Answers
Answers to Odd-Numbered Exercises and Problems
Solutions to questions posed in the Part Overview captions can be found at the end of this answer list.
Chapter 1
17.
7
8
6
5
4
1.
ar
ar
ar
x
Skid
begins
Stops
3
ar
2
r
7.
vavg
1
Stop
r
9. a.
b. Greater
v01
19.
Dvr
r
v12
Known
v0 = 0 t0 = 0 x0 = 0
a0 = 1.5 m/s2
v1 = 7.5 m/s
ar0
x
x0, v0, t0
x1, v1, t1
Find
x1
r
11.
vi
r
a
r
21.
23.
25.
27.
29.
35.
vf
r
a
r
vf
r
vi
r
r
a
r
a
a
r
a. 9.12 3 1026 s b. 3.42 3 103 m c. 440 m/s d. 22.2 m/s
a. 3.60 3 103 s b. 8.64 3 104 s c. 3.16 3 107 s d. 9.75 m/s2
6.40 3 103 m2 and 8.25 3 103 m2
a. 3 b. 3 c. 3 d. 2
a. 846 b. 7.9 c. 5.77 d. 13.1
Pictorial representation
ar0
x
r
a
r
ar1 = 0
vf
0
x0, v0, t0
r
vi
x1, v1, t1
Motion diagram
Accelerate
x2, v2, t2
Coast
v
Starts
v3
r
v2
Stops
r
r
v1
r
v
vr1
ar = 0
r
v
Brakes
v
r
ar = 0
ar
15.
r
ar
r
37.
Pictorial representation
representation
ar0
r
ar1 = 0
Starts
x
x1, v1, t1
x0, v0, t0
Find
x1
r
a
Motion diagram
r
v3
r
r
r
r
ar0
ar0 = 0
ar1 = 0
Water level
v4
v5
Known
x0 = 0 v0 = 60 mph t0 = 0
v1 = 30 mph t1 = 3 s
v2 = 30 mph
x2, v2, t2
r
v2
a0 = 5 m/s2
t1 = 5 s
t2 = 8 s
a1 = 0
Find
x2
r
13.
Known
x0 = 0
v0 = 0
t0 = 0
v2 = v1
vr
r
r
a=0
r
Braking
begins
Braking
stops
v6
Hits bottom
A-9
A-10
ANSWERS
39.
Pictorial representation
y
55. a.
Motion diagram
vr
r
r
a= 0
ar
Ceiling
y1, v1, t1
ar
vr4
ar
r
ar
v3
Known
y0 = 0 v0 = 10 m/s
t0 = 0 y1 = 3.0 m
a0 = −9.8 m/s2
ar0
ar
vr2
ar0
57. a. Neither is zero. b. Velocity is zero, acceleration is not zero.
Find
t1
vr1
y0, v0, t0
Chapter 2
Start
1. b.
x (m)
1200
41.
900
Known
u = 20°
x0 = 0 v0 = 10 m/s
t0 = 0 a < 0
v1 = 0
Pictorial representation
x
ar
600
x1, v1, t1
300
h
u
Find
h = x1 sin u
0
Motion diagram
Stops
vr
ar⊥
vr
ar
5.
7.
9.
11.
13.
4
6
8
10
x
43.
Find
vP0
2
450 m
a. Beth b. 20 min
a. 48 mph b. 50 mph
a. 26 m, 28 m, 26 m b. At t 5 3 s
a.
v (m/s)
2
1
0
−1
−2
Pictorial representation
Known
xP0 = 0 xB0 = 15 m
t0 = 0 vB0 = 4 m/s
aP = aB = 0
xP1 = xB1 = 20 m
vB1 = 4 m/s
t (s)
0
0
x0, v0, t0
Origin
t (s)
2
4
6
8
10
2
4
6
8
10
2
4
6
8
10
x (m)
0
10
xP0, vP0, t0
xB0, vB0, t0
xB1, vB1, t1
xP1, vP1, t1
Puck at t = 0
8
6
r
Bruce
Motion diagram
Start
vr
Puck
vr
r
4
a= 0
2
End
t (s)
0
r
a= 0
−2
51. a.
r
ax (m/s2)
v
ar
1
53. a.
ar0
ar1
vr
vr
t (s)
0
Stops
15.
17.
19.
21.
23.
25.
27.
b. 1 m/s2
a. 2.68 m/s2 b. 27.3% c. 134 m or 440 ft
22.8 m/s2
a. 78.4 m b. 239.2 m/s
3.2 s
134 m
a. 15 m b. 23 m/s c. 24 m/s2
16 m/s
Answers to Odd-Numbered Exercises and Problems
29. a.
43.
x (m)
s
7
6
5
t
0
4
vs
3
2
t
0
1
t (s)
0
−1
2
1
3
4
as
5
−2
c. 22 m/s d. 22 m e. 2 m
f.
Turn
around at
t = 2.0 s
t
0
vr
45.
r
a
r
a
v0 < 0
r
v
s=0
Ball rolls off left edge
31. vA 5 210 m/s, vB 5 220 m/s vC 5 75 m/s
33. 0, 5, 20, 30, and 30 m/s
35. a.
ax (m/s2)
47. a. 179 mph b. Yes c. 35 s d. No
49. Yes
51. a. 100 m
b.
x (m)
3
2
1
0
2
4
6
8
100
t (s)
10
80
−1
Stop
60
−2
Brake
40
Coast
20
vx (m/s)
0
6
t (s)
0
1
2
3
4
4
2
0
2
4
6
8
t (s)
10
53. a. 54.8 km b. 228 s
c.
vy (m/s)
−2
Fuel out
900
−4
600
Max altitude
300
t
0
vs
0
as
t
0
t
150
0
b. Displaced upward by 2.0 m/s
37. a. 0 s and 3 s b. 12 m and 218 m/s2; 215 m and 18 m/s2
39. 2.0 m/s3
41.
s
−300
30
90
t (s)
210
−600
−900
Impact
55.
57.
59.
61.
63.
65.
67.
69.
71.
73.
75.
77.
79.
81.
83.
19.7 m
216 m
9.9 m/s
a. 2.32 m/s b. 5.00 m/s c. 0%
Yes
a. 214 km/hr b. 16%
14 m/s
a. 900 m b. 60 m/s
No
5.5 m/s2
c. 17.2 m/s
c. x1 5 250 m, x2 5 750 m
70 m/s
a. 10.0 s b. 3.83 m/s2 c. 6.4%
24500 m/s2
A-11
A-12
ANSWERS
Chapter 3
r
29. a.
r
b.
