Givens Solutions
Copyright © Holt, Rinehart and Winston. All rights reserved.
Section Two—Problem Workbook Solutions II Ch. 19–5
II
Copyright © Holt, Rinehart and Winston. All rights reserved.
Section Two—Problem Workbook Solutions II Ch. 20–1
1. A
i
= 6.04 × 10
5
m
2
A
f
=
1
2
(6.04 × 10
5
m
2
)
B = 6.0 × 10
−5
T
emf = 0.80 V
N = 1 turn
q = 0.0°
emf =−N =
∆t =∆A
∆t = (A
f
− A
i
)
∆t = (6.04 × 10
5
m
2
)
1
2
− 1
∆t = 23 s
−(1)(6.0 × 10
−5
T)(cos 0.0°)
(0.80 V)
−NB cos q
emf
−NB cos q
emf
−N∆[AB cos q]
∆t
∆Φ
M
∆t
Additional Practice A
Givens Solutions
4. A
f
= 3.2 × 10
4
m
2
A
i
= 0.0 m
2
∆t = 20.0 min
B = 4.0 × 10
−2
T
N = 300 turns
q = 0.0°
emf =−N ==−NB cos q = (A
f
− A
i
)
emf = [(3.2 × 10
4
m
2
) − (0.0 m
2
)]
emf =−3.2 × 10
2
V
−(300)(4.0 × 10
−2
T)(cos 0.0°)
(20.0 min)
1
6
m
0
i
s
n
−NB cos q
∆t
∆A
∆t
−N∆[AB cos q]
∆t
∆Φ
M
∆t
2. r =
100
2
.0 m
= 50.0 m
B
i
= 0.800 T
B
f
= 0.000 T
q = 0.00°
emf = 46.7 V
N = 1 turn
emf =−N =
∆t =−NA cos q =
∆t =
∆t = 135 s
−(1)(p)(50.0 m)
2
(cos 0.0°)(0.000 T − 0.800 T)
(46.7 V)
−N(pr
2
)(cos q)(B
f
− B
i
)
emf
∆B
emf
−N∆[AB cos q]
∆t
∆Φ
M
∆t
Electromagnetic
Induction
Problem Workbook Solutions
3. emf = 32.0 × 10
6
V
B
i
= 1.00 × 10
3
T
B
f
= 0.00 T
A = 4.00 × 10
−2
m
2
N = 50 turns
q = 0.00°
emf =−N =
∆t =−NA cos q =
∆t =
∆t = 6.3 × 10
−5
s
−(50)(4.00 × 10
−2
m
2
)(cos 0.00°)[(0.00 T) − (1.00 × 10
3
T)]
(32.0 × 10
6
V)
−NAcos q(B
f
− B
i
)
emf
∆B
emf
−N∆[AB cos q]
∆t
∆Φ
M
∆t
II
Copyright © Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualII Ch. 20–2
5. B
i
= 8.0 × 10
−15
T
B
f
= 10 B
i
= 8.0 × 10
−14
T
∆t = 3.0 × 10
−2
s
A = 1.00 m
2
emf =−1.92 × 10
−11
V
q = 0.0°
emf =−N =
N ==
N =
N = 8 turns
−(−1.92 × 10
−11
V)(3.0 × 10
−2
s)
(1.00 m
2
)(cos 0.0°)[(8.0 × 10
−14
T) − (8.0 × 10
−15
T)]
−(emf)(∆t)
A cos q(B
f
− B
i
)
−(emf)(∆t)
A cos q ∆B
−N∆[AB cos q]
∆t
∆Φ
M
∆t
6. B
i
= 0.50 T
B
f
= 0.00 T
N = 880 turns
∆t = 12 s
emf = 147 V
q = 0.0°
emf =−N ==−NA cos q
∆
∆
B
t
A ==
A =
A = 4.0 m
2
−(147 V)(12 s)
(880)(cos 0.0°)(0.00 T − 0.50 T)
−(emf)(∆t)
N cos q (B
f
− B
i
)
−(emf)(∆t)
N cos q ∆B
−N∆[AB cos q]
∆t
Φ
M
∆t
Givens Solutions
1. ∆V
rms
= 120 V
R = 6.0 × 10
−2
Ω
= 0.707
1
2
a. I
rms
=
∆V
R
rms
I
rms
=
(6.0
(1
×
2
1
0
0
V
−2
)
Ω)
I
rms
=
b. I
max
= (I
rms
)
2
I
max
=
(2.0
(0
×
.7
1
0
0
7
3
)
A)
I
max
=
c. P = (I
rms
)(∆V
rms
)
P = (2.0 × 10
3
A)(120 V)
P = 2.4 × 10
5
W
2.8 × 10
3
A
2.0 × 10
3
A
Additional Practice B
Section Two—Problem Workbook Solutions II Ch. 20–3
II
Copyright © Holt, Rinehart and Winston. All rights reserved.
2. P = 10.0(Acoustic power)
Acoustic power =
30.8 × 10
3
W
∆V
rms
= 120.0 V
= 0.707
1
2
P =∆V
rms
I
rms
I
rms
=
∆V
P
rms
I
rms
=
I
ma
2
x
I
ma
2
x
=
∆V
P
rms
I
max
=
∆
P
V
rm
2
s
I
max
=
I
max
= 3.63 × 10
3
A
(10.0)(30.8 × 10
3
W)
(120.0 V)(0.707)
Givens Solutions
3. P = 1.325 × 10
8
W
∆V
rms
= 5.4 × 10
4
V
= 0.707
1
2
P =∆V
rms
I
rms
= (I
rms
)
2
R =
(∆V
R
rms
)
2
I
rms
=
I
ma
2
x
I
max
=
2
I
rms
=
∆
V
2
rm
P
s
I
max
=
I
max
=
R =
(∆V
P
rms
)
2
R =
(1
(5
.3
.4
25
×
×
10
1
4
0
8
V
W
)
2
)
R = 22 Ω
3.5 × 10
3
A
1.325 × 10
8
W
(5.4 × 10
4
V)(0.707)
4. ∆V
rms
= 1.024 × 10
6
V
I
rms
= 2.9 × 10
−2
A
= 0.707
1
2
∆V
max
=∆V
rms
2
∆V
max
=
(1.02
(0
4
.7
×
0
1
7
0
)
6
V)
∆V
max
=
I
max
= I
rms
2
I
max
=
(2.9
(0
×
.7
1
0
0
7
−
)
2
A)
I
max
= 4.1 × 10
−2
A
1.45 × 10
6
V = 1.45 MV
Holt Physics Solution ManualII Ch. 20–4
II
Copyright © Holt, Rinehart and Winston. All rights reserved.
R =
∆
I
V
m
m
ax
ax
=
∆
I
V
rm
rm
s
s
R =
(
(
0
3
.
2
8
0
0
V
A
)
)
=
(
(
0
2
.
3
5
0
7
V
A
)
)
R = 4.0 × 10
2
Ω
Givens Solutions
6. I
max
= 75 A
R = 480 Ω
= 0.707
1
2
∆V
rms
=
∆V
m
2
ax
∆V
max
= (I
max
)(R)
∆V
rms
=
I
m
a
2
x
R
∆V
rms
= (75 A)(480 Ω)(0.707)
∆V
rms
= 2.5 × 10
4
V = 25 kV
7. P
tot
= 6.2 × 10
7
W
P
tot
= 24 P
R = 1.2 × 10
5
Ω
= 0.707
1
2
P = (I
rms
)
2
R =
P
2
t
4
ot
P =
6.2 ×
2
1
4
0
7
W
P =
I
rms
=
R
P
I
rms
=
(
(
2
1
.
.
6
2
×
×
1
1
0
0
6
5
W
Ω
)
)
I
rms
=
I
max
=
2
I
rms
I
max
=
0
4
.
.
7
7
0
A
7
I
max
= 6.6 A
4.7 A
2.6 × 10
6
W = 2.6 MW
5. ∆V
max
= 320 V
I
max
= 0.80 A
= 0.707
1
2
∆V
rms
=
∆V
m
2
ax
∆V
rms
= (320 V)(0.707)
∆V
rms
=
I
rms
=
I
ma
2
x
I
rms
= (0.80 A)(0.707)
I
rms
= 0.57 A
2.3 × 10
2
V
Section Two—Problem Workbook Solutions II Ch. 20–5
II
Copyright © Holt, Rinehart and Winston. All rights reserved.
1. N
1
= 5600 turns
N
2
= 240 turns
∆V
2
= 4.1 × 10
2
V
∆V
1
=∆V
2
N
N
1
2
∆V
1
=(4.1 × 10
3
V)
5
2
6
4
0
0
0
∆V
1
= 9.6 × 10
4
V = 96 kV
Additional Practice C
Givens Solutions
2. N
1
= 74 turns
N
2
= 403 turns
∆V
2
= 650 V
∆V
1
=∆V
2
N
N
1
2
∆V
1
= (650 V)
4
7
0
4
3
∆V
1
= 120 V
4. ∆V
1
= 765 × 10
3
V
∆V
2
= 540 × 10
3
V
N
1
= 2.8 × 10
3
turns
∆
∆
V
V
1
2
=
N
N
2
1
N
2
=
∆
∆
V
V
1
2
N
1
N
2
=
5
7
4
6
0
5
×
×
1
1
0
0
3
3
V
V
(2.8 × 10
3
)
N
2
= 2.0 × 10
3
turns
3. ∆V
1
= 2.0 × 10
−2
V
N
1
= 400 turns
N
2
= 3600 turns
∆V
2
= 2.0 × 10
−2
V
∆V
2
=∆V
1
N
N
2
1
∆V
2
= (2.0 × 10
−2
V)
3
4
6
0
0
0
0
∆V
2
=
∆V
1
=∆V
2
N
N
1
2
∆V
1
= (2.0 × 10
−2
V)
3
4
6
0
0
0
0
∆V
1
= 2.2 × 10
−3
V
0.18 V
Holt Physics Solution ManualII Ch. 20–6
II
Copyright © Holt, Rinehart and Winston. All rights reserved.
N
N
1
2
=
∆
∆
V
V
2
1
N
1
= N
2
∆
∆
V
V
1
2
N
1
= (660)
1
2
2
2
0
0
V
V
N
1
= 360 turns
Givens Solutions
6. P = 20.0 W
∆V
1
= 120 V
N
N
1
2
= 0.36
a. P = (∆V
1
)(I
1
)
I
1
=
∆
P
V
1
=
(
(
2
1
0
2
.0
0
W
V)
)
I
1
=
b.
∆
∆
V
V
1
2
=
N
N
2
1
∆V
2
=
N
N
2
1
∆V
1
∆V
2
=
0.
1
36
(120 V)
∆V
2
= 3.3 × 10
2
V
0.17 A
5. ∆V
1
= 230 × 10
3
V
∆V
2
= 345 × 10
3
V
N
1
= 1.2 × 10
4
turns
N
N
1
2
=
∆
∆
V
V
2
1
N
2
= N
1
∆
∆
V
V
2
1
N
2
= (1.2 × 10
4
)
3
2
4
3
5
0
×
×
1
1
0
0
3
3
V
V
N
2
= 1.8 × 10
4
turns
7. ∆V
1
= 120 V
∆V
2
= 220 V
I
2
= 30.0 A
N
2
= 660 turns
P
1
= P
2
∆V
1
I
1
=∆V
2
I
2
I
1
=
∆
∆
V
V
2
1
I
2
I
1
=
2
1
2
2
0
0
V
V
(30.0 A)
I
1
= 55 A
II
Copyright © Holt, Rinehart and Winston. All rights reserved.
Section Two—Problem Workbook Solutions II Ch. 21–1
1. E = 1.29 × 10
−15
J
C = 3.00 × 10
8
m/s
h = 6.63 × 10
−34
J
•
s
l =
h
E
c
=
l = 1.54 × 10
−10
m = 0.154 nm
(6.63 × 10
−34
J
•
s)(3.00 × 10
8
m/s)
1.29 × 10
−15
J
Additional Practice A
Givens Solutions
2. E = 6.6 × 10
−19
J
C = 3.00 × 10
8
m/s
h = 6.63 × 10
−34
J
•
s
l =
h
E
c
=
l = 3.0 × 10
−7
m
(6.63 × 10
−34
J
•
s)(3.00 × 10
8
m/s)
6.6 × 10
−19
J
3. E = 5.92 × 10
−6
eV
C = 3.00 × 10
8
m/s
h = 6.63 × 10
−34
J
•
s
l =
h
E
c
=
l = 0.210 m
(6.63 × 10
−34
J
•
s)(3.00 × 10
8
m/s)
(5.92 × 10
−6
eV)(1.60 × 10
−19
J/eV)
Atomic Physics
4. E = 2.18 × 10
−23
J
h = 6.63 × 10
−34
J
•
s
E = hf
f =
E
h
f =
6
2
.6
.1
3
8
×
×
1
1
0
0
−
−
34
23
J
J
•
s
f = 3.29 × 10
10
Hz
Problem Workbook Solutions
5. E = 1.85 × 10
−23
J
h = 6.63 × 10
−34
J
•
s
f =
E
h
=
6
1
.6
.8
3
5
×
×
1
1
0
0
−
−
3
2
4
3
J/
J
s
= 2.79 × 10
10
Hz
6. f = 9 192 631 770 s
−1
h = 6.626 0755 × 10
−34
J
•
s
1 eV = 1.602 117 33 × 10
−19
J
E = hf
E =
E = 3.801 9108 × 10
−5
eV
(6.626 0755 × 10
−34
J
•
s)(9 192 631 770 s
−1
)
1.602 117 33 × 10
−19
J/eV
7. l = 92 cm = 92 × 10
−2
m
c = 3.00 × 10
8
m/s
h = 6.63 × 10
−34
J
•
s
h = 4.14 × 10
−15
eV
•
s
f =
l
c
f =
3.
9
0
2
0
×
×
1
1
0
0
−
8
2
m
m
/s
f =
E = hf
3.3 × 10
8
Hz = 330 MHz
II
Copyright © Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualII Ch. 21–2
Givens Solutions
8. v = 1.80 × 10
−17
m/s
∆t = 1.00 year
l =∆x
c = 3.00 × 10
8
m/s
h = 6.63 × 10
−34
J
•
s
∆x = v∆t
∆x = (1.80 × 10
−17
m/s)(1.00 year)
365
1
.2
y
5
ea
d
r
ays
1
24
da
h
y
36
1
0
h
0s
∆x =
E = hf =
h
l
c
=
∆
h
x
c
E =
E = 3.50 × 10
−16
J
(6.63 × 10
−34
J
•
s)(3.00 × 10
8
m/s)
5.68 × 10
−10
m
5.68 × 10
−10
m
E = (6.63 × 10
−34
J
•
s)(3.3 × 10
8
Hz)
E =
E = (4.14 × 10
−15
eV
•
s)(3.3 × 10
8
Hz)
E = 1.4 × 10
−6
eV
2.2 × 10
−25
J
Additional Practice B
1. hf
t
= 4.5 eV
KE
max
= 3.8 eV
h = 4.14 × 10
−15
eV
•
s
f =
[KE
ma
h
x
+ hf
t
]
=
4
[3
.1
.8
4
e
×
V
10
+
−
4
1
.
5
5
e
e
V
V
•
]
s
= 2.0 × 10
15
Hz
2. hf
t
= 4.3 eV
KE
max
= 3.2 eV
h = 4.14 × 10
−15
eV
•
s
KE
max
= hf − hf
t
f =
KE
ma
h
x
+ hf
t
f =
4.
3
1
.
4
2
×
eV
10
+
−
4
15
.3
e
e
V
V
•
s
f = 1.8 × 10
15
Hz
3. hf
t,Cs
= 2.14 eV
hf
t,Se
= 5.9 eV
h = 4.14 × 10
−15
eV
•
s
c = 3.00 × 10
8
m/s
KE
max
= 0.0 eV for both
cases
a. KE
max
= hf − hf
t
= 0.0 eV =
h
l
c
− hf
t
l =
h
h
f
c
t
l
Cs
=
hf
h
t,
c
Cs
=
l
Cs
=
b. l
Se
=
hf
h
t,
c
Se
=
l
Se
= 2.1 × 10
−7
m = 2.1 × 10
2
nm
(4.14 × 10
−15
eV
•
s)(3.00 × 10
8
m/s)
5.9 eV
5.80 × 10
−7
m = 5.80 × 10
2
nm
(4.14 × 10
−15
eV
•
s)(3.00 × 10
8
m/s)
2.14 eV
Section Two—Problem Workbook Solutions II Ch. 21–3
II
Copyright © Holt, Rinehart and Winston. All rights reserved.
4. l = 2.00 × 10
2
nm =
2.00 × 10
−7
m
v = 6.50 × 10
5
m/s
m
e
= 9.109 × 10
−31
kg
c = 3.00 × 10
8
m/s
h = 4.14 × 10
−15
eV
•
s
KE
max
=
1
2
m
e
v
2
= hf − hf
t
1
2
m
e
v
2
=
h
l
c
− hf
t
hf
t
=
h
l
c
−
1
2
m
e
v
2
hf
t
=−
hf
t
= 6.21 eV − 1.20 eV
hf
t
=
f
t
=
4.14 ×
5.0
1
1
0
−
e
1
V
5
eV
•
s
= 1.21 × 10
15
Hz
5.01 eV
(0.5)(9.109 × 10
−31
kg)(6.50 × 10
5
m/s)
2
1.60 × 10
−19
J/eV
(4.14 × 10
−15
eV
•
s)(3.00 × 10
8
m/s)
2.00 × 10
−7
m
6. l = 2.00 × 10
2
nm =
2.00 × 10
−7
m
KE
max
= 0.46 eV
h = 4.14 × 10
−15
eV
•
s
c = 3.00 × 10
8
m/s
KE
max
= hf − hf
t
hf
t
= hf − KE
max
=
h
l
c
− KE
max
hf
t
=−0.46 eV
hf
t
= 6.21 eV − 0.46 eV
hf
t
=
f
t
=
4.14 ×
5.
1
8
0
e
−
V
15
eV
•
s
= 1.4 × 10
15
Hz
5.8 eV
(4.14 × 10
−15
eV
•
s)(3.00 × 10
8
m/s)
2.00 × 10
−7
m
7. l = 589 nm = 589 × 10
−9
m
hf
t
= 2.3 eV
c = 3.00 × 10
8
m/s
h = 4.14 × 10
−15
eV
•
s
KE
max
= hf − hf
t
=
h
l
c
− hf
t
KE
max
=−2.3 eV
KE
max
= 2.11 eV − 2.3 eV
KE
max
=
No. The photons in the light produced by sodium vapor need 0.2 eV more energy
to liberate photoelectrons from the solid sodium.
−0.2 eV
(4.14 × 10
−15
eV
•
s)(3.00 × 10
8
m/s)
589 × 10
−9
m
5. f = 2.2 × 10
15
Hz
KE
max
= 4.4 eV
h = 4.14 × 10
−15
eV
•
s
KE
max
= hf − hf
t
hf
t
= hf − KE
max
hf
t
= (4.14 × 10
−15
eV
•
s)(2.2 × 10
15
Hz) − 4.4 eV
hf
t
= 9.1 eV − 4.4 eV =
f
t
=
4.14 ×
4
1
.7
0
−
e
1
V
5
eV
•
s
= 1.1 × 10
15
Hz
4.7 eV
Givens Solutions
Holt Physics Solution ManualII Ch. 21–4
II
Copyright © Holt, Rinehart and Winston. All rights reserved.
8. hf
t
= 2.3 eV
l = 410 nm = 4.1 × 10
−7
m
h = 4.14 × 10
−15
eV
•
s
c = 3.00 × 10
8
m/s
Givens Solutions
9. hf
t,Zn
= 4.3 eV
hf
t,Pb
= 4.1 eV
KE
max,Zn
= 0.0 eV
m
e
= 9.109 × 10
−31
kg
KE
max
= hf − hf
t
KE
max,Pb
= hf − hf
t,Pb
= (KE
max,Zn
+ hf
t,Zn
) − hf
t,Pb
KE
max,Pb
=
1
2
m
e
v
2
1
2
m
e
v
2
= (KE
max,Zn
+ hf
t,Zn
) − hf
t,Pb
v =
v =
v =
9
.1
(
0
2
9
)
(
×
0
.
1
2
0
e
−
V
31
)
k
g
1
.6
0
1
×
e
1
V
0
−
19
J
= 3 × 10
5
m/s
1.60 × 10
−19
J
1 eV
(2)(0.0 eV + 4.3 eV − 4.1 eV)
9.109 × 10
−31
kg
2(KE
max,Zn
+ hf
t,Zn
− hf
t,Pb
)
m
e
KE
max
=
h
l
c
− hf
t
KE =−2.3 eV
KE = 3.03 eV − 2.3 eV = 0.7 eV
(4.14 × 10
−15
eV
•
s)(3.00 × 10
8
m/s)
4.1 × 10
−7
m
1. l = 671.9 nm
E
final
= E
1
= 0 eV
E = E
initial
− E
final
= E
initial
− E
1
E =
h
l
c
E
initial
=
+ 0 eV
E
initial
= 1.85 eV + 0 eV =
The photon is produced by the transition of the electron from the E
2
energy level
to E
1
.
1.85 eV
1 eV
1.60 × 10
−19
J
10
9
nm
1 m
(6.63 × 10
−34
J
•
s)(3.00 × 10
8
m/s)
671.9 nm
Additional Practice C
2. E
initial
= E
4
= 5.24 eV
E
final
= E
1
= 0 eV
E = E
initial
− E
final
= E
4
− E
1
E =
h
l
c
l =
h
E
c
=
l =
l = 2.37 × 10
−7
m = 237 nm
1 eV
1.60 × 10
−19
J
(6.63 × 10
−34
J
•
s)(3.00 × 10
8
m/s)
5.24 eV − 0 eV
hc
E
4
− E
1
II
3. E
initial
= E
3
= 4.69 eV
E
final
= E
1
= 0 eV
E = E
initial
− E
final
= E
3
− E
1
E =
⎯
h
l
c
⎯
l =
⎯
h
E
c
⎯
=
l =
l = 2.65 × 10
−7
m = 265 nm
1 eV
⎯⎯
1.60 × 10
−19
J
(6.63 × 10
−34
J
•
s)(3.00 × 10
8
m/s)
⎯⎯⎯⎯
4.69 eV − 0 eV
hc
⎯
E
3
− E
1
Givens Solutions
Copyright © Holt, Rinehart and Winston. All rights reserved.
Section Two—Problem Workbook Solutions II Ch. 21–5
4. E
initial
= E
2
= 3.15 eV
E
final
= E
1
= 0 eV
E = E
initial
− E
final
= E
2
− E
1
E =
⎯
h
l
c
⎯
l =
⎯
h
E
c
⎯
=
l =
l = 3.95 × 10
−7
m = 395 nm
1 eV
⎯⎯
1.60 × 10
−19
J
(6.63 × 10
−34
J
•
s)(3.00 × 10
8
m/s)
⎯⎯⎯⎯
3.15 eV − 0 eV
hc
⎯
E
2
− E
1
1. v = 3.2 m/s
l = 3.0 × 10
−32
m
h = 6.63 × 10
−34
J
•
s
m =
⎯
l
h
v
⎯
==
2. l = 6.4 × 10
−11
m
6.9 × 10
−3
kg
6.63 × 10
−34
J
•
s
⎯⎯⎯
(3.0 × 10
−32
m)(3.2 m/s)
Additional Practice D
v = 64 m/s
h = 6.63 × 10
−34
J
•
s
mv =
⎯
l
h
⎯
m =
⎯
l
h
v
⎯
m =
m = 1.6 × 10
−25
kg
6.63 × 10
−34
J
•
s
⎯⎯⎯
(6.4 × 10
−11
m)(64 m/s)
3. q = (2)(1.60 × 10
−19
C) =
3.20 × 10
−19
C
ΔV = 240 V
h = 6.63 × 10
−34
J
•
s
l = 4.4 × 10
−13
m
KE = qΔV =
⎯
1
2
⎯
mv
2
m =
⎯
2q
V
Δ
2
V
⎯
v =
⎯
l
h
m
⎯
==1.0 × 10
5
m/s
m =
m = 1.5 × 10
−26
kg
2(3.20 × 10
−19
C)(240 V)
⎯⎯⎯
(1.0 × 10
5
m/s)
2
6.63 × 10
−34
J
•
s
⎯⎯⎯⎯
(4.4 × 10
−13
m)(1.5 × 10
−26
kg)
4. l = 2.5 nm = 2.5 × 10
−9
m
m
n
= 1.675 × 10
−27
kg
h = 6.63 × 10
−34
J
•
s
mv =
⎯
l
h
⎯
v =
⎯
lm
h
n
⎯
v =
v = 1.6 × 10
2
m/s
6.63 × 10
−34
J
•
s
⎯⎯⎯⎯
(2.5 × 10
−9
m)(1.675 × 10
−27
kg)
Givens Solutions
5. m = 7.65 × 10
−70
kg
l = 5.0 × 10
32
m
h = 6.63 × 10
−34
J
•
s
mv =
⎯
l
h
⎯
v =
⎯
l
h
m
⎯
v =
v = 1.7 × 10
3
m/s
6.63 × 10
−34
J
•
s
⎯⎯⎯⎯
(5.0 × 10
32
m)(7.65 × 10
−70
kg)
6. m = 1.6 g = 1.6 × 10
−3
kg
v = 3.8 m/s
h = 6.63 × 10
−34
J
•
s
mv =
⎯
l
h
⎯
l =
⎯
m
h
v
⎯
l =
l = 1.1 × 10
−31
m
6.63 × 10
−34
J
•
s
⎯⎯⎯
(1.6 × 10
−3
kg)(3.8 m/s)
7. Δx = 42 195 m
Δt = 3 h 47 min = 227 min
m = 0.080 kg
h = 6.63 × 10
−34
J
•
s
v =
⎯
Δ
Δ
x
t
⎯
==
⎯
l
h
⎯
= mv
l =
⎯
m
h
v
⎯
l =
l = 2.7 × 10
−33
m
6.63 × 10
−34
J
•
s
⎯⎯⎯
(0.080 kg)(3.10 m/s)
3.10 m/s
42 195 m
⎯⎯
(227 min)
⎯
1
6
m
0
i
s
n
⎯
Holt Physics Solution ManualII Ch. 21–6
II
Subatomic Physics
Problem Workbook Solutions
II
1. E = 610 TW
•
h
atomic mass of
1
2
H =
2.014 102 u
atomic mass of
26
56
Fe =
55.934 940 u
atomic mass of
226
88
Ra =
226.025 402 u
a. ∆m =
c
E
2
=
∆m =
b. n =
atomic
∆
m
m
ass of
1
2
H
=
n =
c. n ==
n =
d. n ==
n = 6.4 × 10
25 226
88
Ra nuclei
24 kg
(1.66 × 10
−27
kg/u)(226.025 402 u)
∆m
atomic mass of
226
88
Ra
2.6 × 10
26
26
56
Fe nuclei
24 kg
(1.66 × 10
−27
kg/u)(55.934 940 u)
∆m
atomic mass of
26
56
Fe
7.2 × 10
27
1
2
H nuclei
24 kg
(1.66 × 10
−27
kg/u)(2.014 102 u)
24 kg
(610 × 10
9
kW
•
h)(3.6 × 10
6
J/kW
•
h)
(3.00 × 10
8
m/s)
2
Additional Practice A
Givens Solutions
HRW material copyrighted under notice appearing earlier in this book.
2. m = 4.1 × 10
7
kg
h = 10.0 cm
Z = 26
N = 56 − 26 = 30
m
H
= 1.007 825 u
m
n
= 1.008 665 u
atomic mass of
26
56
Fe =
55.934 940 u
a. E = mgh = (4.1 × 10
7
kg)(9.81 m/s
2
)(0.100 m)
E =
b. E
tot
==2.5 × 10
20
MeV
∆m
tot
==2.7 × 10
17
u
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of
26
56
Fe
∆m = 26(1.007 825 u) + 30(1.008 665 u) − 55.934 940 u
∆m = 0.528 460 u
E
bind
= (0.528 460 u)
931.49
M
u
eV
E
bind
= 492.26 MeV
n =
E
E
b
t
i
o
n
t
d
==5.1 × 10
17
reactions
m
tot
= (5.1 × 10
17
)(55.934 940 u)
1.66 × 10
−27
k
u
g
= 4.7 × 10
−8
kg
2.5 × 10
20
MeV
492.26 MeV
2.5 × 10
20
MeV
931.49 MeV/u
(4.0 × 10
7
J)(1 × 10
−6
MeV/eV)
(1.60 × 10
−19
J/eV)
4.0 × 10
7
J
Section Two—Problem Workbook Solutions II Ch. 22–1
6. P = 42 MW = 42 × 10
6
W
atomic mass of
14
7
N =
14.003 074 u
atomic mass of H =
1.007 825 u
m
n
= 1.008 665 u
Z = 7
N = 14 − 7 = 7
∆t = 24 h
II
Givens Solutions
HRW material copyrighted under notice appearing earlier in this book.
3. E = 2.0 × 10
3
TW
•
h =
2.0 × 10
15
W
•
h
atomic mass of
235
92
U =
235.043 924 u
atomic mass of H =
1.007 825 u
m
n
= 1.008 665 u
Z = 92
N = 235 − 92 = 143
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of
235
92
U
∆m = 92(1.007 825 u) + 143(1.008 665 u) − 235.043 924 u = 1.915 071 u
E
bind
= (1.915 071 u)
931.49
M
u
eV
= 1.7839 × 10
3
MeV = 1.7839 × 10
9
eV
E
bind
= (1.7839 × 10
9
eV)
1.60 × 10
−19
e
J
V
= 2.85 × 10
−10
J
E = (2.0 × 10
15
W
•
h)
3.60 ×
h
10
3
s
= 7.2 × 10
18
J
n =
E
b
E
ind
=
2
7
.8
.2
5
×
×
1
1
0
0
1
−
8
10
J
J
= 2.5 × 10
28
reactions
m
tot
= (2.5 × 10
28
)(235.043 924 u)
1.66 × 10
−27
k
u
g
= 9.8 × 10
3
kg
4. E = 2.1 × 10
19
J
atomic mass of
12
6
C =
12.000 000 u
atomic mass of H =
1.007 825 u
m
n
= 1.008 665 u
Z = 6
N = 12 − 6 = 6
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of
12
6
C
∆m = 6(1.007 825 u) + 6(1.008 665 u) − 12.000 000 u
∆m = 9.8940 × 10
−2
u
E
bind
= (9.8940 × 10
−2
u)
931.49
M
u
eV
= 92.162 MeV
E
bind
= (92.162 × 10
6
eV)
1.60 × 10
−19
e
J
V
= 1.47 × 10
−11
J
n =
E
b
E
ind
=
1
2
.4
.1
7
×
×
1
1
0
0
1
−
9
11
J
J
= 1.4 × 10
30
reactions
m
tot
= (1.4 × 10
30
)(12.000 000 u)
1.66 × 10
−27
k
u
g
= 2.8 × 10
4
kg
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of
14
7
N
∆m = 7(1.007 825 u) + 7(1.008 665 u) − 14.003 074 u
∆m = 0.112 356 u
E
bind
= (0.112 356 u)
931.49
M
u
eV
= 104.66 MeV
E
bind
= (104.66 × 10
6
eV)
1.60 × 10
−19
e
J
V
= 1.67 × 10
−11
J
n =
E
P
b
∆
in
t
d
==2.2 × 10
23
reactions
m
tot
= (2.2 × 10
23
)(14.003 074 u)
1.66 × 10
−27
k
u
g
= 5.1 × 10
−3
kg = 5.1 g
(42 × 10
6
W)(24 h)(3600 s/h)
1.67 × 10
−11
J
5. P
tot
= 3.9 × 10
26
J/s
Z = 2
N = 4 − 2 = 2
atomic mass of
4
2
He =
4.002 602 u
atomic mass of H =
1.007 825 u
m
n
=1.008 665 u
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of
4
2
He
∆m = (2)(1.007 825 u) + (2)(1.008 665 u) − 4.002 602 u
∆m = 0.030 378 u
E = (0.030 378 u)
931.49
M
u
eV
E = 28.297 MeV
∆
n
t
=
P
E
tot
=
∆
n
t
= 8.6 × 10
37
reactions/s
(3.9 × 10
26
J/s)(1 × 10
−6
MeV/eV)
(1.60 × 10
−19
J/eV)(28.297 MeV)
Holt Physics Solution ManualII Ch. 22–2
II
Givens Solutions
HRW material copyrighted under notice appearing earlier in this book.
7. P = 3.84 × 10
7
W
atomic mass of
12
6
C =
12.000 000 u
atomic mass of H =
1.007 825 u
m
n
= 1.008 665 u
Z = 6
N = 12 − 6 = 6
∆m = Z(atomic mass of H) + Nm
n
− atomic mass of
12
6
C
∆m = 6(1.007 825 u) + 6(1.008 665 u) − 12.000 000 u
∆m = 9.8940 × 10
−2
u
E
bind
= (9.8940 × 10
−2
u)
931.49 × 10
6
e
u
V
1.60 × 10
−19
e
J
V
E
bind
= 1.47 × 10
−11
J
∆
n
t
=
E
b
P
ind
=
1
3
.
.
4
8
7
4
×
×
1
1
0
0
−
7
1
W
1
J
= 2.61 × 10
18
reactions/s
m
∆
t
t
ot
= (2.61 × 10
18
s
−1
)(12.000 000 u)
1.66 × 10
−27
k
u
g
= 5.20 × 10
−8
kg/s
1.
238
92
U +
0
1
n → X
X →
939
93
Np +
−1
0
e + v
239
93
Np →
239
94
Pu +
−1
0
e + v
mass number of X = 238 + 1 = 239
atomic number of X = 92 + 0 = 92 (uranium)
X =
239
92
U
The equations are as follows:
238
92
U +
0
1
n →
239
92
U
239
92
U →
939
93
Np +
−1
0
e + v
239
93
Np →
239
94
Pu +
−1
0
e + v
Additional Practice B
3. X →
135
56
Ba +
−1
0
e + v
mass number of X = 135 + 0 = 135
atomic number of X = 56 + (−1) = 55 (cesium)
X =
135
55
Cs
135
55
Cs →
135
56
Ba +
−1
0
e + v
2. X → Y +
4
2
He
Y → Z +
4
2
He
Z →
212
83
Bi +
−1
0
e + v
mass number of Z = 212 + 0 = 212
atomic number of Z = 83 − 1 = 82 (lead)
Z =
212
82
Pb
mass number of Y = 212 + 4 = 216
atomic number of Y = 82 + 2 = 84 (polonium)
Y =
216
84
Po
mass number of X = 216 + 4 = 220
atomic number of X = 84 + 2 = 86 (radon)
X =
220
86
Rn
The equations are as follows:
220
86
Rn →
216
84
Po +
4
2
He
216
84
Po →
212
82
Pb +
4
2
He
212
82
Pb →
212
83
Bi +
−1
0
e + v
Section Two—Problem Workbook Solutions II Ch. 22–3
II
Givens Solutions
HRW material copyrighted under notice appearing earlier in this book.
5.
228
90
Th → X +
4
2
He + g
mass number of X = 228 − 4 = 224
atomic number X = 90 − 2 = 88 (radium)
X =
224
88
Ra
228
90
Th →
224
88
Ra +
4
2
He + g
6.
1
1
p +
7
3
Li → X +
4
2
He
mass number of X = 1 + 7 − 4 = 4
atomic number of X = 1 + 3 − 2 = 2 (helium)
X =
4
2
He
1
1
p +
7
3
Li →
4
2
He +
4
2
He
7.