E
r
a. Yes b. No
r
r
r
r
a. If B is in the same direction as A. b. If B is opposite to A.
11.9 m/s
a. (70.7, 270.7) m b. (282, 103) m/s c. (0, 25.0) m/s2
d. (240, 30) N
r
r
11. C: (23.04, 0.815) m; D: (12.8, 222.2)
13. a. 7.21, 56.3° below 1x-axis b. 94.3 m, 58.0° above the 1x-axis
c. 44.7 m/s, 63.4° above the 2x-axis
d. 6.3 m/s2, 18.4° right of the 2y-axis
y
15.
r
4
Known
r
^
^
A = 2i + 3j
r
^
^
B = 4i − 2j
r
C
2
r
E
r
1.
3.
7.
9.
–B
E
r
D
F
r
r
r
r
D + 2E
r
r
D+E+F
D
r
c.
2E
r
–2E
r
D
r
F
r
r
r
D − 2E + F
31. 0.707 i^ 1 0.707j^
33. a. 100 m lower
b. (500 m, east) 1 (5000 m, north) 2 (100 m, vertical)
35. a.
(North)
y
A
r
–B
Find
r
r
r
C=A−B
−4
−2
x
0
2
Known
r
r
r
A B C
4
r
B
−2
17. a. 8 i^ 1 7j^
b.
u
0
(West)
x (East)
r
Find
r
D D u
r
A
D
r
C
30°
y
r
B
8
Known
r
^
^
A = 5i + 2j
r
^
^
B = −3i − 5j
Find
r
r
r
D=A−B
D and u
(South)
r
D
4
u
−4
37.
39.
41.
43.
45.
47.
49.
r
A
0
x
4
r
8
B
−4
c. 10.6, 41.2° above the 1x-axis
19. a. 17 i^ 1 22j^
b.
b. 360 m, 59.4° north of east
7.5 m
86.6 m/s
385 paces, 24.6° west of north
215.0 m/s
a. 23.4 m/s b. 29.4 m/s
4.36 units, 83.4° below the 2x-axis
7.29 N, 79.2° below the 2x-axis
y
Chapter 4
24
Known
r
^
^
A = 5i + 2j
r
^
^
B = −3i − 5j
3.
16
r
F
Find
r
r
r
F = A − 4B
F and u
8
r
A
r
Weight w
x
r
0
B
c. 27.8, 52.3° above the 1x-axis
r
r
21. Coordinate system 1: A 5 24j^ m, B 5 (24.33 i^ 1 2.50j^ ) m;
r
r
^
Coordinate system 2: A 5 (22.00j 2 3.46j^ ) m, B 5 (22.50 i^ 1
4.33j^ ) m
y
23. a.
Known
uA = 20° uB = 60°
A=3
B=2
f = 180° − (uB − uA) = 140°
Find
C uc
Normal force nr
r
Kinetic friction fk
16
8
5. m1 5 0.08 kg; m3 5 0.50 kg
9. 0.25 kg
11. a. <0.05 N b. <100 N
13.
r
F1
r
F2
2
r
f
C
r
uB
B
Force identification
r
uC
uA
B
19.
a
r
F3
r
A
y
x
2
Free-body diagram
4
b. 4.71, 35.8° above the 1x-axis c. 4.71, 35.8° above the 1x-axis
25. a. 26 i^ 1 2j^ b. 6.32, 18.4° above the 2x-axis
27. (4.90 i^ 1 2.83j^ ) m
nr
x
r
Normal force n
r
Weight w
r
w
A-13
Answers to Odd-Numbered Exercises and Problems
21.
Force identification
35.
Free-body diagram
y
nr
y
x
r
fk
r
r
nr
Fnet
T
ar
r
r
Weight w
fk
r
w
x
r
vr
r
w
Normal force n r
Kinetic friction fk
r
37.
y
Tension T
vr
23.
Motion diagrams
r
T
vr
ar
x
r
ar
ar
r
r
Weight w
r
Fnet
w
r
Fnet
Fnet
39.
vr
(b)
(a)
r
r
Drag D
Thrust Fthrust
vr
25.
ar
Fx (N)
Weight wr
Normal force nr
0.75
y
0.50
nr
0.25
r
r
Fthrust
D
0
1
2
3
r
4
w
r
Fnet
−0.25
27.
x
t (s)
ax (m/s2)
41.
3.0
r
y
Wind Fw
r
v
nr
r
r
fk
2.0
r
Weight w
ar
Fnet
r
Fw
x
r
w
Normal force nr
r
Kinetic friction fk
1.0
t (s)
0
1
2
3
4
43.
−1.0
y
r
vr
Drag D
29. a. 16 m/s2 b. 4 m/s2 c. 8 m/s2 d. 32 m/s2
ar
x
r
D
31.
y
r
r
w
r
Weight w
Fnet
r
n
r
r
Fthrust
D
r
w
x
r
45.
r
Fnet = 0
ar
r
r
a=0
x
r
vr
33.
y
vr
w
r
Weight w
r
Fnet
y
47.
r
w
y
vr
x
vr
r
vr
nr Fnet
r
r
Fnet
ar
ar
r
Weight w
fs
Normal force nr
r
Static friction fk
r
w
x
A-14
ANSWERS
49. a.
First contact
Loses contact
ar
ar
vr
ar
Expanding
Magnified view of
ball in contact with
ground
Compressing
vr
c.
r
Weight w
T 5 144 N
u 5 11.3°
Green
b. 134 s and 402 s c. No
Chapter 6
1. a. (2 i^ 2 2j^ ) m/s2 b. (22 i^ 2 16j^ ) m, (9 i^ 2 9j^ ) m/s, 12.7 m/s
3. a.
Turning point
b.
67.
69.
71.
73.
y
y (m)
nr
Normal force nr
5
r
Fnet
x
r
w
−10
Chapter 5
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
33.
35.