217
85
At → X +
4
2
He
mass number of X = 217 − 4 = 213
atomic number of X = 85 − 2 = 83 (bismuth)
X =
213
83
Bi
217
85
At →
213
83
Bi +
4
2
He
1. T
1/2
= 26 min, 43.53 s
l =
0
T
.6
1
9
/2
3
=
l =
5 times the run time = 5 half-lives
percent of sample remaining = (0.5)
5
(100)
percent decayed = 100 − percent remaining = 100 − (0.5)
5
(100) = 96.875 percent
4.32 × 10
−4
s
−1
0.693
(26 min)(60 s/min) + 43.53 s
Additional Practice C
4.
235
92
U +
1
0
n →
144
56
Ba +
89
36
Kr + X
mass number of X = 235 + 1 − 144 − 89 = 3
atomic number of X = 92 + 0 − 56 − 36 = 0 (neutron)
X = 3
1
0
n
235
92
U +
1
0
n →
144
56
Ba +
89
36
Kr + 3
1
0
n
235
92
U +
1
0
n →
140
54
Xe + Y +
2
1
0
n
mass number of Y = 235 + 1 − 140 − 2 = 94
atomic number of Y = 92 + 0 − 54 − 0 = 38 (strontium)
Y =
94
38
Sr
235
92
U +
1
0
n →
140
54
Xe +
94
38
Sr + 2
1
0
n
Holt Physics Solution ManualII Ch. 22–4
II
Givens Solutions
HRW material copyrighted under notice appearing earlier in this book.
2. T
1/2
= 1.91 years
decrease = 93.75 percent =
0.9375
If 0.9375 of the sample has decayed, 1.0000 − 0.9375 = 0.0625 of the sample remains.
0.0625 = (0.5)
4
, so 4 half-lives have passed.
∆t = 4T
1/2
= (4)(1.91 years) = 7.64 years
3. T
1/2
= 11.9 s
N
i
= 1.00 × 10
13
atoms
N
f
= 1.25 × 10
12
atoms
∆
N
N
i
==0.875
If 0.875 of the sample has decayed, 1.000 − 0.875 = 0.125 of the sample remains.
0.125 = (0.5)
3
, so 3 half-lives have passed.
∆t = 3T
1/2
= (3)(11.9 s) = 35.7 s
1.00 × 10
13
− 1.25 × 10
12
1.00 × 10
13
4. ∆t = 4800 years
T
1/2
= 1600 years
T
∆
1
t
/2
=
4
1
8
6
0
0
0
0
y
y
e
e
a
a
r
r
s
s
= 3 half-lives
amount remaining after 3T
1/2
= (0.5)
3
= 0.125 = 12.5 percent
7. T = 4.4 × 10
−22
s
T
1
= l =
0
T
.6
1
9
/2
3
T =
0
T
.6
1
9
/2
3
T
1/2
= (0.693)(T ) = (0.693)(4.4 × 10
−22
s) = 3.0 × 10
−22
s
5. ∆t = 88 years
amount of sample
remaining =
1
1
6
= 0.0625
0.0625 = (0.5)
4
, so 4 half-lives have passed.
T
1/2
=
1
4
∆t =
88 y
4
ears
= 22 years
l =
0
T
.6
1
9
/2
3
=
22
0.
y
6
e
9
a
3
rs
l = 3.2 × 10
−2
years
−1
6. ∆t = 34 days, 6 h, 26 min
amount of sample
remaining =
5
1
12
= 1.95 × 10
−3
∆t = (34 days)
2
d
4
ay
h
60
h
min
+ (6 h)
60
h
min
+ 26 min
∆t = 4.9346 × 10
4
min
1.95 × 10
−3
= (0.5)
9
, so 9 half-lives have passed.
T
1/2
=
1
9
∆t =
4.9346 ×
9
10
4
min
= 5482.9 min
l =
0
T
.6
1
9
/2
3
=
548
0
2
.6
.9
93
min
l = 1.26 × 10
−4
min
−1
= 0.182 days
−1
Section Two—Problem Workbook Solutions II Ch. 22–5
Section Two—Problem Workbook Solutions Appendix J–1
Appendix J
Advanced Topics
II
1. r = 10.0 km
∆q =+15.0 rad
∆s = r∆q = (10.0 km)(15.0 rad) =
The particle moves in the positive, or
, direction around the
neutron star’s “north” pole.
counterclockwise
1.50 × 10
2
km
Additional Practice A
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
2. ∆q = 3(2p rad)
r = 6560 km
∆s = r∆q = (6560 km)[(3)(2p rad)] = 1.24 × 10
5
km
3. r =
1.40 ×
2
10
5
km
= 7.00 × 10
4
km
∆q = 1.72 rad
r
E
= 6.37 × 10
3
km
a. ∆s = r∆q = (7.00 × 10
4
km)(1.72 rad) =
b. ∆q
E
=
∆
r
E
s
= = 3.00 rev, or 3.00 orbits
(1.20 × 10
5
km)(1 rev/2p rad)
6.37 × 10
3
km
1.20 × 10
5
km
4. ∆q = 225 rad
∆s = 1.50 × 10
6
km
r =
∆
∆
q
s
=
1.50
22
×
5
1
r
0
a
6
d
km
= 6.67 × 10
3
km
5. r = 5.8 × 10
7
km
∆s = 1.5 × 10
8
km
∆q =
∆
r
s
=
1
5
.
.
5
8
×
×
1
1
0
0
8
7
k
k
m
m
= 2.6 rad
6. ∆s =−1.79 × 10
4
km
r = 6.37 × 10
3
km
∆q =
∆
r
s
=
−
6
1
.3
.7
7
9
×
×
1
1
0
0
3
4
k
k
m
m
=−2.81 rad
Additional Practice B
1. r = 1.82 m
w
avg
= 1.00 × 10
−1
rad/s
∆t = 60.0 s
∆q = w
avg
∆t = (1.00 × 10
−1
rad/s)(60.0 s) =
∆s = r∆q = (1.82 m)(6.00 rad) = 10.9 m
6.00 rad
2. ∆t = 120 s
w
avg
= 0.40 rad/s
∆q = w
avg
∆t = (0.40 rad/s)(120 s) = 48 rad
3. r = 30.0 m
∆s = 5.0 × 10
2
m
∆t = 120 s
w
avg
=
∆
∆
q
t
=
r
∆
∆
s
t
=
(3
5
0
.
.
0
0
×
m
1
)(
0
1
2
2
m
0s)
= 0.14 rad/s
Holt Physics Solution ManualAppendix J–2
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
4. ∆q = 16 rev
∆t = 4.5 min
w
avg
=
∆
∆
q
t
==0.37 s
(16 rev)(2p rad/rev)
(4.5 min)(60 s/min)
Givens Solutions
5. w
avg
= 2p rad/24 h
∆q = 0.262 rad
∆t =
w
∆
a
q
vg
= = 1.00 h
0.262 rad
2
2
p
4
r
h
ad
6. r = 2.00 m
∆s = 1.70 × 10
2
km
w
avg
= 5.90 rad/s
∆t =
w
∆
a
q
vg
=
rw
∆
a
s
vg
==1.44 × 10
4
s = 4.00 h
1.70 × 10
5
m
(2.00 m)(5.90 rad/s)
1. a
avg
= 2.0 rad/s
2
w
1
= 0 rad/s
w
2
= 9.4 rad/s
∆t =
w
2
a
−
avg
w
1
∆t =
∆t = 4.7 s
9.4 rad/s − 0.0 rad/s
2.0 rad/s
2
2. ∆t
J
= 9.83 h
a
avg
=−3.0 × 10
−8
rad/s
2
w
2
= 0 rad/s
w
1
=
∆
∆
t
q
J
=
(9.83 h
2p
)(3
ra
6
d
00 s/h)
= 1.78 × 10
−4
rad/s
∆t =
w
2
a
−
avg
w
1
=
∆t = 5.9 × 10
3
s
0.00 rad/s − 1.78 × 10
−4
rad/s
−3.0 × 10
−8
rad/s
2
3. w
1
= 2.00 rad/s
w
2
= 3.15 rad/s
∆t = 3.6 s
a
avg
=
w
2
∆
−
t
w
1
==
1.1
3
5
.6
ra
s
d/s
a
avg
= 0.32 rad/s
2
3.15 rad/s − 2.00 rad/s
3.6 s
Additional Practice C
4. w
1
= 8.0 rad/s
w
2
= 3w
1
= 24 rad/s
∆t = 25 s
a
avg
=
w
2
∆
−
t
w
1
=
24 rad/s
2
−
5
8
s
.0 rad/s
=
16
2
r
5
ad
s
/s
a
avg
= 0.64 rad/s
2
5. ∆t
1
= 365 days
∆q
1
= 2p rad
a
avg
= 6.05 × 10
−13
rad/s
2
∆t
2
= 12.0 days
w
1
=
∆
∆
q
t
2
1
= = 1.99 × 10
−7
rad/s
w
2
= w
1
+ a
avg
∆t
2
= 1.99 × 10
−7
rad/s + (6.05 × 10
−13
rad/s
2
)(12.0 days)
(24 h/day)(3600 s/h)
w
2
= 1.99 × 10
−7
rad/s + 6.27 × 10
−7
rad/s = 8.26 × 10
−7
rad/s
2p rad
(365 days)(24 h/day)(3600 s/h)
6. w
1
= 0 rad/s
a
avg
= 0.800 rad/s
2
∆t = 8.40 s
a
avg
=
w
2
∆
−
t
w
1
w
2
= w
1
+ a
avg
∆t
w
2
= 0 rad/s + (0.800 rad/s
2
)(8.40 s)
w
2
= 6.72 rad/s
II
Additional Practice D
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. w
i
= 5.0 rad/s
a = 0.60 rad/s
2
∆t = 0.50 min
w
f
= w
i
+ a∆t
w
f
= 5.0 rad/s + (0.60 rad/s
2
)(0.50 min)(60.0 s/min)
w
f
= 5.0 rad/s + 18 rad/s
w
f
= 23 rad/s
2. a = 1.0 × 10
−10
rad/s
2
∆t = 12 h
w
i
=
27
2
.
p
3
r
d
a
a
d
ys
w
i
=
27
2
.
p
3
r
d
a
a
d
ys
1
24
da
h
y
36
1
0
h
0s
= 2.66 × 10
−6
rad/s
w
f
= w
i
+ a∆t = 2.66 × 10
−6
rad/s + (1.0 × 10
−10
rad/s
2
)(12 h)(3600 s/h)
w
f
= 2.66 × 10
−6
rad/s + 4.3 × 10
−6
rad/s = 7.0 × 10
−6
rad/s
3. r =
2
4
p
3
r
m
ad
w
i
= 0 rad/s
∆s = 160 m
a = 5.00 × 10
−2
rad/s
2
∆q =
∆
r
s
w
f
2
= w
i
2
+ 2a∆q = w
i
2
+
2a
r
∆s
w
f
=
w
i
2
+
2
a
r
∆
s
=
(0 rad/s)
2
+
w
f
= 1.5 rad/s
(2)(5.00 × 10
−2
rad/s
2
)(160 m)
2
4
p
3
r
m
ad
4. ∆s = 52.5 m
a =−3.2 × 10
−5
rad/s
2
w
f
= 0.080 rad/s
r = 8.0 cm
∆q =
∆
r
s
w
f
2
= w
i
2
+ 2a∆q = w
i
2
+
2a
r
∆s
w
i
=
w
f
2
−
2
a
r
∆
s
=
(0
.0
80
r
ad
/s
)
2
−
w
i
=
6.
4
×
1
0
−
3
ra
d
2
/
s
2
+
4
.2
×
1
0
−
2
ra
d
2
/
s
2
=
4.
8
×
1
0
−
2
ra
d
2
/
s
2
w
i
= 0.22 rad/s
(2)(−3.2 × 10
−5
rad/s
2
)(52.5 m)
8.0 × 10
−2
m
5. r = 3.0 m
w
i
= 0.820 rad/s
w
f
= 0.360 rad/s
∆s = 20.0 m
∆q =
∆
r
s
a =
w
f
2
2
∆
−
q
w
i
2
==
a ==
a =−4.1 × 10
−2
rad/s
2
−0.542 rad
2
/s
2
(2)
2
3
0
.
.
0
0
m
m
0.130 rad
2
/s
2
− 0.672 rad
2
/s
2
(2)
2
3
0
.
.
0
0
m
m
(0.360 rad/s)
2
− (0.820 rad/s)
2
(2)
2
3
0
.
.
0
0
m
m
w
f
2
− w
i
2
2
∆
r
s
Section Two—Problem Workbook Solutions Appendix J–3
II
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
6. r = 1.0 km
w
i
= 5.0 × 10
−3
rad/s
∆t = 14.0 min
∆q = 2p rad
∆q = w
i
∆t +
1
2
a∆t
2
a =
2(∆q
∆
−
t
2
w
i
∆t)
=
a == = 6.0 × 10
−6
rad/s
2
(2)(2.1 rad)
[(14.0 min)(60 s/min)]
2
(2)(6.3 rad − 4.2 rad)
[(14.0 min)(60 s/min)]
2
(2)[2p rad − (5.0 × 10
−3
rad/s)(14.0 min)(60 s/min)]
[(14.0 min)(60 s/min)]
2
7. w
i
= 7.20 × 10
−2
rad/s
∆q = 12.6 rad
∆t = 4 min, 22 s
∆t = (4 min)(60 s/min) + 22 s = 262 s
∆q = w
i
∆t +
1
2
a∆t
2
a =
2(∆q
∆
−
t
2
w
i
∆t)
=
a ==
(2)(
(
−
2
6
6
.
2
3
s
r
)
a
2
d/s)
=−1.8 × 10
−4
rad/s
2
(2)(12.6 rad − 18.9 rad)
(262 s)
2
(2)[12.6 rad − (7.20 × 10
−2
rad/s)(262 s)]
(262 s)
2
8. w
i
= 27.0 rad/s
w
f
= 32.0 rad/s
∆t = 6.83 s
a
avg
=
w
f
∆
−
t
w
i
==
5.
6
0
.8
r
3
ad
s
/s
a
avg
= 0.73 rad/s
2
32.0 rad/s − 27.0 rad/s
6.83 s
9. a = 2.68 × 10
−5
rad/s
2
∆t = 120.0 s
w
i
=
2p
1
r
2
ad
∆q = w
i
∆t +
1
2
a∆t
2
∆q =
2
1
p
2
r
h
ad
(1 h/3600 s)(120.0 s) +
1
2
(2.68 × 10
−5
rad/s
2
)(120.0 s)
2
∆q = 1.7 × 10
−2
rad + 1.93 × 10
−1
rad = 0.210 rad
10. w
i
= 6.0 × 10
−3
rad/s
w
f
= 3w
i
= 18 × 10
−3
rad/s
a = 2.5 × 10
−4
rad/s
2
∆q =
w
f
2
2
−
a
w
i
2
∆q = =
∆q = = 0.56 rad
2.8 × 10
−4
rad
2
/s
2
5.0 × 10
−4
rad/s
2
3.2 × 10
−4
rad
2
/s
2
− 3.6 × 10
−5
rad
2
/s
2
(2)(2.5 × 10
−4
rad/s
2
)
(18 × 10
−3
rad/s)
2
− (6.0 × 10
−3
rad/s)
2
(2)(2.5 × 10
−4
rad/s
2
)
11. w
i
= 9.0 × 10
−7
rad/s
w
f
= 5.0 × 10
−6
rad/s
a = 7.5 × 10
−10
rad/s
2
∆t =
w
f
a
− w
i
∆t ==
∆t = 5.5 × 10
3
s = 1.5 h
4.1 × 10
−6
rad/s
7.5 × 10
−10
rad/s
2
5.0 × 10
−6
rad/s − 9.0 × 10
−7
rad/s
7.5 × 10
−10
rad/s
2
Holt Physics Solution ManualAppendix J–4
II
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
12. r = 7.1 m
∆s = 500.0 m
w
i
= 0.40 rad/s
a = 4.0 × 10
−3
rad/s
2
∆q =
∆
r
s
= w
i
∆t +
1
2
a∆t
2
1
2
a∆t
2
+ w
i
∆t −
∆
r
s
= 0
Using the quadratic equation:
∆t =
∆t =
∆t = =
Choose the positive value:
∆t ==
0.4
ra
5
d
r
/
a
s
d
2
/s
= 1.1 × 10
2
s
−0.40 rad/s + 0.85 rad/s
4.0 × 10
−3
rad/s
2
– 0.40 rad/s ±
0.
72
r
ad
2
/
s
2
4.0 × 10
−3
rad/s
2
−0.40 rad/s ±
0.
16
r
ad
2
/
s
2
+
0
.5
6
ra
d
2
/
s
2
4.0 × 10
−3
rad/s
2
−0.40 rad/s ±
(0
.4
0
ra
d
/s
)
2
+
(
4)
1
2
(
4.
0
×
1
0
−
3
ra
d
/s
2
)
5
0
7
0
.
1
.0
m
m
(2)
1
2
(4.0 × 10
−3
rad/s
2
)
−w
i
±
w
i
2
−
4
1
2
a
−
∆
r
s
2
1
2
a
Additional Practice E
1. w = 4.44 rad/s
v
t
= 4.44 m/s
r =
w
v
t
=
4
4
.4
.4
4
4
r
m
ad
/
/
s
s
= 1.00 m
2. v
t
= 16.0 m/s
w = 1.82 × 10
−5
rad/s
r =
w
v
t
=
1.82
1
×
6.
1
0
0
m
−5
/
r
s
ad/s
=
circumference = 2pr = (2p)(879 km) = 5.52 × 10
3
km
8.79 × 10
5
m = 879 km
3. w = 5.24 × 10
3
rad/s
v
t
= 131 m/s
r =
w
v
t
=
5.24
1
×
31
10
m
3
/
r
s
ad/s
= 2.50 × 10
−2
m = 2.50 cm
4. v
t
= 29.7 km/s
r = 1.50 × 10
8
km
w =
v
r
t
=
1.5
2
0
9.