10
−5
T1 5 86.7 N, T2 5 50.0 N
147 N
a. ax 5 1.0 m/s2, ay 5 0 m/s2 b. ax 5 1.0 m/s2, ay 5 0 m/s2
8 N, 0 N, 212 N
a. 0 N b. 0 N c. 250 N
307 N
a. 590 N b. 740 N c. 590 N
0.25
136 m
2550 m
192 m/s
<3 m/s2
4.0 m/s
Left first, then right.
a. 0.0036 N b. 0.0104 N
a. 784 N b. 1050 N
a. 58.8 N b. 67.8° c. 79.0 N
a. 6670 N b. 600 ms
c.
vx (m/s)
400
r
40
20
t (ms)
300
a. 3.96 N b. 2.32 N
a. 15.7 N b. 2.87 m/s c. 4.36 m/s
0.165
0.68 m
a. 3.79 m b. 6.97 m/s
0.12
14.3
23.1 N
51 m/s
b. 12.3 m/s2
Defective cable
13.0 m/s2
600
x (m)
0
100
11.
13.
15.
17.
19.
21.
23.
25.
0
r
b. 0 m, 2.0 m/s at t 5 0 s; 0 m, 8.3 m/s at t 5 4 s
c. 290° at t 5 0 s; 14° at t 5 4 s
5. 38.8 m
9. a. At t 5 6 s, x 5 240 m, y 5 3.6 m, vx 5 40 m/s, vy 5 228.8 m/s,
v 5 49.3 m/s
b.
y (m)
200
37.
39.
41.
43.
45.
47.
49.
51.
53.
55.
57.
59.
x (m)
0
27.
29.
31.
33.
35.
37.
39.
41.
43.
45.
47.
49.
51.
200
a. 0.0639 s b. 782 m/s
2.0 km/hr
0.40 m
a. 39.1 mi b. 19.5 mph
a. 55.6 hr b. 0.0917° c. Yes
6.56 3 1012 m/s2
a. v02 sin2 u/2g b. h 5 14.4 m, 28.8 m, 43.2 m; d 5 99.8 m, 115.2 m,
99.8 m
a. Launch point 80.8 m higher b. 34.4 m
c. 49.8 m/s, 72.5° below horizontal
a. 276 m b. 12.75 s
Clears by 1.01 m
No
34.3°
678 m
a. 239 m b. 42.9 m
106 m/s
4.48 m/s
105 m
Crocodile food.
2.96 m
b. u 5 11.5°
b. x1 5 229.2 m
Answers to Odd-Numbered Exercises and Problems
53. a. On the opposite bank 150 m east of where she started.
(north)
b.
y
r
R
r
r'
rr
x (east)
0
55. a. 44.4° above the 2xr-axis
b.
y' (m)
24
16
8
57.
59.
61.
63.
65.
67.
69.
x' (m)
−40
−80
0
10.1°
a. 30° toward the rear of the car b. 17.3 m/s
a. 7.18° south of east b. 2.48 hr
3.0 3 108 m/s
40.6° below horizontal
4.78 m/s
a. Rotate the spacecraft 153.4° counterclockwise so that the exhaust
is 26.6° below the positive x-axis. Fire with a thrust of 103,300 N
for 433 s.
b.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
33.
35.
37.
39.
41.
43.
45.
47.
49.
51.
53.
55.
57.
59.
61.
63.
a. 1.5p rad/s b. 1.33 s
a. 3.0 3 104 m/s b. 2.0 3 1027 rad/s c. 6.0 3 1023 m/s2
5.65 m/s and 106 m/s2
34.3 m/s
a. 3.93 m/s b. 6.18 N
7.27°
2.0 3 1020 N
1.58 m/s2
12.1 m/s
19.8 m/s
ar 5 2.72 m/s2; at 5 1.27 m/s2
a. 22.618 m/s2 b. 31.25 rev
49.5°
a. 0.967 m/s2 b. 14.3g
2.5 N higher at the north pole.
172 N
34.5 m/s
No
a. 5.00 N b. 30.2 rpm
24.4 rpm
a. 29.80 m/s2 b. 212.92 m/s2 c. 26.68 m/s2
a. 4.9 N b. 2.9 N c. 32.5 N
a. 319 N and 1397 N b. 5.68 s
29.9 rpm
2.63 m right of the point where the string was cut.
a. 1.90 m/s2 at 20.6° from the r-axis b. 23.5 s
3.75 rev
b. v 5 20 rad/s
b. vf 5 0.40 rad/s
14.19 N and 8.31 N
c. 94.5 rpm
Chapter 8
r
1.
FWL on BB
y (km)
200
r
wE on BB
100
r
FBB on WL
nrS on WL
x (km)
0
100
200
300
400 433
r
w
E on WL
Chapter 7
r
r
w
WL on E wBB on E
1. b.
v (rad/s)
nrWL on S
2p
y
1
22p
24p
26p
y
t (s)
0
2
3
r
4
nrS on WL
FWL on BB
x
x
BB
r
w
E on BB
r
FBB on WL
wrE on WL
A-15
A-16
ANSWERS
3.
Bowling
ball (BB)
11.
13.
15.
17.
19.
Soccer
ball (SB)
Surface (S)
Earth (E)
588 N
a. 20 N b. 21 N
66.6 N at 36°
60 N
(i)
T (N)
r
r
nS on BB
nS on SB
20
r
r
FSB on BB
FBB on SB
10
r
w
E on BB
y (m)
r
w
E on SB
0
r
w
SB on E
r
w
BB on E
1
2
3
S
nrBB on S
(ii)
21. No
23. 99.0 m
25. 1.48 s
27. a. 3.92 N b. 2.16 m/s2
29. 154.7 N
31. 200 kg
33. 98.9 kg
35. 2.29 m/s2
37. a. 19.6 N b. Down c. 20.6 N
39. a. 3770 N b. 28.2 m/s
41. 3.27 m/s2
43. 3590 N
47. a. 1.0 m/s b. 90 N
49. b. 8.99 N
nrSB on S
y
y
nrS on BB
nrS on SB
r
r
FSB on BB
FBB on SB
x
x
r
w
BB
(iii)
r
w
SB
5. a.
r
r
FS on P
FP on S
r
FP on R
r
nrA on B
Pulley P
r
FR on P
r
FB on R
FR on B
Rope R
Block B
Surface S
r
r
fA on B
FA on R
r
r
w
E on B
nrS on A fB on A
r
FR on A
r
fS on A
nrB on A
Block A
r
w
E on B
nrA on S
r
fA on S
r
w
B on E
r
w
A on E
Earth E
y
nrA on B
y
nrS on A
x
r
fB on A
x
r
FR on A
r
fS on A
r
r
FR on B
fA on B
nrB on A
r
w
B
r
w
A
Block B
Block A
y
y
x
x
r
FS on P
r
r
FB on R
FP on R
r
FA on R
Rope
7. a. 784 N b. 1580 N
9. F2 on 3 5 6 N; F2 on 1 5 10 N
r
FR on P
Pulley
Chapter 9
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
33.
35.
37.
39.
41.
43.
45.
47.
49.
51.
53.
55.
57.
59.
a. 1.5 3 104 kgm/s b. 8.0 kgm/s
1500 N
5.0 Ns
a. 1.5 m/s to the right b. 0.5 m/s to the right
0.50 s
0.20 s
1.43 m/s
0.20 m/s
3.6 m/s
2.0 mph
1.7 m/s 45° north of east
2.89 3 1034 kgm2 /s
a. (1.083, 0.625) kgm/s when thrown, (1.083, 0) kgm/s at the top
a. 6.4 m/s b. 360 N
a. 0.432 Ns upward c. 40 to 80 N is reasonable estimate
a. 0.588 Ns b. 20.588 Ns
a. 6.7 3 1028 m/s b. 2 3 10210%
13.3 s
1.73 m/s at 54.7° south of east
7.57 cm in the direction Brutus was running
402 m
a. 286 ms, 26,200 N b. 0.0214 m/s
27.8 m/s
5 s21
1.46 3 107 m/s in the forward direction
14 u
b. and c. 1.40 3 10222 kgm/s in the direction of the electron
0.850 m/s, 72.5° below the x-axis
1.97 3 103 m/s
4.5 rpm
Answers to Odd-Numbered Exercises and Problems
61.
63.
65.
67.
69.
71.
a. 2.80 m/s b. 2.22 m/s at a radius of 25.2 cm
c. (vix ) 2 5 6.0 m/s
c. (vfx ) 1 5 212 m/s
5.65 m/s
90.3 m/s
8
19. a.
A-17
U (J)
10
8
6
Chapter 10
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
33.
35.
37.
39.
41.
43.
45.
47.
49.
51.
53.
55.
57.
59.
61.
65.
67.
69.
71.
73.
The bullet
112 km/hr
a. 6.75 3 105 J b. 45.9 m c. No
a. 12.9 m/s b. 14.0 m/s
7.67 m/s
a. 1.403 m/s b. 30°
a. Yes b. 14.1 m/s
a. 49 N b. 1450 N/m c. 3.4 cm
98 N/m
10 J
2.00 m/s
3.00 m/s
0.857 m/s and 2.86 m/s
a. 25.0 m/s and 5.0 m/s b. Both 2.5 m/s
a. Right b. 20.0 m/s at x 5 2.0 m c. 1.0 and 6.0 m
63.2 m/s
Yes
a. No b. 17.3 m/s
a. Left b. Yes c. 200 N/m d. 19.0 m/s
v0 / !2
25.8 cm
51.0 cm
19.6 N/m
a. 14.8 m/s b. Go hungry.
a. 21,600 N/m b. 18.6 m/s
a. 3.33 m/s b. 11.8 cm c. 0.833 m/s and 6.45 cm
a. 32 R b. 15 m
2.5R
7.94 m/s
100 g ball 0.80 m/s to the left; 400 g ball 2.2 m/s to the right
a. Vibrates about an equilibrium position on one side of the H3 plane
or the other.
b. Oscillates from one side of the H3 plane to the other side.
c. k 5 35.6 N/m
vf 5 2.65 m/s
a. 1.46 m b. 19.6 cm
b. 453 m/s
100 g ball to 79.3°, 200 g ball to 14.7°
4
2
0
x (m)
0
4
2
+
Ki
10
+
Ui
+ Wext =
Kf
+
Uf
+ DEth
600
400
200
+
0
+
=
+
+
−
27.
29.
31.
33.
35.
6.26 m/s
a. 176.4 J b. 58.8 J
Night light
a. 102 N b. 416 W, 832 W, and 1248 W
U (J)
a.
80
60
TE
51.25
40
20
x (m)
0
0
1
2
3
4
5
b. 51.25 J d. 2.56 m
37.
Fx (N)
U (J)
x (m)
0.5
Chapter 11
a. 15.3 b. 24.0 c. 0
a. 230 b. 0
a. 12.0 J b. 26.0 J
0J
r
r
12,500 J by the weight, 27920 J by T 1, 24580 J by T 2
4.0 J, 24.0 J, 4.0 J, 0 J, 23.0 J
7.35 m/s, 9.17 m/s, 9.70 m/s
8.0 N
230 N at 1 m, 20 N at 3 m
8
b. 2.5 N, 0.40 N, and 0.156 N
21. 1360 m/s
23. a. Potential energy is transformed to kinetic and thermal energy.
b. 548 J
Energy (J)
25.
0
1.
3.
5.
7.
9.
11.
13.
15.
17.
6
−0 .5
0
−1
−4
(a)
39.
41.
43.
45.
47.
49.
51.
53.
55.
4
1
x (m)
0.5
(b)
a. 298,000 J b. 108,000 J c. 10,000 J d. 4.47 m/s
a. and b. 3.97 m/s
2.37 m/s
0.037
a. 1.70 m/s b. No
a. 571 J b. 2196 J c. 238.5 J d. 0 J
a. 2.16 m/s b. 0.0058
a. 9.90 m/s b. 9.39 m/s c. 93.9 cm d. 10
a. !2gh b. h 2 mkL
1
A-18
ANSWERS
57. a. N/m3
b.
47. a. 3.46 3 108
b.
U ( × 1010 J)
Fx
1
x
0
2
3
4
0
−5
r (× 108 m)
Crossover
point
Moon
−10
−15
−20
61.
63.
65.
67.
69.
71.
73.
75.
c. 14 qx4 d. 10 m/s
233 W
a. 2245 J b. 255,000 kg
<15 m/s
a. 6.53 m/s2 b. 16.7 m/s c. 2.56 s
c. v1 5 6.34 m/s
c. P 5 32.4 kW
6.68 m
a.
U(r)
0
r
49.
51.
53.
55.
57.
59.
61.
63.
65.
67.
69.
71.
73.