×
7
1
k
0
m
8
/
k
s
m
= 1.98 × 10
−7
rad/s
5. r =
19.0
2
mm
= 9.50 mm
w = 25.6 rad/s
v
t
= rw = (9.50 × 10
−3
m)(25.6 rad/s) = 0.243 m/s
Section Two—Problem Workbook Solutions Appendix J–5
II
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. r = 32 m
a
t
= 0.20 m/s
2
a =
a
r
t
=
0.2
3
0
2
m
m
/s
2
a = 6.2 × 10
−3
rad/s
2
Additional Practice F
2. r = 8.0 m
a
t
=−1.44 m/s
2
a=
a
r
t
=
−1.
8
4
.
4
0
m
m
/s
2
=−0.18 rad/s
2
3. ∆w =−2.4 × 10
−2
rad/s
∆t = 6.0 s
a
t
=−0.16 m/s
2
a =
∆
∆
w
t
=
−2.4 ×
6
1
.0
0
−
s
2
rad/s
=−4.0 × 10
−3
rad/s
2
r =
a
a
t
=
−4.0
−0
×
.1
1
6
0
−
m
3
/
r
s
a
2
d/s
2
= 4.0 × 10
1
m
4. ∆q′=14 628 turns
∆t′=1.000 h
a
t
= 33.0 m/s
2
w
i
= 0 rad/s
∆q = 2p rad
r =
a
a
t
a =
w
f
2
2∆
−
q
w
i
2
w
f
=
r =
=
r =
2
− (0 rad/s)
2
= 0.636 m
(14 628 turns)(2p rad/turn)
(1.000 h)(3600 s/h)
2a
t
∆q
∆
∆
q
t′
′
2
− w
i
2
∆
∆
q
t′
′
2
− w
i
2
2∆q
∆q′
∆t′
5. r = 56.24 m
w
i
= 6.00 rad/s
w
f
= 6.30 rad/s
∆t = 0.60 s
a
t
= ra
a =
w
f
∆
−
t
w
i
a
t
= r
w
f
∆
−
t
w
i
= (56.24 m)
=
a
t
= 28 m/s
2
(56.24 m)(0.30 rad/s)
0.60 s
6.30 rad/s − 6.00 rad/s
0.60 s
a
t
(2)(33.0 m/s
2
)(2p rad)
6. r = 1.3 m
∆q = 2p rad
∆t = 1.8 s
w
i
= 0 rad/s
a
t
= ra
α=
2(∆q
∆
−
t
2
w
i
∆t)
a
t
= r
2(∆q
∆
−
t
2
w
i
∆t)
= (1.3 m)
a
t
= 5.0 m/s
2
(2)[2p rad − (0 rad/s)(1.8 s)]
(1.8 s)
2
Holt Physics Solution ManualAppendix J–6
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. t
1
= 2.00 × 10
5
N
•
m
t
2
= 1.20 × 10
5
N
•
m
h = 24 m
Apply the second condition of equilibrium, choosing the base of the cactus as the
pivot point.
t
net
= t
1
− t
2
− Fd(sin q) = 0
Fd(sin q) = t
1
− t
2
For F to be minimum, d and sin q must be maximum. This occurs when the force is
perpendicular to the cactus (q = 90°) and is applied to the top of the cactus (d = h =
24 m).
F
min
=
t
1
−
h
t
2
=
F
min
= = 3.3 × 10
3
N applied to the top of the cactus
8.0 × 10
4
N
•
m
24 m
2.00 × 10
5
N
•
m − 1.20 × 10
5
N
•
m
24 m
Givens Solutions
2. m
1
= 40.0 kg
m
2
= 5.4 kg
d
1
= 70.0 cm
d
2
= 100.0 cm − 70.0 cm
= 30.0 cm
g = 9.81 m/s
2
Apply the first condition of equilibrium.
F
n
− m
1
g − m
2
g − F
applied
= 0
F
n
= m
1
g + m
2
g + F
applied
= (40.0 kg)(9.81 m/s
2
) + (5.4 kg)(9.81 m/s
2
) + F
applied
F
n
= 392 N + 53 N + F
applied
= 455 N + F
applied
Apply the second condition of equilibrium, using the fulcrum as the location for the
axis of rotation.
F
applied
d
2
+ m
2
gd
2
− m
1
gd
1
= 0
F
applied
=
m
1
gd
1
d
−
2
m
2
gd
2
=
F
applied
= =
F
applied
=
Substitute the value for F
applied
into the first-condition equation to solve for F
n
.
F
n
= 455 N + 863 N = 1318 N
863 N
259 N
•
m
0.300 m
275 N
•
m − 16 N
•
m
0.300 m
(40.0 kg)(9.81 m/s
2
)(0.700 m) − (5.4 kg)(9.81 m/s
2
)(0.300 m)
0.300 m
3. m = 134 kg
d
1
= 2.00 m
d
2
= 7.00 m − 2.00 m = 5.00 m
q = 60.0°
g = 9.81 m/s
2
Apply the first condition of equilibrium in the x and y directions.
F
x
= F
applied
(cos q) − F
f
= 0
F
y
= F
n
− F
applied
(sin q) − mg = 0
To solve for F
applied
, apply the second condition of equilibrium, using the fulcrum as
the pivot point.
F
applied
(sin q)d
2
− mgd
1
= 0
F
applied
=
d
2
m
(s
g
in
d
1
q)
=
F
applied
=
Substitute the value for F
applied
into the first-condition equations to solve for F
n
and
F
f
.
F
n
= F
applied
(sin q) + mg = (607 N)(sin 60.0°) + (134 kg)(9.81 m/s
2
)
F
n
= 526 N + 1.31 × 10
3
N =
F
f
= F
applied
(cos q) = (607 N)(cos 60.0°) = 304 N
1.84 × 10
3
N
607 N
(134 kg)(9.81 m/s
2
)(2.00 m)
(5.00 m)(sin 60.0°)
Additional Practice G
Section Two—Problem Workbook Solutions Appendix J–7
II
4. m = 8.8 × 10
3
kg
d
1
= 3.0 m
d
2
= 15 m − 3.0 m = 12 m
q = 20.0°
g = 9.81 m/s
2
Apply the first condition of equilibrium in the x and y directions.
F
x
= F
fulcrum
,
x
− F (sin q) = 0
F
y
F
fulcrum
,
y
− F (cos q) − mg = 0
To solve for F, apply the second condition of equilibrium •, using the fulcrum as the
pivot point.
Fd
2
− mg d
1
(cos q) = 0
F =
mg d
1
d
(
2
cos q)
=
F =
Substitute the value for F into the first-condition equations to solve for the compo-
nents of F
fulcrum
.
F
fulcrum
,
x
= F (sin q) = (2.0 × 10
4
N)(sin 20.0°)
F
fulcrum
,
x
=
F
fulcrum
,
y
= F (cos q) + mg = (2.0 × 10
4
N)(cos 20.0°) + (8.8 × 10
4
kg)(9.81 m/s
2
)
F
fulcrum
,
y
= 1.9 × 10
4
N + 8.6 × 10
5
N = 8.8 × 10
5
N
6.8 × 10
3
N
2.0 × 10
4
N
(8.8 × 10
3
kg)(9.81 m/s
2
)(3.0 m)(cos 20.0°)
12 m
Givens Solutions
6. m
1
= 3.6 × 10
2
kg
m
2
= 6.0 × 10
2
kg
l
= 15 m
l
1
= 5.0 m
g = 9.81 m/s
2
Apply the second condition of equilibrium, using the pool’s edge as the pivot point.
Assume the total mass of the board is concentrated at its center.
m
1
g d − m
2
g
−
l
1
= 0
d = =
d = =
d = = 4.2 m from the pool’s edge
(6.0 × 10
2
kg)(2.5 m)
3.6 × 10
2
kg
(6.0 × 10
2
kg)(7.5 m − 5.0 m)
3.6 × 10
2
kg
(6.0 × 10
2
kg)
15
2
m
− 5.0 m
3.6 × 10
2
kg
m
2
2
l
−
l
1
m
1
m
2
g
2
l
−
l
1
m
1
g
l
2
5. m
1
= 64 kg
m
2
= 27 kg
d
1
= d
2
=
3.0
2
0m
= 1.50 m
F
n
= 1.50 × 10
3
N
g = 9.81 m/s
2
Apply the first condition of equilibrium to solve for F
applied
.
F
n
− m
1
g − m
2
g − F
applied
= 0
F
applied
= F
n
− m
1
g − m
2
g = 1.50 × 10
3
N − (64 kg)(9.81 m/s
2
) − (27 kg)(9.81 m/s
2
)
F
applied
= 1.50 × 10
3
N − 6.3 × 10
2
N − 2.6 × 10
3
N = 6.1 × 10
2
N
To solve for the lever arm for F
applied
, apply the second condition of equilibrium,
using the fulcrum as the pivot point.
F
applied
d + m
2
g d
2
− m
1
g d
1
= 0
d =
m
1
gd
F
1
ap
−
pl
m
ied
2
gd
2
=
d = =
d = 0.89 m from the fulcrum, on the same side as the less massive seal
5.4 × 10
2
N
•
m
6.1 × 10
2
N
9.4 × 10
2
N
•
m − 4.0 × 10
2
N
•
m
6.1 × 10
2
N
(64 kg)(9.81 m/s
2
)(1.50 m) − (27 kg)(9.81 m/s
2
)(1.50 m)
6.1 × 10
2
N
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualAppendix J–8
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
7. m = 449 kg
l
= 5.0 m
F
1
= 2.70 × 10
3
N
g = 9.81 m/s
2
Apply the first condition of equilibrium to solve for F
2
.
F
1
+ F
2
− mg = 0
F
2
= mg − F
1
F
2
= (449 kg)(9.81 m/s
2
) − 2.70 × 10
3
N = 4.40 × 10
3
N − 2.70 × 10
3
N = 1.70 × 10
3
N
Apply the second condition of equilibrium, using the left end of the platform as the
pivot point.
F
2
l
− m g d = 0
d ==
d = 1.9 m from the platform’s left end
(1.70 × 10
3
N)(5.0 m)
(449 kg)(9.81 m/s
2
)
F
2
l
mg
Givens Solutions
8. m
1
= 414 kg
l
= 5.00 m
m
2
= 40.0 kg
F
1
= 50.0 N
g = 9.81 m/s
2
Apply the first condition of equilibrium to solve for F
2
.
F
1
+ F
2
− m
1
g − m
2
g = 0
F
2
= m
1
g + m
2
g − F
1
= (m
1
+ m
2
) g − F
1
F
2
= (414 kg + 40.0 kg)(9.81 m/s
2
) − 50.0 N = (454 kg)(9.81 m/s
2
) − 50.0 N = 4.45 ×
10
3
N − 50.0 N
F
2
= 4.40 × 10
3
N
Apply the second condition of equilibrium, using the supported end (F
1
) of the stick
as the rotation axis.
F
2
d − m
1
g
− m
2
g
l
= 0
d = =
d = =
d = 2.75 m from the supported end
(247 kg)(9.81 m/s
2
)(5.00 m)
4.40 × 10
3
N
(207 kg + 40.0 kg)(9.81 m/s
2
)(5.00 m)
4.40 × 10
3
N
414
2
kg
+ 40.0 kg
(9.81 m/s
2
)(5.0 m)
4.40 × 10
3
N
m
2
1
+ m
2
g
l
F
2
l
2
1. R = 50.0 m
M = 1.20 × 10
6
kg
t = 1.0 × 10
9
N
•
m
a =
t
I
=
M
t
R
2
=
a = 0.33 rad/s
2
1.0 × 10
9
N
•
m
(1.20 × 10
6
kg)(50.0
2
)
Additional Practice H
2. M = 22 kg
R = 0.36 m
t = 5.7 N
•
m
a =
t
I
=
M
t
R
2
=
a = 2.0 rad/s
2
5.7 N
•
m
(22 kg)(0.36 m)
2
Section Two—Problem Workbook Solutions Appendix J–9
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
3. M = 24 kg
l
= 2.74 m
F = 1.8 N
The force is applied perpendicular to the lever arm, which is half the pencil’s length.
Therefore,
t = F d (sin q) = F
a =
t
I
= =
a = 0.16 rad/s
2
(1.8 N)
2.7
2
4m
1
1
2
(24 kg)(2.74 m)
2
F
l
2
1
1
2
M
l
2
l
2
Givens Solutions
4. M = 4.07 × 10
5
kg
R = 5.0 m
t = 5.0 × 10
4
N
•
m
a =
t
I
=
a =
a = 9.8 × 10
−3
rad/s
2
(5.0 × 10
4
N
•
m)
1
2
(4.07 × 10
5
kg)(5.0 m)
2
t
1
2
MR
2
5. R = 2.00 m
F = 208 N
a = 3.20 × 10
−2
rad/s
2
The force is applied perpendicular to the lever arm, which is the ball’s radius.
Therefore,
t = F d (sin q) = F R
T =
a
t
=
F
a
R
=
I = 1.30 × 10
4
kg
•
m
2
(208 N)(2.00 m)
3.20 × 10
−2
rad/s
2
6. r = 8.0 m
t = 7.3 × 10
3
N
•
m
a = 0.60 rad/s
2
I =
a
t
= mr
2
I = =
m =
r
I
2
= = 1.9 × 10
2
kg
1.2 × 10
4
kg
•
m
2
(8.0 m)
2
1.2 × 10
4
kg
•
m
2
7.3 × 10
3
N
•
m
0.60 rad/s
2
7. v
t,i
= 2.0 km/s
l
= 15.0 cm
∆t = 80.0 s
t =−0.20 N
•
m
v
t,f
= 0 m/s
I =
a
t
==
−0.20 N
•
m
I =
=
I = 6.0 × 10
−4
kg
•
m
2
0 m/s − 2.0 × 10
3
m/s
0.15
2
0m
(80.0 s)
v
t,f
− v
t,i
l
d
2
∆t
t
w
f
∆
−
t
w
i
t
−0.20 N
•
m
(0
−
.0
2
7
.0
5
×
m
1
)
0
(
3
80
m
.0
/s
s)
Holt Physics Solution ManualAppendix J–10
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
8. R =
1.7
2
0m
= 0.85 m
t = 125 N
•
m
∆t = 2.0 s
w
i
= 0 rad/s
w
f
= 12 rad/s
I =
a
t
= MR
2
I =
a
t
= = =
I =
M =
R
I
2
= = 29 kg
21 kg
•
m
2
(0.85 m)
2
21 kg
•
m
2
125 N
•
m
6.0 rad/s
2
125 N
•
m
12 rad/
2
s
.0
−
s
0rad/s
t
w
f
∆
−
t
w
i
Givens Solutions
9. R = 3.00 m
M = 17 × 10
3
kg
w
i
= 0 rad/s
w
f
= 3.46 rad/s
∆t = 12 s
t = I a =
1
2
MR
2
w
f
∆
−
t
w
i
t = = 2.2 × 10
4
N
•
m
(17 × 10
3
kg)(3.00 m)
2
(3.46 rad/s − 0 rad/s)
(2)(12 s)
10. R = 4.0 m
M = 1.0 × 10
8
kg
w
i
= 0 rad/s
w
f
= 0.080 rad/s
∆t = 60.0 s
t = Ia =
1
2
MR
2
w
f
∆
−
t
w
i
t = = 1.1 × 10
6
N
•
m
(1.0 × 10
8
kg)(4.0 m)
2
(0.080 rad/s − 0 rad/s)
(2)(60.0 s)
11. I = 2.40 × 10
3
kg
•
m
2
∆q = 2(2p rad) = 4p rad
∆t = 6.00 s
w
i
= 0 rad/s
∆q = w
i
∆t +
1
2
a ∆t
2
Because w
i
= 0,
∆q =
1
2
a∆t
2
a =
2
∆
∆
t
2
q
t = Ia =
2
∆
I
t
∆
2
q
=
t = 1.68 × 10
3
N
•
m
(2)(2.40 × 10
3
kg
•
m
2
)(4p rad)
(6.00 s)
2
12. m = 7.0 × 10
3
kg
r = 18.3 m
a
t
= 25 m/s
2
t = Ia = (mr
2
)
a
r
t
= mra
t
t = (7.0 × 10
3
kg)(18.3 m)(25 m/s
2
)
t = 3.2 × 10
6
N
•
m
Section Two—Problem Workbook Solutions Appendix J–11
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. r
i
= 4.95 × 10
7
km
v
i
= 2.54 × 10
5
Km/h
v
f
= 1.81 × 10
5
km/h
L
i
= L
f
I
i
w
i
= I
f
w
f
mr
i
2
v
r
i
i
= mr
f
2
v
r
f
f
r
i
v
i
= r
f
v
f
r
f
=
r
i
v
v
f
i
=
r
f
= 6.95 × 10
7
km
(4.95 × 10
7
km)(2.54 × 10
5
km/h)
1.81 × 10
5
km/h
Additional Practice I
Givens Solutions
2. v
i
= 399 km/h
v
f
= 456 km/h
R = 0.20 m
∆q = 20 rev
L
i
= L
f
I
i
w
i
= I
f
w
f
m r
i
2
v
r
i
i
= mr
f
2
v
r
f
f
r
i
v
i
= r
f
v
f
r
f
= r
i
−∆s = r
i
− R ∆q
r
i
v
i
= (r
i
− R ∆q) v
f
r
i
(v
f
− v
i
) = (R ∆q) v
f
r
i
=
v
v
f
f
R
−
∆
v
q
i
=
=
r
i
= 2.0 × 10
2
m
(456 km/h)(0.20 m)(20 rev)(2p rad/rev)
57 km/h
(456 km/h)(0.20 m)(20 rev)(2p rad/rev)
456 km/h − 399 km/h
3. M = 25.0 kg
R = 15.0 cm
w
i
= 4.70 × 10
−3
rad/s
w
f
= 4.74 × 10
−3
rad/s
L
i
= L
f
I
i
w
i
= I
f
w
f
I
f
= =
2
5
MR
2
w
i
I
f
= = 0.223 kg
•
m
2
I
i
=
2
5
MR
2
=
2
5
(25.0 kg)(0.150 m)
2
= 0.225 kg
•
m
2
∆I = I
f
− I
i
= 0.223 kg
•
m
2
− 0.225 kg
•
m
2
=−0.002 kg
•
m
2
The moment of inertia decreases by 0.002 kg
•
m
2
.