75.
c. 22.24 3 1010 J d. 9.60 3 109 J e. 11.0 km/s
3.0 3 104 m/s
1.405 hr
a. 6.95 m/s b. 12.3 m/s
8.67 3 107 m
a. y 5 (q/p)x 1 (logC)/p b. linear c. q/p e. 1.996 3 1030 kg
317 m (8.26 3 1025%) and 2.9 s (1.25 3 1024%)
9.33 3 1010 m
3.71 km/s
4.49 km/s
Yes
c. 1.00 3 108 m
vf1 5 596 m/s, vf2 5 298 m/s
a. 2.05 3 108 yr d. 9.4 3 1010
Crash.
Chapter 13
1.
a (rad/s2)
b. Infinity c. 689,000 m/s and 172,000 m/s
50
t (s)
0
−50
Chapter 12
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
33.
35.
37.
39.
41.
43.
45.
a. 3.53 3 1022 N b. 1.99 3 1020 N c. 0.56%
6.00 3 1024
1.60 3 1027
a. 8.97 N
a. 1.62 m/s2 b. 25.9 m/s2
2430 m
a. 3.0 3 1024 kg b. 0.889 m/s2
418 km
60.2 km/s
a. 1.80 3 107 m b. 9410 m/s
a. 7680 m/s b. 92.4 min
4.2 hr
2.01 3 1030 kg
6.72 3 108 J
46 kg and 104 kg
1.19 3 1023 rad or 0.0679°
(11.7 cm, 0 cm)
a. (4.72 3 1027 N, 45° ccw from 2y-axis)
b. (4.56 3 1027 N, 7.6° cw from y-axis)
a. 210.0 3 1028 J b. 29.65 3 1028 J
a. 1.38 3 107 m b. 4450 m/s
a. 2.82 3 106 m b. 3670 m/s
32,600 m/s
a. !16GM/7R b. !4GM/3R
1 2
3
4
5
6
7
−100
3. a.
a (rad/s2)
5
4
3
2
1
t (s)
0
−1
4
8
12
16
−2
−3
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
13.2 m/s
a. 2100.5 rad/s2 b. 50.0
36.3 cm/s
20.20 Nm
175.5 N
12,500 Nm
a. (0.0571 m, 0.0571 m) b. 0.0080 kgm2
a. (0.060 m, 0.040 m) b. 0.0020 kgm2 c. 0.00128 kgm2
0.75 rad/s
0.0471 Nm
11.76 Nm
Answers to Odd-Numbered Exercises and Problems
27.
29.
31.
33.
35.
37.
39.
1.40 m
15.8 J
1.75 J
0.375 J
a. (20.78, out of page) b. (24, into page)
a. j^ b. j^
a. i^ 1 3j^ 1 11k^
z
b.
12
r
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
r
A×B
10
8
6
x(t) 5 (4.0 cm) cos 3 (8.0p rad/s)t 2 p/2 4
a. 22p/3 rad or 2120° b. 22p/3 rad, 0 rad, 2p/3 rad, 4p/3 rad
5.48 N/m
a. 0.50 s b. 4p rad/s c. 5.54 cm d. 0.445 rad e. 69.6 cm/s
f. 875 cm/s2 g. 0.484 J h. 3.81 cm
a. 10.0 cm b. 34.6 cm/s
a. 0.169 kg b. 0.565 m/s
c. 12° d. 10° e. 0º to 10º
35.7 cm
0.330 m
5.0 s
21
x (cm)
4
2
r
A
4
2
4
6
8
r
x
t (s)
2
y
8
Original
0
10
B
6
With
changes
20
2
10
4
6
8
−20
(a)
41.
43.
45.
47.
49.
51.
250k^ N m
a. 8.97 s b. 0.448 kg m2/s
1.20k^ kg m2/s or (1.20 kg m2 /s, out of page)
20.0251 i^ kg m2 /s or (0.0251 kg m2/s, into page)
28.3 m/s
a. 0.010 kg m2 b. 0.030 kg m2
53.
55.
57.
59.
61.
63.
65.
67.
69.
71.
73.
75.
77.
79.
81.
83.
85.
87.
a. 12 M(R2 1 r2 ) c. 1.37 m/s
1
2
6 ML
Yes
1.00 m
a. (20 cm, 80 cm) b. 0.48 kg m2 c. 1.0 N m d. 56.4°
a. 24.4 yr b. 4080 m/s and 12,250 m/s
a. 177 s b. 5.55 3 105 J c. 139 kW d. 1300 N m
1.11 s
1.57 N
4.25 m
a. !2g/R b. !8gR
20t/13MR2
a. 42.9 cm b. No
50 rpm
a. No b. 2000 m/s c. 4000 m/s
a. 3v0/2d b. No
393 m/s
a. 68,700 m b. 4.32 3 106 m/s
x (cm)
2
33. a. 2p/3 rad or 260° b. 6.80 cm/s b. 7.85 cm/s
35. a. 0.25 Hz, 3.0 s b. 6.0 s, 1.5 s c. 2.25
37. 1.405 s,
x (m)
0.3
1
1
−3
−4
2
−0.3
2
−2
t (s)
0
3
t (s)
1.0
8
(b)
4
0.5
t (s)
4
−20
1. 2.27 ms
3. a. 3.3 s b. 0.303 Hz c. 1.904 rad/s d. 0.25 m e. 0.476 m/s
5. a. 10 cm b. 0.50 Hz c. p/3 rad or 60°
7.
x (cm)
0
Original
6
0
Chapter 14
−1
With
changes
20
39.
43.
45.
47.
49.
51.
53.
55.
57.
59.
61.
63.
65.
67.
69.
71.
73.
77.
79.
A-19
0.0955 s
a. 6.40 cm b. 160 cm/s2 c. 26.40 cm d. 0.283 m/s
1.02 m/s
a. 3.18 Hz b. 0.0707 m c. 5.0 J
a. 1.125 Hz b. 23.5 cm c.-4.09 cm
a. 47,400 N/m b. 1.80 Hz
a. 0.314 s b. It would be unchanged.