(2)(25.0 kg)(0.150 m)
2
(4.70 × 10
−3
rad/s)
(5)(4.74 × 10
−3
rad/s)
w
f
I
i
w
i
w
f
Holt Physics Solution ManualAppendix J–12
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
4. v
i
= 395 km/h
r
i
= 1.20 × 10
2
m
∆
∆
r
t
= 0.79 m/s
∆t = 33 s
r
f
= r
i
−
∆
∆
r
t
∆t
L
i
= L
f
I
i
w
i
= L
f
w
f
mr
i
2
v
r
i
i
= mr
f
2
v
r
f
f
r
i
v
i
= r
f
v
f
=
r
i
−
∆
∆
r
t
∆t
v
f
v
f
= =
v
f
= =
v
f
= 5.0 × 10
2
km/h
(1.20 × 10
2
m)(395 km/h)
94 m
(1.20 × 10
2
m)(395 km/h)
1.20 × 10
2
m − 26 m
(1.20 × 10
2
m)(395 km/h)
1.20 × 10
2
− (0.79 m/s)(33 s)
r
i
v
i
[r
i
−
∆
∆
r
t
∆t]
Givens Solutions
5. r
i
=
10.
2
0m
= 5.00 m
r
f
=
4.0
2
0m
= 2.00 m
w
i
= 1.26 rad/s
L
i
= L
f
I
i
w
i
= I
f
w
f
mr
i
2
w
i
= mr
f
2
w
f
w
f
=
r
i
r
2
f
w
2
i
=
w
f
= 7.88 rad/s
(5.00 m)
2
(1.26 rad/s)
(2.00 m)
2
6. R = 3.00 m
M = 1.68 × 10
4
kg
r
i
= 2.50 m
r
f
= 3.00 m
m = 2.00 × 10
2
kg
w
i
= 3.46 rad/s
L
i
= L
f
I
i
w
i
= I
f
w
f
2
1
MR
2
+ mr
i
2
w
i
=
1
2
MR
2
+ mr
f
2
w
f
w
f
=
w
f
=
2
1
(1.68 × 10
4
kg)(3.00 m)
2
+ (2.00 × 10
2
kg)(2.50 m)
2
(3.46 rad/s)
2
1
(1.68 × 10
4
kg)(3.00 m)
2
+ (2.00 × 10
2
kg)(3.00 m)
2
w
f
=
w
f
=
w
f
= 3.43 rad/s
∆w = w
f
− w
i
= 3.43 rad/s − 3.46 rad/s =−0.03 rad/s
The angular speed decreases by 0.03 rad/s.
(7.68 × 10
4
kg
•
m
2
)(3.46 rad/s)
7.74 × 10
4
kg
•
m
2
(7.56 × 10
4
kg
•
m
2
+ 1.25 × 10
3
kg
•
m
2
)(3.46 rad/s)
7.56 × 10
4
kg
•
m
2
+ 1.80 × 10
3
kg
•
m
2
2
1
MR
2
+ mr
i
2
w
i
1
2
MR
2
+ mr
f
2
Section Two—Problem Workbook Solutions Appendix J–13
1. m = 407 kg
h = 57.0 m
v
f
= 12.4 m/s
w
f
= 28.0 rad/s
g = 9.81 m/s
2
ME
i
= ME
f
mgh =
1
2
mv
f
2
+
1
2
I w
f
2
1
2
I w
f
2
= mgh −
1
2
mv
f
2
I =
2mgh
w
−
f
2
mv
f
2
=
m(2g
w
h
f
2
− v
f
2
)
I =
I = =
I = 5.0 × 10
2
kg
•
m
2
(407 kg)(9.7 × 10
2
m
2
/s
2
)
(28.0 rad/s)
2
(407 kg)(1.12 × 10
3
m
2
/s
2
− 154 m
2
/s
2
)
(28.0 rad/s)
2
(407 kg)[(2)(9.81 m/s
2
)(57.0 m) − (12.4 m/s)
2
]
(28.0 rad/s)
2
Givens Solutions
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Additonal Practice J
2. h = 5.0 m
g = 9.81 m/s
2
ME
i
= ME
f
mgh =
1
2
mv
f
2
+
2
1
Iw
f
2
mgh =
1
2
mv
f
2
+
1
2
(mr
2
)
v
r
f
2
2
mgh = mv
f
2
1
2
+
1
2
= mv
f
2
v
f
=
gh
=
(9
.8
1
m
/s
2
)
(5
.0
m
)
v
f
= the mass is not required7.0 m/s
3. h = 1.2 m
g = 9.81 m/s
2
ME
i
= ME
f
1
2
mv
i
2
+
1
2
Iw
i
2
= mgh
2
1
mv
i
2
+
1
2
1
2
mr
2
v
r
i
2
2
= mgh
mv
i
2
1
2
+
1
4
=
3
4
mv
i
2
= mgh
v
i
=
4
3
g
h
=
= 4.0 m/s
(4)(9.81 m/s
2
)(1.2 m)
3
4. v
f
= 12.0 m/s
I = 0.80mr
2
g = 9.81 m/s
2
ME
i
= ME
f
mgh =
2
1
mv
f
2
+
2
1
Iw
f
2
=
2
1
mv
f
2
+
2
1
(0.80 mr
2
)
v
r
f
2
mgh = mv
f
2
2
1
+
0.
2
80
= 0.90 mv
f
2
h =
0.90
g
v
f
2
=
(0.9
9
0
.
)
8
(
1
12
m
.0
/s
m
2
/s)
2
h = 13 m
Holt Physics Solution ManualAppendix J–14
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
5. v
i
= 5.4 m/s
g = 9.81 m/s
2
q = 30.0°
ME
i
= ME
f
2
1
mv
i
2
+
2
1
Iw
i
2
= mgh = mgd(sin q)
mgd(sin q) =
2
1
mv
i
2
+
2
1
2
5
mr
2
v
r
i
2
2
mgd(sin q) = mv
i
2
2
1
+
1
5
=
1
7
0
mv
i
2
d =
10 g
7
(
v
si
i
n
2
q)
==4.2 m
(7)(5.4 m/s)
2
(10)(9.81 m/s
2
)(sin 30.0°)
Givens Solutions
6. r = 2.0 m
w
f
= 5.0 rad/s
g = 9.81 m/s
2
m = 4.8 × 10
3
kg
ME
i
= ME
f
mgh =
2
1
mv
f
2
+
2
1
Iw
f
2
mgh =
2
1
mr
2
w
f
2
+
2
1
2
5
mr
2
w
f
2
mgh = mr
2
w
f
2
2
1
+
1
5
=
1
7
0
mr
2
w
f
2
h ==
h =
KE
trans
=
2
1
mv
f
2
=
2
1
mr
2
w
f
2
KE
trans
=
2
1
(4.8 × 10
3
kg)(2.0 m)
2
(5.0 rad/s)
2
KE
trans
= 2.4 × 10
5
J
7.1 m
(7)(2.0 m)
2
(5.0 rad/s)
2
(10)(9.81 m/s
2
)
1
7
0
r
2
w
f
2
g
7. m = 5.55 kg
h = 1.40 m
g = 9.81 m/s
2
ME
i
= ME
f
mgh =
2
1
mv
f
2
+
2
1
Iw
f
2
mgh =
2
1
mv
f
2
+
2
1
2
5
mr
2
v
r
f
2
2
mgh = mv
f
2
2
1
+
1
5
=
1
7
0
mv
f
2
v
f
=
10
7
g
h
=
= 4.43 m/s
KE
rot
=
2
1
Iw
f
2
=
5
1
mv
f
2
KE
rot
==21.8 J
(5.55 kg)(4.43 m/s)
2
5
(10)(9.81 m/s
2
)(1.40 m)
7
Section Two—Problem Workbook Solutions Appendix J–15
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. P
1
= (1 + 0.12)P
2
= 1.12 P
2
v
1
= 0.60 m/s
v
2
= 4.80 m/s
ρ
= 1.00 × 10
3
kg/m
3
h
1
= h
2
P
1
+
1
2
ρ
v
1
2
+
ρ
gh
1
= P
2
+
1
2
ρ
v
2
2
+
ρ
gh
2
h
1
= h
2
, and P
2
=
1
P
.1
1
2
, so the equation simplifies to
P
1
+
1
2
ρ
v
1
2
=
1
P
.1
1
2
+
1
2
ρ
v
2
2
P
1
1 −
1.
1
12
=
1
2
ρ
(v
2
2
− v
1
2
)
P
1
==
P
1
=
P
1
==1.06 × 10
5
Pa
(1.00 × 10
3
kg/m
3
)(22.6 m
2
/s
2
)
(2)(0.107)
(1.00 × 10
3
kg/m
3
)(23.0 m
2
/s
2
− 0.36 m
2
/s
2
)
(2)(1 − 0.893)
(1.00 × 10
3
kg/m
3
)[(4.80 m/s)
2
− (0.60 m/s)
2
]
(2)
1 −
1.
1
12
ρ
(v
2
2
− v
1
2
)
(2)
1 −
1.
1
12
Additional Practice K
Givens Solutions
2. r
1
=
4.1
2
0m
= 2.05 m
v
1
= 3.0 m/s
r
2
=
2.7
2
0m
= 1.35 m
P
2
= 82 kPa
ρ
= 1.00 × 10
3
kg/m
3
h
1
= h
2
A
1
v
1
= A
2
v
2
v
2
=
A
A
1
v
2
1
=
π
π
r
1
r
2
2
v
2
1
=
r
1
r
2
2
2
v
1
v
2
==6.9 m/s
P
1
+
1
2
rv
1
2
+
ρ
gh
1
= P
2
+
1
2
rv
2
2
+
ρ
gh
2
h
1
= h
2
, so the equation simplifies to
P
1
+
2
1
rv
1
2
= P
2
+
2
1
rv
2
2
P
1
= P
2
+
2
1
r(v
2
2
− v
1
2
)
P
1
= 82 × 10
3
Pa +
2
1
(1.00 × 10
3
kg/m
3
)[(6.9 m/s)
2
− (3.0 m/s)
2
]
P
1
= 82 × 10
3
Pa +
2
1
(1.00 × 10
3
kg/m
3
)(48 m
2
/s
2
− 9.0 m
2
s
2
)
P
1
= 82 × 10
3
Pa +
2
1
(1.00 × 10
3
kg/m
3
)(39 m
2
/s
2
)
P
1
= 82 × 10
3
Pa + 2.0 × 10
4
Pa = 10.2 × 10
4
Pa = 102 kPa
(2.05 m)
2
(3.0 m/s)
(1.35 m)
2
3. h
2
− h
1
=
1
2
h
∆x = 19.7 m
To find the horizontal speed of the cider, recall that for a projectile with no initial
vertical speed,
∆x = v∆t
∆y =−
1
2
g ∆t
2
=−
1
2
h
∆t =
h
g
v =
∆
∆
x
t
==
g
∆
h
x
2
P
1
+
1
2
ρ
v
1
2
+
ρ
gh
1
= P
2
+
1
2
ρ
v
2
2
+
ρ
gh
2
∆x
h
g
Holt Physics Solution ManualAppendix J–16
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Assuming the vat is open to the atmosphere, P
1
= P
2
.
Also assume v
2
≈ 0. Therefore, the equation simplifies to
1
2
ρ
v
1
2
+
ρ
gh
1
=
ρ
gh
2
1
2
v
1
2
=
1
2
g
∆
h
x
2
2
= g(h
2
− h
1
) = g
1
2
h
g ∆
h
x
2
= gh
h
2
=∆x
2
h =∆x = 19.7 m
Givens Solutions
4. v
1
= 59 m/s
g = 9.81 m/s
2
P
1
+
2
1
rv
1
2
+ rgh
1
= P
2
+
2
1
rv
2
2
+ rgh
2
Assume v
2
≈ 0 and P
1
= P
2
= P
0
.
2
1
rv
1
2
+ rgh
1
= rgh
2
h
2
− h
1
=
v
2
1
g
2
=
(2)
(
(
5
9
9
.8
m
1
/
m
s)
/
2
s
2
)
= 1.8 × 10
2
m
5. h
2
− h
1
= 66.0 m
g = 9.81 m/s
2
P
1
+
2
1
rv
1
2
+ rgh
1
= P
2
+
2
1
rv
2
2
+ rgh
2
Assume v
2
≈ 0 and P
1
= P
2
= P
0
.
2
1
rv
1
2
+ rgh
1
= rgh
2
v
1
=
2g
(h
2
−
h
1
)
=
(2
)(
9.
81
m
/s
2
)
(6
6.
0
m
)
= 36.0 m/s
6. h
2
− h
1
= 3.00 × 10
2
m
g = 9.81 m/s
2
P
1
+
2
1
rv
1
2
+ rgh
1
= P
2
+
2
1
rv
2
2
+ rgh
2
Assume v
2
≈ 0 and P
1
= P
2
= P
0
.
2
1
rv
1
2
+ rgh
1
= rgh
2
v
1
=
2g
(h
2
−
h
1
)
=
(2
)(
9.
81
m
/s
2
)
(3
.0
0
×
1
0
2
m
)
= 76.7 m/s
7. h
2
− h
1
= 6.0 m
g = 9.81 m/s
2
P
1
+
2
1
rv
1
2
+ rgh
1
= P
2
+
2
1
rv
2
2
+ rgh
2
Assume v
2
≈ 0 and P
1
= P
2
= P
0
.
2
1
rv
1
2
+ rgh
1
= rgh
2
v
1
=
2g
(h
2
−
h
1
)
=
(2
)(
9.
81
m
/s
2
)
(6
.0
m
)
= 11 m/s
Section Two—Problem Workbook Solutions Appendix J–17
1. V = 3.4 × 10
5
m
3
T = 280 K
N = 1.4 × 10
30
atoms
k
B
= 1.38 × 10
−23
J/K
PV = Nk
B
T
P =
Nk
V
B
T
=
P = 1.6 × 10
4
Pa
(1.4 × 10
30
atoms)(1.38 × 10
−23
J/K)(280 K)
3.4 × 10
5
m
3
Additional Practice L
Givens Solutions
2. V = 1.0 × 10
−3
m
3
N = 1.2 × 10
13
molecules
T = 300.0 K
k
B
= 1.38 × 10
−23
J/K
PV = Nk
B
T
P =
Nk
V
B
T
=
P = 5.0 × 10
−5
Pa
(1.2 × 10
13
molecules)(1.38 × 10
−23
J/K)(300.0 K)
1.0 × 10
−3
m
3
3. V = 3.3 × 10
6
m
3
N = 1.5 × 10
32
molecules
T = 360 K
k
B
= 1.38 × 10
−23
J/K
P V = Nk
B
T
P =
Nk
V
B
T
=
P = 2.3 × 10
5
Pa
(1.5 × 10
32
molecules)(1.38 × 10
−23
J/K)(360 K)
3.3 × 10
6
m
3
4. N = 1.00 × 10
27
molecules
T = 2.70 × 10
2
K
P = 36.2 Pa
k
B
= 1.38 × 10
−23
J/K
P V = Nk
B
T
V =
Nk
P
B
T
=
V = 1.03 × 10
5
m
3
(1.00 × 10
27
molecules)(1.38 × 10
−23
J/K)(2.70 × 10
2
K)
36.2 Pa
5. V
1
= 3.4 × 10
5
m
2
T
1
= 280 K
P
1
= 1.6 × 10
4
Pa
T
2
= 240 K
P
2
= 1.7 × 10
4
Pa
P
1
T
V
1
1
=
P
T
2
V
2
2
V
2
=
P
1
P
V
2
T
1
1
T
2
=
V
2
= 2.7 × 10
5
m
3
(1.6 × 10
4
Pa)(3.4 × 10
5
m
3
)(240 K)
(1.7 × 10
4
Pa)(280 K)
6. A = 2.50 × 10
2
m
2
T = 3.00 × 10
2
K
P = 101 kPa
N = 4.34 × 10
31
molecules
k
B
= 1.38 × 10
−23
J/K
P V = Nk
B
T
V =
Nk
P
B
T
=
V =
V =
lA
l =
V
A
=
1
2
.
.
7
5
8
0
×
×
1
1
0
0
6
2
m
m
3
2
= 7.12 × 10
3
m
1.78 × 10
6
m
3
(4.34 × 10
31
molecules)(1.38 × 10
−23
J/K)(3.00 × 10
2
K)
101 × 10
3
Pa
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualAppendix J–18
II
Copyright © by Holt, Rinehart and Winston. All rights reserved.
7. V = 7.36 × 10
4
m
3
P = 1.00 × 10
5
Pa
N = 1.63 × 10
30
particles
k
B
= 1.38 × 10
−23
J/K
PV = Nk
B
T
T =
N
P
k
V
B
=
T = 327 K
(1.00 × 10
5
Pa)(7.36 × 10
4
m
3
)
(1.63 × 10
30
particles)(1.38 × 10
−23
J/K)
Givens Solutions
8. l = 3053 m
A = 0.040 m
2
N = 3.6 × 10
27
molecules
P = 105 kPa
k
B
= 1.38 × 10
−23
J/K
P V = Nk
B
T
T = P
N
V
k
B
=
P
N
A
k
B
l
T ==260 K
(105 × 10
3
Pa)(0.040 m
2
)(3053 m)
(3.6 × 10
27
molecules)(1.38 × 10
−23
J/K)
9. P
1
= 2.50 × 10
6
Pa
T
1
= 495 K
V
1
= 3.00 m
3
V
2
= 57.0 m
3
P
2
= 1.01 × 10
5
Pa
P
1
T
V
1
1
=
P
T
2
V
2
2
T
2
=
P
2
P
V
1
V
2
T
1
1
=
T
2
=
P
1
T
V
1
1
=
P
T
2
V
2
2
T
2
=
P
2
P
V
1
V
2
T
1
1
=
(1.01 × 10
5
Pa)(57.0 m
3
)(495 K)
(2.50 × 10
6
Pa)(3.00 m
3
)
3.80 × 10
2
K
(1.01 × 10
5
Pa)(57.0 m
3
)(495 K)
(2.50 × 10
6
Pa)(3.00 m
3
)
1. f = 833 Hz
D = 5.0 cm 0.050 m
B = 8.0 × 10
−2
T
maximum emf 330 V
maximum emf = NABw = NAB(2pf )
A pr
2
p
D
2
2
p
0.05
2
m
2
2.0 10
3
m
2
N
ma
A
xi
B
m
(
u
2p
m
f)
emf
N = 4.0 × 10
2
turns
330 V
(2.0 10
–3
m
2
)(2p)(833 Hz)(8.0 10
–2
T)
Additional Practice M
3. r =
19.