0.716
0.669 s
a. 200.9 s b. 200.4 s c. Yes d. 9.77 m/s2
0.110 m at 1.72 s
a. 502 m/s b. No
f 5 (1/2p) !2T/mL
T 5 2p !R/g
gX 5 5.86 m/s2
a. 6.03 cm b. 6.32 s
7.3°
1.83 Hz
2.23 cm
A-20
ANSWERS
31. a. 12.02 atm
b.
p (atm)
Chapter 15
1200 kg/m3
1.44 3 105 kg
1097 atm
2440 kg
3153 m
88,000 Pa
55.2 cm
Ethyl alcohol
45.8 kg
1.87 N
3.18 m/s
1.27v0
2.0 kg
1.0 mm
0.2%
a. 5830 N b. 5990 N
a. 0.377 N b. 20.4 m/s
5.27 3 1018 kg
a. 10.85 m b. 10.21 m
a. 0.483 m b. 2.34 cm
3.7 mm
a. 12 rgwd 2 b. 1.76 3 109 N
a. 8080 m b. 1.05 kg/m3, 82%
667 kg/m3
74.7 N
43.9 N
8.38 cm
(r 2 r1 )/(r2 2 r1 )
5.22 cm
14.1 cm
a. patmos b. 4.61 m
a. Lower b. 835 Pa c. 75,100 N
a. 144 m/s and 5.78 m/s b. 4.54 3 1024 m3 /s
a. 3.34 L/min b. 1.06 mm/min
1.23 mm
1.30 L
3.6 g
e. 18.9 s
60
40
20
V (31026 m3)
0
0
33.
35.
37.
39.
41.
43.
45.
47.
49.
51.
53.
55.
100
200
a. Isothermal b. Both are 914 K c. 300 cm3
0.228 nm
a. 7.03 3 10221 J b. 2060 m/s
1.1 3 1015 m23
a. 1.32 3 10213 b. 1.24 3 1011 molecules
174°C
92.8 cm3
34.7 psi
174.3°C
a. 3.05 3 1021 b. 2.02 mg
No
p
2p1
2
Isochoric
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
33.
35.
37.
39.
41.
43.
45.
47.
49.
51.
53.
55.
57.
59.
61.
63.
65.
67.
69.
71.
73.
75.
1
Isothermal
p1
3
Isobaric
0
V
0
2V1
V1
57. a. 884 kPa b. 323°C, 249.5°C, 397.5°C
59. a. Both 366 K 5 93°C b. Isothermal c. 1098 K 5 825°C
61. a. 0.509 atm b. 2112°C
c.
p (atm)
3
3
Isobaric
2
Chapter 16
2
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
22.6 m3
8.33 cm
4.82 3 1023 atoms
a. 6.02 3 1028 atoms/m3 b. 3.28 3 1028 atoms/m3
2.17 cm
Lowest: 288°C 5 185 K; highest 58°C 5 331 K
a. 171°Z b. 671°C 5 944 K
a. 32.02°F, 608 Pa b. 268.8°F, 5.06 3 105 Pa
Freezing point lower, boiling point higher.
a. 0.0497 m3 b. 1.33 atm
18.8 atm
a. 55.1 mol b. 1.234 m3
a. 5.41 3 1023 atoms b. 3.59 g c. 2.30 3 1026 m23 d. 1.52 kg/m3
a. 0.732 atm b. 0.523 atm
a. 9520 kPa
p (Pa)
b.
10,000
Isothermal
1
1
V (cm3)
0
5,000
0
10,000
63. a. 4.0 atm, 273°C
b.
p (atm)
3
4
Isobaric
2
Isothermal
3
2
1
2
1
5,000
0
V (cm3)
0
0
50
V
0
1
100
1
V
4 1
1
V
2 1
3
V
4 1
V1
Answers to Odd-Numbered Exercises and Problems
65. b.
p (atm)
6
Isotherm
4
2
V (cm3)
0
100
0
c. 6 atm
67. b.
200
300
p
Isobaric
508C
4008C
V (cm3)
0
100 200
300 400 500
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
33.
35.
37.
39.
41.
43.
45.
47.
49.
51.
53.
55.
57.
c. 417 cm3
69. a. 23.5 cm b. 7.8 cm
71. a. 2.73 m b. 10.96 atm
73. 1.02 cm
700 J from the system
12,500 J
6864 J
6.79 3 104 J
27.5°C
73.5°C
Iron
a. 91.2 J b. 140°C
a. 1.14 atm b. 48.5°C
a. 26.4 b. 7.07
8.73 hr
994 cm3
256.4°C
Aluminum
87.3 min
a. 83.3 J/kgK b. 2.0 3 105 J/kg
0.0605 kg 5 60.5 g
5450 J
a. 245 J b. 944 m/s
1660 J
a. 253°C b. 32.6 cm
7750 J
a. 4290 cm3, 606°C b. 3050 J c. 1.0 atm d. 2180 J
e.
p (atm)
Isobaric
1
2
3
Isochoric
2
Chapter 17
1
1. 490 J
3. 40 J
5. 200 cm3
7.
3
V (cm3)
0
0
Eth i +
W
+
Q
= Eth f
+
0
+
+
1000
2000
3000
4000
5000
59. A: 21010 J, B: 1419 J
61. a. 810 J b. 2486 J c. 0 J
63. a. A: 2.46 3 1023 m3, 300 K; B: 1.80 3 1023 m3, 220 K
b.
p (atm)
=
i
3
Isothermal
2
−
Adiabatic
1
9.
Eth i +
W
+
Q
f
= Eth f
+
V (cm3)
0
0
0
f
+
+
=
−
65.
67.
69.
71.
800
1600
2400
a. 250.7 J b. 224.8 J c.25.9 J
1100 K, 23.9 cm3
a. 39.3 b. 171
a. 0.5 atm b. 21074 J c. 1074 J d. 0 J
e.
p (atm)
2
11.
Eth i +
W
+
Q
= Eth f
+
1
0
+
+
Isothermal
=
V (L)
0
−
10
20
30
A-21
A-22
ANSWERS
73. a. 5460 K b. 0 J c. 5.39 3 104 J d. 20
e.
p (atm)
Chapter 19
1.
3.
5.
7.
9.
11.
f
20
Isochoric
10
DEth
i
0
5
V (L)
10
75. b. 0.0156 mol
77. b. 0.472 kg
79. a. At 1: 3.0 atm, 946°C, 1000 cm3. At 2: 1.0 atm, 946°C, 3000 cm3.
At 3: 0.48 atm, 310°C, 3000 cm3. b. 2334 J, 0 J, 239 J
c. 334 J, 2239 J, 0 J
81. 14.5 atm
Chapter 18
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
33.
35.
37.
39.
41.
43.
45.
51.
53.
55.
57.