2
3m
= 9.65 m
w = 0.52 rad/s
maximum emf = 2.5 V
N = 40 turns
maximum emf = NABw
B =
ma
N
xi
(
m
p
u
r
2
m
)w
emf
B =
B = 4.1 × 10
−4
T
2.5 V
(40)(p)(9.65 m)
2
(0.52 rad/s)
2. w = 335 rad/s
maximum emf = 214 V
B = 8.00 × 10
−2
T
A = 0.400 m
2
maximum emf = NABw
N =
maxim
AB
u
w
memf
N =
N = 20.0 turns
214 V
(0.400 m
2
)(0.0800 T)(335 rad/s)
Section Two—Problem Workbook Solutions Appendix J–19
II
4. maximum emf =
8.00 × 10
3
V
N = 236
A = (6.90 m)
2
w = 57.1 rad/s
maximum emf = NABw
B =
maxi
N
m
A
u
w
memf
B =
B = 1.25 × 10
−2
T
8.00 × 10
3
V
(236)(6.90 m)
2
(57.1 rad/s)
Givens Solutions
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Physics Solution ManualAppendix J–20
5. N = 1000 turns
A = 8.0 × 10
−4
m
2
B = 2.4 × 10
−3
T
maximum emf = 3.0 V
maximum emf = NABw
w =
maxim
NA
um
B
emf
w =
w = 1.6 × 10
3
rad/s
3.0 V
(1000)(8.0 × 10
−4
m
2
)(2.4 × 10
−3
T)
6. N = 640 turns
A = 0.127 m
2
maximum emf =
24.6 × 10
3
V
B = 8.00 × 10
−2
T
maximum emf = NABw
w =
maxim
NA
um
B
emf
w =
w = 3.78 × 10
3
rad/s
24.6 × 10
3
V
(640)(0.127 m
2
)(8.00 × 10
−2
T)
7. f = 1.0 × 10
3
Hz
B = 0.22 T
N = 250 turns
r = 12 × 10
−2
m
maximum emf = NABw = NAB(2pf ) = N(pr
3
)Bw = N(pr
2
)B(2pf )
maximum emf = (250)(p)(12 × 10
−2
m)
2
(0.22 T)(2p)(1.0 × 10
3
Hz)
maximum emf = 1.6 × 10
4
V = 16 kV
solutions
Study Guide
Worksheets Answers
III
Section
Holt Physics
III
Section Three—Study Guide Answers III–1
III
Copyright © by Holt, Rinehart and Winston. All rights reserved.
The Science of Physics
Study Guide Answers
1. a. mechanics (laws of motion)
b. vibrations and waves (sound or acoustics)
c. optics
d. thermodynamics
e. electricity
f. nuclear physics
2. a. No. Scientist do not vote about their knowledge.
They use evidence to support or disprove scientific
arguments
b. No. Speed of light is determined in nature. We can
only measure it.
c. Yes, by sharing their scientific arguments. Science is
a body of knowledge about the universe. Scientists
around the world work together to make it grow.
What Is Physics? p. 1
1. 10
18
2. 10
9
3. 10
7
4. a. 3.582 × 10
12
bytes
b. 9.2331 × 10
−7
W
c. 5.3657 × 10
−5
s
d. 5.32 × 10
−3
g
e. 8.8900 × 10
10
Hz
f. 8.3 × 10
−9
m
5. a. 36.582472 Mgrams
b. 452 nm
c. 53.236 kV
d. 4.62 ms
6. 4.2947842; 4.29478; 4.295; 4.3
Measurements in Experiments, p. 2
1. a. 6.0 × 10
8
b. 1.5 × 10
2
c. 1.5 × 10
−3
d. 6.0 × 10
3
e. 1.5 × 10
3
f. 6.0 × 10
−7
2. a. 4 × 10
5
b. 6 × 10
5
c. 8 × 10
−9
d. 7 × 10
−5
e. 7 × 10
6
f. 7 × 10
−4
3. a. 10
4
b. 10
−1
4. a. about 10 cm by 25 cm
b. Check student responses,
which should indicate that
volume = (width)
2
× (height).
c. Check student responses for
consistency with a and b.
The Language of Physics, p. 3
1. a. 2.2 × 10
5
s
b. 3.5 × 10
7
mm
c. 4.3 × 10
−4
km
d. 2.2 × 10
−5
kg
e. 6.71 × 10
11
mg
f. 8.76 × 10
−5
GW
g. 1.753 × 10
−1
ps
2. a. 3
b. 4
c. 10
d. 3
e. 2
f. 4
3. a. 4
b. 5
c. 3
4. a. 1.0054; −0.9952; 5.080 × 10
−3
;
5.076 × 10
−3
b. 4.597 × 10
7
; 3.866 × 10
7
;
1.546 × 10
14
; 11.58
5. 15.9 m
2
6. The graph should be a straight line.
Mixed Review, pp. 5–6
Motion In One
Dimension
Study Guide Answers
1. Yes, from t
1
to t
4
and from t
6
to t
7
.
2. Yes, from t
4
to t
5
.
3. greater than
4. greater than
5. Yes, from 0 to t
1
and from t
5
to t
6
.
6. Yes, from t
1
to t
2
, from t
2
to t
4
, from t
4
to t
5
, and from
t
6
to t
7
.
7. −5.0 m (or 5.0 m to the west of where it started)
Displacement and Velocity, p. 7
Holt Physics Solution ManualIII–2
III
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. v
f
= 0. The car is stopped.
2. v
i
=
2
∆
∆
t
x
3. a =
−
∆
v
t
i
4. a =
−
2∆
v
i
x
2
5. v
i
=−a∆t ∆x =
1
2
v
i
∆t
Acceleration, p. 8
1. a. −g
b. initial speed = g(∆t/2)
c. elapsed time =∆t/2
d. height = g∆t
2
/8
2. a. −9.81 m/s
2
b. 12 m/s
2. a. v
f
= a(∆t)
b. v
f
= v
i
+ a(∆t); ∆x =
1
2
(v
i
+ v
f
)∆t or ∆x = v
i
(∆t) +
1
2
a(∆t)
2
c. 1.2 s
Falling Objects, p. 9
1. a. t
1
= d
1
/v
1
;t
2
= d
2
/v
2
;t
3
= d
3
/v
3
b. total distance = d
1
+ d
2
+ d
3
c. total time = t
1
+ t
2
+ t
3
3.
Time interval Type of motion v (m/s) a(m/s
2
)
A speeding up ++
B speeding up ++
C constant velocity + 0
D slowing down +−
E slowing down +−
4. a. b. 1 s
c. 2 s
Time (s) Position (m) v (m/s) a(m/s
2
)
1 4.9 0 −9.81
20−9.8 −9.81
3 −14.7 −19.6 −9.81
4 −39.2 −29.4 −9.81
Mixed Review, pp. 11–12
Section Three—Study Guide Answers III–3
III
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Two-Dimensional
Motion and Vectors
Study Guide Answers
1. {A, C, E, H, I}; {D, G}, {B, F, J}
2. {A, D, H}, {B, C, G}, {I, J}
3. {A, H}
4. Both diagrams should show a vector A that is twice as
long as the original vector A, but still pointing up. The
first diagram should have the tip of 2A next to the tail of
B. The second diagram should have the tip of B next to
the tail of 2A. The resultant vectors should have the
same magnitude and direction, slanting towards the
upper right.
5. Both diagrams should show a vector B that is half as
long as the original vector B. The first diagram should
have the tip of A next to the tail of −B/2, and −B/2
should be pointing to the left. The second diagram
should have the tip of B/2 next to the tail of −A, and
−A should be pointing down. The resultant vectors
should have the same magnitude but opposite direc-
tions. The first will slant towards the upper left. The
second will slant towards the lower right.
Introduction to Vectors, p. 13
1. Check students’ graph for accuracy.
2. Shot 1: 45 m; 45 m
Shot 2: 110 m; 64 m
Shot 3: 65 m; 33 m
Shot 4: 0 m; 14.89 m
3. 220 m
Vector Operations, p. 14
1. ∆t = v
i
sin q/g
2. h = v
i
2
(sin q)
2
/2g
3. x = v
i
(cos q)(∆t) =
v
i
2
sin
g
q cos q
4. R =
2v
i
2
sin
g
q cos q
5.
Launch angle Maximum height (m) Range (m)
15° 8.5 130
30° 32 220
45° 64 250
60° 96 220
75° 119 130
Projectile Motion, p. 15
1. v
BL
= v
BW
+ v
WL
2. Student diagrams should show v
BW
twice as long as
v
WL
but both are in the same direction as v
BL
, which is
long as both together.
3. Student diagrams should show v
WL
and v
BW
, longer
and opposite in direction. The vector v
BL
should be as
long as the difference between the two, and in the same
direction and in the same direction as v
BW
.
4. Student diagrams should show v
WL
and v
BW
at a right
angle with v
BL
forming the hypotenuse of a right triangle.
5. a. 6.0 km/h, due east
b. 2.0 km/h, due west
c. 4.5 km/h, q = 26.6°
Relative Motion, p. 16
Holt Physics Solution ManualIII–4
III
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. a. The diagram should indicate the relative distances
and directions for each segment of the path.
b. 5.0 km, slightly north of northwest
c. 11.0 km
2. a. The same
b. Twice as large
c. 1.58
3. a. 2.5 m/s, in the direction of the sidewalk’s motion
b. 1.0 m/s, in the direction of the sidewalk’s motion
c. 4.5 m/s, in the direction of the sidewalk’s motion
d. 2.5 m/s, in the direction opposite to the sidewalk’s
motion
e. 4.7 m/s, q = 32°
4. a. 4.0 × 10
1
seconds
b. 6.0 × 10
1
seconds
Mixed Review, pp. 17–18
Section Three—Study Guide Answers III–5
III
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Forces and the
Laws of Motion
Study Guide Answers
1. The diagram should show two forces: 1) F
g
(or mg)
pointing down; 2) an equal and opposite force of the
floor on the box pointing up.
2. The diagram should show four forces: 1) F
g
(or mg)
pointing down; 2) an equal and opposite force of the
floor on the box pointing up; 3) F pointing to the right,
parallel to the ground; 4) F
resistance
pointing to the left,
parallel to the ground.
3. The diagram should show four forces: 1) F
g
(or mg)
pointing down; 2) F pointing to the right at a 50° angle
to the horizontal; 3) a force equal to F
g
minus the vertical
component of the force F being applied at a 50° angle;
and 4) F
resistance
to the left, parallel to the ground.
Changes in Motion, p. 19
1. F
net
= F
1
+ F
2
+ F
3
= 0
2. String 1: 0, −mg
String 2: −F
2
cos q
1
,F
2
sin q
1
String 3: F
3
cos q
2
,F
3
sin q
2
3. F
xnet
=−F
2
cos q
1
+ F
3
cos q
2
= 0
F
y net
=
−F
2
sin q
1
+ F
3
sin q
2
+ F
1
= 0
4. F
1
= 20.6 N
F
2
= 10.3 N
F
3
= 17.8 N
Newton’s First Law, p. 20
1. F
s on b
and F
b on s
;F
g on s
and F
s on g
;F
fr,1
and −F
fr,1
;
F
fr,2
and −F
fr,2
.
2. F
s on b
,F
b on s
, −F
fr,1
3. F
g on s
,F
s on g
;F
b on s
,F
fr,1
,F,F
fr,2
4. F
x,box
= ma =−F
fr,1
5. F
y,b ox
= F
s on b
− mg = 0
6. F
x,sled
= Ma = F cos q − F
fr,1
− F
fr,2
7. F
y,sled
= F
g on s
+ F sin q − F
b on s
− Mg = 0
Newton’s Second and Third Laws, p. 21
1. 44 N
2. 31 N
3. a. 21 N, up the ramp
b. yes
4. a. 18 N, down the ramp
b. yes
Everyday Forces, p. 22
1. a. at rest, moves to the left, hits back wall
b. moves to the right (with velocity v), at rest, neither
c. moves to the right, moves to the right, hits front wall
2. a. mg, down
b. mg, up
c. no
d. yes
3. a. a =
m
1
+
F
m
2
b. m
2
a
c. F − m
2
a = m
1
a
d.
m
1
m
+
1
m
2
F
4. a. a =
m
F
1
−
+
F
m
k
2
b. m
2
a − F
k
c. F − m
2
a − F
k
= m
1
a − F
k
d.
m
1
m
+
1
m
2
(F − F
k
)
Mixed Review, pp. 23–24
Work and Energy
Study Guide Answers
1. Fd
2.
−m
2
gd
3. 0 J
4. F
k
d
5. 0 N
6. 0 J
Work, p. 25
Holt Physics Solution ManualIII–6
III
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. a.
1
2
mv
i
2
b. 0
c.
1
2
mv
i
2
2. a.
1
2
mv
2
b.
1
2
kx
1
2
c.
1
2
mv
2
+
1
2
kx
1
2
3. a. 0
b.
1
2
kx
2
2
c.
1
2
kx
1
2
4. a.
1
2
mv
i
2
b. 0
c.
1
2
mv
i
2
Energy, p. 26
1. a. 0
b. mgh
A
c.
1
2
mv
B
2
3.
4. The sums are the same.
Location KE
A
PE
A
KE
location
PE
location
v
location
C 0 1.9 × 10
4
J9 × 10
3
J 9.6 × 10
3
J 17 m/s
D 0 1.9 × 10
4
J 1.3 × 10
4
J 6.4 × 10
3
J 2.0 × 10
1
m/s
E 0 1.9 × 10
4
J 1.6 × 10
4
J 3.2 × 10
3
J 22 m/s
F 0 1.9 × 10
4
J3 × 10
3
J 1.6 × 10
4
J 10 m/s
G 0 1.9 × 10
4
J6 × 10
3
J 1.3 × 10
4
J 14 m/s
d. mgh
B
2. a. v
A
= 0
b. v
B
=
2g
(h
A
−
h
B
)
Conservation of Energy, p. 27
1. v =−gt
2. d =−
1
2
gt
2
3. F = mg
4. W = Fd
5. The graph should be a curved line.
6. 4.20 × 10
2
W
Power, p. 28
1. a. 60 J
b. −60 J
2. a. mgh
b. mgh
c. v
B
=
v
A
2
+
2
gh
d. no
e. no
3. a. 2.9 J
b. 1.8 J
c. 1.2 J
d. a, b: different; c: same
4. a.
1
2
mv
i
2
+ mgh
i
=
1
2
mv
f
2
+ mgh
f
+
F
k
d
b. F
k
= mmg(cos 23°)
c. v
f
=
m
v
i
2
+
2
g
(d
s
in
2
3°
−
m
c
o
s
23
°)
Mixed Review, pp. 29–30
Section Three—Study Guide Answers III–7
III
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Momentum
and Collisions
Study Guide Answers
1. Student drawings should show a vector with a length of
9.5 squares to the right.
2. Student drawings should show a vector with a length of
5.0 squares pointing down.
3. 10.7 squares, angle −28°
4. 11 kg
•
m/s
5. 12 m/s
6. use a protractor, or use tan
−1
(5.0/9.5)
7. Student drawings should show one vector with a length
of 6.0 squares to the right and another with a length of
12.5 squares to the right. Final momentum is about
6.5 kg
•
m/s with a final speed of about 43 m/s.
Momentum and Impulse, p. 31
1. 0 kg
•
m/s
2. 0 kg
•
m/s
3. The vectors have equal length and opposite direction.
4.
v
v
sm
bi
a
g
ll
= 50
5. The ratio of velocities is the inverse ratio of the masses.
Conservation of Momentum, p. 32
1. vector A added head-to-tail with
vector K
2. F
3. F
4. vector F subtracted (tail-to-tail)
with vector H
5. J
Elastic and Inelastic Collisions, p. 33
1. a. The change due to the bat is greater than the change
due to the mitt.
b. The impulse due to the bat is greater than the im-
pulse due to the mitt.
c. Check student diagrams. Bat: vector showing initial
momentum and a larger vector in the opposite di-
rection showing impulse of bat, result is the sum of
the vectors. Mitt: vector showing initial momentum
and an equal length vector showing impulse of mitt,
result is the sum, which is equal to zero.
2. a. The impulses are equal, but opposite forces, occur-
ring during the same time interval.
b. The total force on the bowling ball is the sum of
forces on pins. The force on the pins is equal but
opposite of total force on ball.
3. m
1
v
1i
+ m
2
v
2i
= (m
1
+ m
2
)v
f
;
m
1
v
1i
/(m
1
+ m
2
) + m
2
v
2i
/(m
1
+ m
2
) = v
f
4. a. M(6 m/s)
b. 2 m/s
c. objects trade momentum; if masses are equal,
objects trade velocities
Mixed Review, pp. 35–36
Circular Motion
and Gravitation
Study Guide Answers
1. a. yes
b. The car has a non-zero acceleration because the
direction of motion is changing.
c. The direction of centripetal acceleration is toward
the center of the circle. In this case, the direction is
toward the center of the Ferris wheel.
d. 4.8 × 10
−2
m/s
2
2. a. the wire
b. centripetal force
c. The centripetal force acts toward the center of the
circular motion.
d. inertia
e. 32.0 m/s
Circular Motion, p. 37
Holt Physics Solution ManualIII–8
III
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Motion in Space, p. 39
1. a. 2
b. 4
c.
1
4
d. 1
2. a. double one mass, double the force
b. double both masses, quadruple the force
c. double the radius, decrease the force to
1
4
d. If measured in the opposite direction, the force will
be in the opposite direction.
3. Because of inertia, objects tend to go in a straight line.
A force is needed to change the direction of travel.
Newton’s Law of Universal Gravitation, p. 38
1. a. F
d
,F
e
,F
f
,F
g
b. F
e
exerts the largest torque because it has the largest
lever arm.
2. a. 1.2 × 10
4
J
b. 120 N
c. 110 m
d. greater
3. a. 0.92
b. 0.90
c. 0.94
Torque and Simple Mechanics, p. 40
1. a. According to Copernicus, Earth and the other plan-
ets each move in a perfect circle around the sun.
b. According to Kepler’s First Law, Earth and the other
planets each move in an elliptical orbit with the sun
at one focus.
2. ∆t
1
=∆t
2
3. T
2
∝ r
3
4. Newton derived Kepler’s laws from the universal law of
gravitation.
5. T = 3.17 × 10
7
s; v
t
= 2.98 × 10
4
m/s
Section Three—Study Guide Answers III–9
III
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. a. Inertia tends to carry the passenger in a straight line
tangent to the circular motion.
b. Friction between the car’s tires and the road pro-
vides a centripetal force that keeps the car moving in
a circle.
c. 1.4 m/s
2
d. 1.4 × 10
3
N
2. a. doubled
b. quadrupled
c. reduced to
1
4
d. quadrupled
e. reduced to
1
9
3. Student diagrams should show vectors for weight and
normal force from elevator; descent should show normal
force less than weight; stopping should show normal
force greater than weight; “weightlessness” feeling is due
to acceleration.
4. a. 10.0 N
b. 2.22 × 10
−1
m/s
2
c. 8.66 × 10
4
s
d. 3.07 × 10
3
m/s
5. a. If the knob is farther from the hinge, there is
increased torque for a given force.
b. twice as much
c. 2.5 N
•
m
6. a. 4.0 × 10
4
J
b. 4.4 × 10
4
J
c. 4.9 × 10
4
J
d. 0.81
Mixed Review, pp. 41–42
Fluid Mechanics
Study Guide Answers
1. V = 30.0 m
3
2. 1.95 × 10
4
kg
3. F
g
= 1.91 × 10
5
N
4. 0
5. F
b
= 1.91 × 10
5
N
6. 1.95 × 10
4
kg
7. 19.5 m
3
8. 19.5 m
3
; 10.5 m
3
9. Ethanol: F
b
= 1.91 × 10
5
N; 1.95 ×
10
4
kg; 24.2 m
3
; 24.2 m
3
; 5.8 m
3
Fluids and Buoyant Force, p. 43
Holt Physics Solution ManualIII–10
III
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. P = 6.94 × 10
3
Pa
2. P = 6.94 × 10
3
Pa
3. P = 6.94 × 10
3
Pa
4. 12.5 N
5. a. V = 1.44 × 10
−5
m
3
(14.4 cm
3
)
b. 0.02 m
Fluid Mechanics, p. 44
1. 1.20 m
3
/s; 1.20 m
3
/s; 1.20 m
3
/s
2. 6.00 m; 2.00 m; 12.0 m
3. 1 s, 1 s, 1 s
4. 6.00 m/s; 2.00 m/s; 12.0 m/s
5. Speed increases in order to keep
the flow rate constant.
Fluids in Motion, p. 45
1. a. 2.01 × 10
5
N/m
2
(top); 2.51 × 10
5
N/m
2
(bottom)
b. 3.02 × 10
5
N/m
2
; 3.52 × 10
5
N/m
2
c. F
top
= 1.81 × 10
6
N; F
bottom
= 2.11 × 10
6
N
d. F
top
is downward; F
bottom
is upward and greater
e. net force = 3.0 × 10
5
N; F
bottom
f. The crate will sink because the buoyant force is less
than the weight of the crate.
g. V = 30.0 m
3
h. F
b
= 3.00 × 10
5
N. The buoyant force is equal to the
weight of water displace by the crate.
2. a. P
1
= P
2
A
F
1
1
=
A
F
2
2
b. A =πr
2
π
F
r
1
1
2
=
π
F
r
2
2
2
c. F
2
= F
1
r
r
2
1
2
F
2
= (750.0 N)
0
0
.
.
0
5
5
0
0
0
m
m
2
3. a. A
1
v
1
= A
2
v
2
b. A =πr
2
πr
1
2
v
1
=πr
2
2
v
2
c. v
2
= v
1
r
r
1
2
2
v
2
= (0.750 m/s)
0
1
.
.
2
5
5
0
0
m
m
2
v
2
= 27.0 m/s
Mixed Review, pp. 47–48
Section Three—Study Guide Answers III–11
III
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Heat
Study Guide Answers
1. 183 K to 268 K
2. a. 6.30 × 10
2
K; 2.34 × 10
2
K
b. no; yes
3. a. no—tub is 36°C
b. cold
4. a. 77.4 K; 90.2 K
b. The nitrogen is a gas because
the temperature is above its
boiling point. The oxygen is a
liquid because the temperature
is below its boiling point.
Temperature and Thermal Equilibrium, p. 49
1. a. 3.12 × 10
5
J
b. 5.00 × 10
4
J
c. increase, 2.62 × 10
5
J
d. yes; 2.62 × 10
5
J
2. a. 3.92 × 10
4
J; 2.50 × 10
3
J;
4.17 × 10
4
J
b. 0 J; 2.50 × 10
3
J; 2.50 × 10
3
J
c. decreased by 3.92 × 10
4
J
d. increase by 3.92 × 10
4
J;
melting the ice
Defining Heat, p. 50
1. 1.04 × 10
6
J
2. 6.66 × 10
6
J
3. 4.19 × 10
5
J
4. 3-part graph with energy in joules on horizontal axis
and temperature in degrees celsius on the vertical axis:
graph goes up from {0 J, −25°C to 1.04 × 10
6
J, 0°C}, is
horizontal until {7.70 × 10
6
J, 0°C}, then goes up to
8.12 × 10
6
J, 0°C}
Changes in Temperature and Phase, p. 51
1. a. 78.5 J
b. 78.5 J
c. 51.2 J; less than loss in PE
d. 27.3 J
2. a. 2.26 × 10
9
J
b. 1.49 × 10
5
kg
c. 3.62°C
d. 19.4°C
3. a. They are at thermal equilibrium.
b. (100.0 − x)°C; (y − 20.0)°C
c. (2.000 kg)(4.19 × 10
3
J/kg
•
°C)
(100.0 − x)°C
d. (5.000 kg) (8.99 × 10
2
J/kg
•
°C)
(y − 20.0)°C
e. all of the energy was trans-
ferred from the water to the
pipe, no loss and no other
source of energy
f. 72°C
Mixed Review, pp. 53–54
Thermodynamics
Study Guide Answers
1. a. 0.020 m
3
b. 7.0 × 10
3
J
c. 2.0 × 10
3
J increase
2. a. yes, marble to water
b. no, ∆U by heat only
c. decrease; temperature dropped
d. increase; more water, less ice
e. no change, the cup is insulated
Relationships Between Heat and Work, p. 55
Holt Physics Solution ManualIII–12
III
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. a. −320 J
b. The gas lost energy because ∆U was less than 0.
c. Student diagrams should show the W arrow and the
Q arrow pointing OUT of the container.
2. a. 0
b. 540 J out
c. Student diagrams should show the W arrow
pointing IN and the Q arrow pointing OUT.
The First Law of Thermodynamics, p. 56
1. a. 8.0 × 10
3
J
b. 20%
c. 3.2 × 10
2
N
2. a. 7.00 × 10
3
J
b. 1.30 × 10
4
J
c. 4.0 × 10
1
m
3. a. 5.0 × 10
2
J
b. 3.4 × 10
2
J
c. 1.9 × 10
2
J
The Second Law of Thermodynamics, p. 57
1. ∆U = 700 J increase
2. a. 0.005 m
3
b. 1.5 × 10
3
J
c. 1.5 × 10
3
J
3. a. 5.00 × 10
4
J
b. 1.40 × 10
4
J
4. a. ∆U (compressed air) = W (added by person) −
Q (things warm up)
b. Disorder is increased by increasing internal energy
through heat.
5. Graph bars should convey that: PE
1
= max, KE
1
= 0,
U
1
= 0 or U
1
is any amount. Then, PE
2
= 0, KE
2
≤
1
2
PE
1
,
U
2
≥ U
1
+
1
2
PE
1
. Then, PE
3
≤
1
2
PE
1
,KE
3
= 0, U
3
≈ U
2
.
Last: PE
4
= 0, KE
4
≤
1
4
PE
1
, and U
4
≥
4
3
PE
1
.
Mixed Review, pp. 59–60
Section Three—Study Guide Answers III–13
III
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Vibrations and Waves
Study Guide Answers
1. a. 0.21 m
b. 2.0 s
c. 0.5 Hz
d. 0.50 m, 2.0 s, 0.5 Hz
2. a. 49.0 N
b. 4.90 × 10
2
N
c. 41.6 N
d. 15.9 cm
Simple Harmonic Motion, p. 61
1. 0.1 s, 10 Hz
2. a. 5.0 Hz
b. 10, 70
3. a. 4.0 Hz, 0.25 s
b. 4.0 Hz, 0.25 s, 5.0 cm
4. 0.500 Hz, 2.00 s, 0.0621 m
5. a. 1267 kg, 5066 kg
b. increase
Measuring Simple Harmonic Motion, p. 62
1. 37.5 m, 250 m
2. a. 0.02 s, 5 × 10
1
Hz
b. 40.00 m, 2.000 × 10
3
m/s
Properties of Waves, p. 63
1. a. Students’ drawings of amplitudes should have
magnitudes corresponding to 0.25 and 0.35.
b. Students’ drawings should indicate constructive
interference, with a net amplitude of 0.60.
2. a. 1.5 s
b. 10.0 m
c. yes
Wave Interactions, p. 64
1. a. 0.20 s; 5.0 Hz
b. same, same, increase, increase
2. a. 60.0 N/m
b. 0.574 seconds; 1.74 Hz
3. 6.58 m/s
2
;no
4. a. A: 0 s, 2 s, 4 s; B: 0.5 s, 1.5 s, 2.5 s, 3.5 s; C: 1, 3 s
b. PE: 0 s at A, 1 s at C, 2 s at A, 3 s at C, 4 s at A; KE:
0.5 s, 1.5 s, 2.5 s, 3.5 s at B
c. 0.5 s, 2.5 s at B to the right 1.5 s, 3.5 s at B to the left;
0 s, 2 s, 4 s at A to the right, 1 s, 3 s at C to the left
5. 3.00 × 10
2
m/s
6. 3.0 s; 6.0
Mixed Review, pp. 65–66
Sound
Study Guide Answers
1. 336 m/s
2. 1030 m
3. a. 3.00 cm
b. 1.50 cm
c. 3.51 s; 0.234 s
d. 1.14 × 10
4
Hz (no Doppler effect because the train
was stationary)
e. pitch decrease; same; increase
Sound Waves, p. 67
Holt Physics Solution ManualIII–14
III
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. a. 9.95 × 10
−3
to 2.49 × 10
−3
W/m
2
b. 6.22 × 10
−4
to 2.76 × 10
−4
W/m
2
c. 1.59 × 10
−5
W/m
2
,about 70
2. a. 1.00 × 10
−2
W/m
2
b. 3.14 W
c. 5000 m
Sound Intensity and Resonance, p. 68
1. a. 462 m/s
b. Student diagrams should show antinodes, nodes at
both ends; first has one antinode, second has two,
third has three.
c. 69.0 cm
2. a. 880 Hz, 1320 Hz, 1760 Hz
b. Check student graphs for accuracy. Wavelength of
first harmonic should be two wavelengths of second
harmonic, three wavelengths of third harmonic. The
second and third harmonics should have half the
amplitude. The resultant will be a wave with a large
maximum, a smaller peak, a small minimum, and a
large minimum.
Harmonics, p. 69
1. a. 2.19 m; 2.27 m
b. wavelength increases when temperature increases
2. a. arrows pointing East on ambulance, police, and
truck, West on van.
b. police and ambulance (equal), truck, small car, van
3. These objects had the same natural frequency of
330 Hz, so resonance occurred.
4. a. 1460 Hz, 2440 Hz
b. 70.8 cm, 23.6 cm, 14.1 cm
c. 0.177 m
d. 974 Hz, 1460 Hz; 70.8 cm, 35.4 cm, 23.6 cm; 0.354 m
5. a. 5
b. 435 Hz, because it will also provide a difference
of 5 Hz.
Mixed Review, pp. 71–72
Section Three—Study Guide Answers III–15
III
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Light and Reflection
Study Guide Answers
1. a. 499 s
b. 193 s
c. 1.97 × 10
4
s
2. a. 7.1 × 10
14
Hz; 6.7 × 10
14
Hz;
5.5 × 10
14
Hz; 5.0 × 10
14
Hz;
4.3 × 10
14
Hz
b. Frequency decreases when
wavelength increases.
c. No, no
Characteristics of Light, p. 73
1. a. midpoint between mirror and O
b. markings should be at scale: 1 cm for 1 m
c. A’s image is 2.6 m inside.
d. Image locations: B at 3.33 m inside the mirror; C at
2.00 m outside the mirror
2. 2.60 m; 3.33 m; −2.00 m
Curved Mirrors, p. 75
1. 4.07 × 10
16
m
2. a. 3.33 × 10
−5
s
b. 1.00 × 10
−4
m
3. 3.84 × 10
8
m
4. 3.00 × 10
11
Hz
5. Diffuse reflection: (nonshiny surfaces) table top, floor,
walls, car paint, posters (answers will vary)
Specular reflection: metallic surfaces, water, mirrors
(answers will vary)
6. a. Check student drawings for accuracy.
b. B is 4 m from A horizontally, C is 2 m below B
vertically
c. D is 2 m below A vertically, E coincides with C
d. they will overlap the existing images or objects
Mixed Review, pp. 77–78
1. a. Check student drawings for accuracy. Angles of
reflection should be equal.
b. Extensions intersect on the normal through A, 25 cm
inside the mirror.
c. 50 cm
d. No, but the person will see image by receiving the
reflection of some other ray.
e. The person will see the image by receiving reflected
Ray from C.
f. angle at A close to 50°, angle at B close to 60°
g. The eraser’s image is 15 cm inside.
Flat Mirrors, p. 74
1. a. all but green because green is
reflected
b. red, because it lets the type of
light best absorbed by plants to
be transmitted
2. a. white
b. blue
c. black
d. black
3. black
Color and Polarization, p. 76
Holt Physics Solution ManualIII–16
III
Copyright © by Holt, Rinehart and Winston. All rights reserved.
7. a. 9.00 cm
b. p = 30.0 cm; q = 12.9 cm; real; inverted; 2.58 cm tall
p = 24.0 cm; q = 14.4 cm; real, inverted; 3.60 cm tall
p = 18.0 cm; q = 18.0 cm; real; inverted; 6.00 cm tall
p = 12.0 cm; q = 36.0 cm; real; inverted; 2.00 cm tall
p = 6.0 cm; q =−18 cm; virtual; upright; 18 cm tall
8. p = 30.0 cm; q =−6.92 cm; virtual; upright; 1.38 cm tall
p = 24.0 cm; q =−6.55 cm; virtual, upright; 1.64 cm tall
p = 18.0 cm; q =−6.00 cm; virtual; upright; 2.00 cm tall
p = 12.0 cm; q =−5.14 cm; virtual; upright; 2.57 cm tall
p = 6.0 cm; q =−3.6 cm; virtual; upright; 3.6 cm tall
Section Three—Study Guide Answers III–17
III
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Refraction
Study Guide Answers
1. a. n = c/v
b. 2.25 × 10
8
m/s
2. a. 13.0°
b. 13.0°, 20.0°
c. Angles inside glass: 25°,35°,40°; Angles coming out
of glass: 40°,60°,80°
d. Student sketches should indicate that the rays exit-
ing the glass are parallel to the rays entering it.
Refraction, p. 79
1. a. Check student diagrams. Rays should be drawn
straight, according to rules for ray tracing.
b. A is real, inverted, and smaller.
c. B is real, inverted, and smaller; C is virtual, upright,
and larger
2. A: 4.80 cm; B: 7.5 cm; C: −6.00 cm
Thin Lenses, p. 80
1. a. q
r
= 55.8°
b. sin q
r
= 1.28 > 1: internal reflection
c. q
r
= 24.4°
d. q
r
= 38.5°; q
r
= 74.5°; q
r
= 33.4°
2. q
r
= 48.8°, the angle is too large, light with 45° incident
angle will be refracted and exit
Optical Phenomena, p. 81
1. a. Ray 1 at 45°; Ray 2 at 14.9°
b. Rays should intersect inside the aquarium.
c. Because the rays are no longer parallel, they will in-
tersect in the water.
2. a. First boundary: 70.0°, 45.0°
Second boundary: 45.0°, 40.4°
Third boundary: 40.3°, 36.8°
b. Incoming rays get closer and closer to the normal.
Reflected rays get farther away from the normal with
the same angles.