59.
a. 10 J, 110 J b. 0.0833
a. 0.273 b. 15 kJ
a. 250 J b. 150 J
a. 200 J b. 250 J
96,000
2.69 3 1025 m23
a. 3.30 3 1012 m23 b. 1.71 3 106 m
61
a. 0 i^ 1 0j^ b. 59.2 m/s c. 61.6 m/s
a. 9.16 3 104 Pa b. 332 K
1.91 3 1024 s21
2820 m/s, 891 m/s
283 m/s
a. 68.3 K b. 1090 K
7.22 3 1012 K
a. 3400 J b. 3400 J c. 3400 J
a. 4 3 10216 J b. 7 3 105 m/s
3.65 3 107 J
a. 0.0800°C b. 0.0481°C c. 0.0400°C
a. 62.4 J b. 104 J c. 104 J d. 145 J
a. Gas B b. A: 5200 J, B: 7800 J
8.48
a. Helium b. 1367 m/s c. 1.86 3 1026 m
9.6 3 1025 m/s
a. l 5 1/ 3 !2p(N/V)r2 4 b. 1.82 3 1026 Pa or 1.80 3 10211 atm
a. 1.273 3 1025 m23 b. 449 m/s c. 259 m/s d. 1.296 3 1025 s21
e. 56,800 Pa f. 56,700 Pa
a. Helium: 30.4 J; Argon: 121.6 J b. Helium: 47.3 J; Argon: 104.7 J
c. 16.9 J is transferred from the argon to the helium. d. 580 K
e. Helium: 3.11 atm; Argon: 3.45 atm
482 K
a. R 5 8.31 J/molK b. 2R 5 16.6 J/molK
a. 4 b. 1 c. 16
1/2
a. 2.03 3 106 J b. 4.83 3 1026 c. 0.00132 K
a.
b. 9pi Vi
p
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
33.
39.
41.
43.
45.
47.
49.
51.
f
A
1
0
1
B
0
1
1
C
2
1
0
D
2
2
2
p (atm)
3
1
V (cm3)
100
500
or
p (atm)
3
1
V (cm3)
100
500
53. a.
Ws (J)
1S2
3.04
2S3
3S1
V
0
Vi
DEth (J)
13.93
0
210.13
210.13
21.52
25.32
23.80
1.52
1.52
0
b. 8.96% c. 12.7 W
55. a.
i
0
Q (J)
16.97
Ws (J)
pi
Q
40.5 J
a. 0.0952 b. 285 J
24.7
a. b only b. a only
7°C
a. 40% b. 215°C
233 K
a. 6.32 b. 32 W c. 232 J/s
a. 60 J b. 223°C
8.44 3 105 J
5.34 3 104 J
8.25%
47°C and 233°C
2/3
a. 2.5 kW b. $270 and $45
a. 48 m b. 32.1%
37%
Net
2pi
Ws
2Vi
61. c. 436 K, 850 J is transferred from the oxygen to the helium.
1S2
0
2S3
207.2
3S1
250.0
2125.0
157.2
157.2
Net
b. 52.2%
Q (J)
282.2
0
DEth (J)
282.2
2207.2
275.0
0
A-23
Answers to Odd-Numbered Exercises and Problems
57. a. 5.743 3 104 Pa, 4000 3 1026 m3, 229.7 K
b.
DEth (J)
Ws (J)
1S2
425.7
2425.7
2S3
0
3S1
63.
65.
67.
69.
3
4
5
6
7
8
9
10
0
2425.7
128.8
128.8
Ws (J)
Q (J)
1S2
327
2327
0
2S3
1692
677
2369
3S1
22019
0
22019
0
350
350
Net
2
554.5
c. 23.2%
59. a. Point 1: 1.013 3 105 Pa, 1.0 3 1023 m3, 406 K;
Point 2: 5.06 3 105 Pa, 1.0 3 1023 m3, 2030 K;
Point 3: 1.013 3 105 Pa, 5.0 3 1023 m3, 2030 K b. 28.8% c. 80%
61. a. 1620 K, 2407 K, 6479 K
b.
DEth (J)
1
Equilibrium
t=0s
Q (J)
0
0
x (cm)
0
554.5
2425.7
Net
5.
c. 14.8%
345.6 J, 24.0%
b. TH 5 1092°C
b. QH 5 100 J, QC 5 80 J
a.
p (atm)
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
33.
35.
37.
39.
41.
283 m/s
140 m/s
a. 4.19 m b. 47.7 Hz
a. 11.5 Hz b. 1.14 m c. 13.1 m/s
4.0 cm, 12 m, 2.0 Hz
40 cm
34 Hz, 68 Hz
0.076 s
793 m
a. 1715 Hz b. 1.50 GHz c. 987 nm
a. 10 GHz b. 0.167 ms
a. 1.50 3 10211 s b. 3.38 mm
459 nm
6.05 3 105 J
a. 1.11 3 1023 W/m2 b. 1.11 3 1027 J
38.1 m/s
a. 432 Hz b. 429 Hz
a.
D (cm)
1
t = 22 s
x (m)
26
3
2
24
22
0
2
4
6
0
2
4
6
0
2
4
6
0
2
4
6
0
2
4
6
3
1
t = 21 s
2
1
1
x (m)
26
24
22
26
24
22
4
1
x (m)
t=0s
0
V (cm3)
0
50
100
b. 10.13 J c. 12.9%
71. c.
h
1
x (m)
t=1s
26
24
22
1.0
1
26
24
22
r
0
0
10
20
b. 2 m/s c. 2 m/s
43. a.0.80 m b. 2 12 p rad
c. D(x, t) 5 (2.0 mm)sin(2.5px 2 10pt 2 12 p)
45. 25 g
47. 2.34 m, 1.66 m
49.
D (x, t)
30
Chapter 20
1.
x (m)
t=2s
0.5
History graph at x = 6 m
D (cm)
1 cm
0
0
x (m)
1
2
3
t (s)
0
1
2
3.
3
4
5
6
D (cm)
v = 1 m/s
24 23 22 21
1
x (m)
1
21
Snapshot graph at t = 1.0 s
2
51.
53.
55.
57.
61.
1, 4.31, 4.31
0.07°C
a. 2x direction b. 12.0 m/s, 5.0 Hz, 2.62 rad/m c. 21.50 cm
D(y, t) 5 (5.0 cm)sin 3 (4p rad/m)y 1 (16p rad/s)t 4
p/2 rad 5 90°
A-24
ANSWERS
63. a.