3. a. 9.00 cm
b. 12.9 cm, 14.4 cm, 18.0 cm, 36.0 cm, −18.0 cm
2.58 cm, 3.6 cm, 6.00 cm, 18.0 cm, −18.0 cm
real, real, real, real, virtual
4. 18.0 cm, with all images virtual and on the left of the lens
−11.2, −10.3, −9.00, −7.20, −4.50
5. a. 6.00 cm in front of the lens
b. 0.857 cm
Mixed Review, pp. 83–84
Interference and
Diffraction
Study Guide Answers
1. a. First: 1.6°, Second: 3.2°, Third: 4.8°
b. Bright: 16.2°, 34.0°, 4.01°
c. A smaller slit results in more separation between
fringes. With 2 cm, fringes would be so close they
would not be distinguishable.
2. a. 475 nm
b. 7.80°, 11.7°, 15.7°
Interference, p. 85
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III
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. a. 1.25 × 10
−6
m
b. 18° spacing for 400 nm light and 34° for 700 nm
light. More lines per centimeter will give better
resolution
2. a. 1250 lines/cm
b. 4.4°, 8.9°,13°
3. 565 nm
4. 4.38 × 10
−6
m
Diffraction, p. 86
1. Coherent light is individual light waves of the same wave-
length that have the properties of a single light wave.
2. Student diagrams should show a coherent light source
with light waves moving in the same direction. The
incoherent light should have a light source with waves
radiating out in different directions.
3. Lasers convert light, electrical energy, or chemical
energy into coherent light.
4. Answers will vary. Examples are CD players, laser
scalpels, laser range finders.
Lasers, p. 87
1. a. 6.74 × 10
−6
m
b. 47.9°
c. The maximum angle for light to reach the screen in
this arrangement is 45°.
2. a. Longer wavelengths are diffracted with a greater angle.
b. First order group of lines: blue, green, red; second
order: the same
c. White
3. a. A = 5.0 × 10
−6
m, B = 1.1 × 10
−7
m, C = 3.3 × 10
−8
m
b. visible: A; x-ray: A, B, or C; IR: none
4. a. Neither would work because they would act as dif-
ferent sources, so even with the same frequency, they
should not be in phase.
b. Interference is occurring.
Mixed Review, pp. 89–90
Section Three—Study Guide Answers III–19
III
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Electric Forces
and Fields
Study Guide Answers
1. a. Experiment A, no charges were transferred. Experi-
ment B, charges were transferred between the sphere
and the ground. Experiment C, charges were trans-
ferred between the sphere and the rod
b. Student diagrams should show: Sphere A, negative
charges (−) on the left, positive (+) on the right; Sphere
B, excess (−) all over; Sphere C, excess (+) all over.
c. Sphere B has excess (−); Sphere C has excess (+)
d. Experiment A
e. no change in Experiment A or Experiment B; re-
duced charge in Experiment C
Electric Charge, p. 91
1. a. 20.0 cm
b. 0.899 N (attraction along the line q
1
− q
3
)
c. 0.899 N (attraction along the line q
1
− q
2
)
d. 1.40 N repulsion pulling to the right
e. Student diagrams should show F
1
pointing from q
3
toward q
1
and F
2
pointing from q
3
toward q
2
.
f. 36.9°
g. F
1x
=−0.719 N; F
2x
= 0.719 N; F
1y
=−0.540 N;
F
2y
=−0.540 N
h. −1.08 N pointing down
i. downward along the y-axis
Electric Force, p. 92
1. a. 21.2 cm
b. all same strength of 1.60 × 10
−6
N/C along the diag-
onal lines, with E
1
pointing away from q
1
, E
2
from
q
2
, E
3
from q
3
, and E
4
from q
4
c. Resultant electric field E = 0
2. a. 4.61 × 10
−14
N down
b. 4.61 × 10
−14
N up
c. 1.44 × 10
−18
C
d. 9 electrons
The Electric Field, p. 93
1. a. A; 1.87 × 10
13
electrons; B: 3.12 × 10
13
electrons
b. the forces are equal and opposite, no
2. a. Resultant = 1.49 N, left; F(A-C) = 1.35 N, left;
F(B-C) = 0.140 N, left
b. Resultant = 0.788 N, right; F(A-C) = 1.35 N, right;
F(B-C) = 0.562 N, left
c. Resultant = 0.400 N, left; F(A-C) = 0.599 N, right;
F(B-C) = 0.999 N, left
3. a. 1.92 × 10
16
N
b. 2.87 × 10
10
m/s
2
c. 9.81 m/s
2
; this is negligible in comparison with the
acceleration a; alpha particles will move horizontally
4. a. Check students diagrams for accuracy.
b. 1.53 × 10
−2
N
c. 7.65 × 10
3
N/C
5. 1 C = 6.25 × 10
18
;1 mC = 6.25 × 10
12
Mixed Review, pp. 95–96
Electrical Energy
and Current
Study Guide Answers
Holt Physics Solution ManualIII–20
III
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. a. 8.99 × 10
5
V
b. y =−10.0 cm; V = 3.33 × 10
5
V
y =−2.00 cm; V = 8.08 × 10
5
V
y = 2.00 cm; V = 8.08 × 10
5
V
y = 10.0 cm; V = 3.32 × 10
5
V
c. x =−10.0 cm; V = 4.28 × 10
5
V
x =−2.00 cm; V = 1.20 × 10
6
V
x = 2.00 cm; V = 1.20 × 10
6
V
x = 10.0 cm; V = 4.28 × 10
5
V
2. a. 2.16 × 10
6
V
b. 0
c. 0
Electric Potential, p. 97
1. pF = 10
−12
F; nF = 10
−9
F; mC = 10
−6
C; Farads measure
the ratio of charge to potential difference. Coulombs
measure the amount of charge.
2. 1 pF < 1 nF. The 1 pF capacitor has a higher potential
difference (1000 times) because ∆V = Q/C
3. a. 4.00 × 10
−7
F = 4.00 × 10
2
nF
b. Capacitance does not change. Charge doubles (Q is
proportional to ∆V, ∆V doubled and C was the same)
c. 5.00 × 10
−2
J; 2.00 × 10
1
J
Capacitance, p. 98
1. a. −1.28 × 10
−15
J; decreases
b. 1.28 × 10
−15
J; increases
c. 5.3 × 10
7
m/s
2. a. 5.000 × 10
3
V/m; yes, the field is constant
b. ∆V(+plate, A) = 50.0 V; ∆V(+plate, B) = 1.50 ×
10
2
V; ∆V(+plate, C) = 2.50 × 10
2
V
c. PE at positive plate = 4.80 × 10
−17
J; PE
A
= 4.00 ×
10
−17
J; PE
B
= 2.40 × 10
−17
J; PE
C
= 8.00 × 10
−18
J;
PE at negative plate = 0 J
3. a. 2.00 × 10
2
V
b. 4.00 × 10
−3
J
4. a. 4.8 A
b. 8.64 × 10
4
C
c. 580 W
d. 1.0 × 10
7
J
5. a. 144 V
b. 864 W
c. 104 seconds
Mixed Review, pp. 101–102
1. 2.50 × 10
2
A
2. a. 320 s
b. 320 s
c. 320 s
3. a. 1.80 × 10
−3
A; 1.80 A; 1.80 ×
10
2
A
b. C (smaller resistor)
4. 134 V
5. a. 343 Ω to 286 Ω
b. R > 285 Ω
c. R < 387 Ω
Current and Resistance, p. 99
1. a. 932 W
b. 1.68 × 10
7
J = 4.66 kWh
c. 32.6 ¢
2. a. 417 W
b. 3.5 A
3. a. 5.1 Ω
b. 24 A
Electric Power, p. 100
Section Three—Study Guide Answers III–21
III
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Circuits and
Circuit Elements
Study Guide Answers
1. a. Check student diagrams, which should contain 2
bulbs, 2 resistors, 3 switches, and 1 battery, in a
closed cirucit.
b. Check student diagrams to be certain that the switches
labeled S1 and S2 cause short circuits when closed.
c. Check student diagrams to be certain that switch S3
causes a short circuit when closed.
2. a. Students should connect one end of bulb A to the
battery, the other to the switch, then the other end of
the switch to the battery. Also connect one end of B
to the battery, and the other end of B to the switch.
b. Students should connect one end of B to the battery,
the other to the switch, then the other end of the
switch to the battery. Bulb A should simply be left
out with no connections.
c. Students should connect each end of B to one end of
the battery, the other to the switch, then the other
end of the switch to the battery. Also each end of A
should be connected to an end of the battery.
Schematic Diagrams and Circuits, p. 103
1. a. 16.0 Ω
b. 0.750 A for both
c. 12.0 V; 9.0 V; 3.0 V
2. a. 3.00 Ω
b. 12 V
c. 4 A, I
1
= 1 A; I
2
= 3 A
d. 12.0 V
Resistors in Series or in Parallel, p. 104
1. a. 40 Ω
b. I
a
= I
b
= I
c
= 0.600 A; I
d
= I
e
= I
f
= 0.200 A;
∆V
a
=∆V
b
=∆V
c
= 7.20 V; ∆V
d
=∆V
e
=∆V
f
= 2.40 V
2. a. Check diagram
b. 54 Ω; I
a
= I
b
= I
c
= I
f
= 0.444 A; I
d
= I
e
= 0.222 A;
∆V
a
=∆V
b
=∆V
c
=∆V
f
= 5.33 V; ∆V
d
=∆V
e
= 2.67 V
Complex Resistor Combinations, p. 105
1. a. D
b. switch 5
c. • switches 1 and 3 open, switches 2, 4, and 5 closed
• switches 1 and 4 open, switches 2, 3, and 5 closed
• switch 2 open, switches 1, 3, 4, and 5 closed; or
switches 3 and 4 open, switches 1, 2, and 5 closed;
or switches 2, 3, and 4 open, switches 1 and 5 closed
2. a. Check students’ diagrams, which should show a
bulb and a resistor in series with a battery.
b. 15 Ω
c. 6 Ω
3. a. Check students diagrams.
b. 12.0 V, 12.0 V
c. 0.25 A, 2.25 A
d. 5.33 Ω
4. a. R = 6.15 Ω
b. R = 30.4 Ω
Mixed Review, pp. 107–108
Magnetism
Study Guide Answers
Holt Physics Solution ManualIII–22
III
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. a. No
b. No
c. Magnet: A; Iron: B and C.
2. Arrows should point away from S, toward N, building a
composite picture of the magnetic field.
3. Arrows should point away from S, toward N, mostly in
the area between the ends of the magnet and around it.
Magnets and Magnetic Fields, p. 109
1. a. the field at A, B, C is pointing out (dot symbol); the
field at D, E, F is pointing in (× symbol).
b. all reversed: the field at A, B, C is pointing in (× sym-
bol); the field at D, E, F is pointing out (dot symbol)
2. the strength at point A is weaker than B, C, D or E, and
about equal to that at F.
3. All directions of field are opposite to the answers in
questions 1. The relative strengths remain the same.
Magnetism from Electricity, p. 110
1. a. v-arrow to the right, B-arrow upward
b. •; F = 4.8 × 10
−14
N, upward, out of the page
c. 0
2. a. v-arrow to the left, B-arrow upward
b. ×; F = 4.8 × 10
−14
N, downward, into the page
c. 0
3. a. v-arrow to the right, B-arrow upward
b. •; F = 9.6 × 10
−14
N, upward, out of the page
c. 0
4. No. When the force is not zero, it acts perpendicular to
velocity. They move in a circle perpendicular to the
magnetic field.
Magnetic Force, p. 111
1. a. The magnetic field from the leftmost segment is •
and stronger. The magnetic field from the rightmost
segment is × and weaker.
b. At A, both horizontal segments contribute a ×
magnetic field of equal strength
c. B; ×; × weaker; ×; × same
C; ×; × same; ×; × same
D; ×; × stronger; ×; × same
E; ×; • stronger; ×; × same
d. No. They reinforce each other in the same direction.
e. inside
2. a. F = 4.3 N into the page
b. F = 0
3. a. Diagrams should show clockwise current.
b. Starting from the left side: F = 1.1 N into the page;
F = 0; F = 1.1 N out of the page; F = 0
c. Forces are equal and opposite, so no translational
motion will occur, but it could rotate around a verti-
cal axis.
Mixed Review, pp. 113–114
Section Three—Study Guide Answers III–23
III
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Electromagnetic
Induction
Study Guide Answers
1. side a: none, down, down, none, none
side b: none, none, none, none, none
side c: none, none, down, down, none
side d: none, none, none, none, none
2. none, clockwise, none, counterclockwise, none
3. a. 2.56 × 10
−2
m
2
b. 2.0 s
c. 2.0 × 10
−2
V
d. 5.7 × 10
−2
A
Electricity from Magnetism, p. 115
1. A to B
2. increase, increase, increase
3. a. horizontal
b. vertical
c. 0.25 s
d. 1.9 × 10
−3
V
Generators, Motors, and Mutual Inductance, p. 116
1. down through primary coil, and up elsewhere, includ-
ing through the secondary coil
2. a −,b +
3. 24 V
4. no change in field
5. disappearing field is a change which secondary coil
opposes
AC Circuits and Transformers, p. 117
1. e
2. a. 0.50 s
b. 0.26 m
2
c. 2.6 V
3. a. magnetic field, conductor, relative motion
b. answers may vary, but could include the following:
water wheel, windmill, electric motor, combustion
engine
4. a. 6.28 rad/s
b. 7.1 × 10
−2
m
2
Mixed Review, pp. 119–120
Electromagnetic Waves, p. 118
1. The electromagnetic spectrum
2. “High energy” should be on the right side; “low energy”
should be on the left side
3. Both wavelength and frequency, and wavelength and
energy, show an inverse relationship, that is, as one
factor increases, the other decreases. Frequency and
energy display a direct relationship, that is, both factors
increase or decrease together.
4. Answers may include one or more of the following:
a. heat lamps, remote controls, burglar alarms,
night-vision goggles
b. photography, medical, security screening
c. disinfection, science, astronomy, dentistry
d. ovens, communication, cell phones, radar
e. light bulbs, lasers, art, science
f. communication, television, astronomy
g. medicine, astronomy, scientific research
Holt Physics Solution ManualIII–24
III
Copyright © by Holt, Rinehart and Winston. All rights reserved.
c. 110 V
d. 78 V
5. A motor converts electric energy to rotational energy;
generators converts rotational energy to electric energy.
6. a. increases
b. induces current while change occurs
c. It decreases magnetic field which will induce a cur-
rent while the change occurs.
Section Three—Study Guide Answers III–25
III
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Atomic Physics
Study Guide Answers
1. a. This implies that there is an in-
finite energy output.
b. quantization of energy
c. As wavelength gets shorter, en-
ergy in photon gets smaller.
2. a. 2.9 × 10
−31
J
b. 1.8 × 10
−12
eV
3. a. hf
t
= hf − KE
max
b. 2.30 eV
Quantization of Energy, p. 121
1. small positively charged nucleus and electrons in
planetary orbits
2. He expected diffuse positive charge with no scattering.
3. Most atoms went through.
4. As electrons radiated energy, they would spiral in to-
ward nucleus.
Models of the Atom, p. 122
1. a. light radiating from the sun to Earth
b. light scattering off electrons
2. The precision of measurements for very small objects is
relatively less than the precision of measurements of
very large objects.
3. a. 1.47 × 10
−38
m
b. 5.41 × 10
−40
m
c. 8.4 × 10
−37
m
d. 3.7 × 10
−35
m
4. It allowed for electron uncertainty and gave electrons
probable but not definite orbits.
Quantum Mechanics, p. 123
1. There is not enough energy in any individual photon to
liberate the electron.
2. Some energy is used in liberating the electron.
3. a. Atoms contained areas of dense positive charge.
b. The foil is mostly empty space.
4. a. 1.5 × 10
−8
m
b. 5.3 × 10
−34
m
c. The wavelength is too small to detect.
5. a. Simultaneous measurements of position and mo-
mentum cannot be completely certain.
b. A theory of distinct orbits would require precise
knowledge of their location at any given time.
6. A photon does not measurably deflect a planet.
7. 1.16 × 10
15
m
8. No electrons were ejected.
9. It is absorbed by atoms into vibrational motion, etc.
10. Energy is observed in increased temperature.
Mixed Review, pp. 125–126
Holt Physics Solution ManualIII–26
Subatomic Physics
Study Guide Answers
III
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1. a. 16
b. 8
c. 16
d. 2.81 MeV
e. Energy is required to separate the nucleus.
f. No, it is the same element but a different isotope.
2. a. strong interaction
b. decreases
The Nucleus, p. 127
1. alpha—helium nucleus; beta—
electron or positron; gamma—
photons
2. a. O-17
b. Th-231
c. Np-238
d. U-235
3. It is the time required for half of
the sample to decay.
4. It gives decay rate for sample.
5. half-life = 0.693/decay constant
6. 0.050 s
−1
7. 3.15 × 10
7
s
8. 25.0% or 1/4
Nuclear Decay, p. 128
1. a. fission
b. neutron and uranium nucleus
c. barium, krypton, and 3 neutrons
d. yes
e. more fission
f. It has high energy output. In a
nuclear reactor, the high heat
leads to a meltdown.
2. a. fusion
b. proton and helium-3 nucleus
c. alpha (He-4), positron and
neutrino
d. yes
Nuclear Reactions, p. 129
1. Strong: 1, hold nucleons, 10
−15
m; electromagnetic:
10
−2
, charged particles, 1/r
2
; weak: 10
−13
, fission,
10
−18
m; gravitational: 10
−38
, all mass, 1/r
2
2. a. graviton; W and Z bosons; photons; gluons
b. graviton
3. a. It can unify weak and electromagnetic interactions
at high energy.
b. It requires very high energy interaction (1 TeV).
Particle Physics, p. 130
1. a. 143
b. 146
c. 146
d. 1
e. 2
f. 8
g. 10
h. 22
2. a. atomic number
b. number of neutrons
c. same number of neutrons
d. different atomic numbers
e. Both pairs increase mass by
one amu.
f. First pair are isotopes; second
pair are different elements.
3. a. almost the same
b. one higher
c. New one is higher; otherwise, it
wouldn’t decay.
d. new one
4. gravitational interaction
5. No, there are not enough nucleons
to form an alpha particle.
6. mass and charge
Mixed Review, pp. 131–132