D (cm)
D
Snapshot graph at t = 0
A
t=4s
1
v
x (m)
0
0
2150
2100
250
0
50
100
1
0
y (cm)
2
3
4
5
6
7
8
9
10
150
t=5s
D (cm)
2A
1
b. 0 rad c. D(y, t) 5 Asin 3 (12.57 m21 )y 2 (4310 s21 )t 4
d. and e.
0
v = 343 m/s
v = 343 m/s
150
150
100
5
4
3
2
1
3
4
5
6
7
8
9
10
t (s)
0
1
2
3
7. 60 Hz
9. a. 6 b. 2f0
11. a. 12 Hz, 24 m/s
b.
2150
t = 0.729 ms
f. 2 12 p rad and 2 32 p rad
4
6
5
1.0 m
D (cm)
1
l3
x (cm)
0
0
2
4
6
8
10
15.9 Hz, 2.0 cm
a. 0.040 W/m2 b. 637,000 W/m2
a. 250 mW/m2 b. 15.8 km
85.8 m/s, away from you
796 nm, infrared
$200 million
8
b. 5.17 3 10211 s
t=0s
D (cm)
1 m/s
1
13.
15.
17.
19.
21.
23.
25.
27.
a. 700 Hz b. 56.4 N
400 m/s
10.5 m
4.8 cm
a. 0.25 m b. 0.25 m
1.0 m, 3.0 m, 5.0 m
200 nm
a. Out of phase b.
Dr
r2
r1
Chapter 21
1.
10
1
2100
1
t=0
67.
69.
71.
73.
77.
79.
81.
83.
9
0
2150
65.
8
2
250
2
2100
7
D (cm)
x
0
3
250
6
x (m)
2
5. a. t 5 4 s
b.
4
x
0
5
t=6s
1
0
50
Crest at 12.5 cm
at t = 0
4
100
5
50
3
0
6
6
2
1
v = 343 m/s
v = 343 m/s
1
D (cm)
y (cm)
y (cm)
x (m)
0
C/D
P
2l
3l
l
Q
3l
1.5l
1.5l
C
R
2.5l
3l
0.5l
C
D
29. Perfect destructive
31. 527 Hz
33.
D (cm)
1 m/s
1
x (m)
0
0
1
2
3
4
5
6
7
8
9
D (cm)
x (m)
0
10
1
t=1s
2
3
4
5
6
7
8
9
10
21
x (m)
0
1
2
3
4
5
6
7
8
9
10
D (cm)
t=2s
1
x (m)
0
0
1
2
3
4
5
6
7
8
9
10
D (cm)
t=3s
2
1
x (m)
0
0
1
2
3
4
5
6
7
8
9
10
35.
37.
39.
41.
43.
45.
47.
49.
51.
53.
55.
59.
12
13
At t = 0.05 s
1
0
11
0.62 cm, 1.18 cm, 1.62 cm, 1.90 cm, 2.00 cm
1.41 cm
1.23 m
28.4 cm
8.19 m/s2
18 cm
13.0 cm
328 m/s
26.1 cm, 55.6 cm, 85.2 cm
450 N
1605 Hz
7.89 cm
14
Answers to Odd-Numbered Exercises and Problems
61.
63.
65.
67.
69.
71.
73.
75.
77.
79.
81.
83.
85.
a. 850 Hz b. 2 12 p rad
345 nm
7.15 cm
20
a. 170 Hz b. 510 Hz and 850 Hz
150 MHz
a. a b. 1.0 m c. 9
a. 5 beats/s b. 4.6 mm
7.0 m/s
b. 2.0%
8.00 m/s2
c. 2.09 cm/s d. 2.2 mm
a. 14 l b. 12 p rad c. 14 T d. 75 m, 250 ns
Chapter 23
Chapter 22
1. a.
Blocked
One-slit
pattern
Intensity
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
33.
35.
37.
39.
a. 3.33 ns b. 0.75 m, 0.67 m, 0.51 m
8.0 cm
668 m
9.0 cm
42°
433 cm
65.0°
1.37
76.7°
3.18 cm
1.52
b. 1.1°
1580 nm
Inverted image 15 cm behind the lens
Upright image 6 cm in front of the lens
68 cm
2203 cm
1.54 cm
54.6 km
b. Relative to the intersection of the two mirrors, 3 images are at
coordinates (11 m, 22 m), (21 m, 12 m), and (11 m, 12 m)
c.
C
D
x
0
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
33.
35.
37.
39.
41.
43.
45.
47.
49.
51.
53.
55.
57.
59.
61.
63.
65.
67.
69.
71.
73.
A-25
0.020 rad 5 1.15°
500 nm
0.40 mm
530
a. 1.258 m b. 7
14.5 cm
4.0 mm
611 nm
7.56 m
0.25 mm
0.01525 rad 5 0.874°
30,467
19
a. Single slit b. 0.15 mm
0.286°
1.33 mm
500 nm
500 nm
667.8 nm
396 nm
533 to 700 nm
500 nm
0.118 mm
a. 2 b. 1.15 c. 1
0.10 mm
0.122 mm
a. 550 nm b. 0.40 mm
a. No b. 0.0295° c. 0.30 cm d. 103 cm
a. 3.0 mm b. 14 c. 12 p rad d. 0.75 mm toward the slit
14.2 mm closer to the beam splitter
a. 376 nm b. 1319 c. 1319
1.5525
12.0 mm
b. 0.022°, 0.058°
b. 211.5°, 253.1°
c. 1.3 m
A
O
41.
43.
45.
47.
49.
51.
53.
55.
57.
59.
61.
63.
65.
67.
69.
71.
73.
75.
77.
79.
81.
10.0 m
41.8°
82.8°
a. Bottom of tank coming up b. 60.0 cm
4.73 m
a. Deep b. 17.5 m
1.552
a. 17.9° b. 27.9° to the left of the normal
3.0 cm
b. 40 cm, 2 cm
b. 260 cm, 8.0 cm
b. 28.6 cm, 1.14 cm
44.4 cm, 67 cm
c. <3.6 cm
15.7 cm
b. 20 cm in front of second lens, 2.0 cm tall
11.5 km
a. 2 mm b. 165 MB
b. 1.574
b. 40 cm, 156.5 cm
a. 2200 cm
Chapter 24
1.
3.
5.
7.
410.3 nm, 389.0 nm, 379.9 nm
n58
63.8°
4
B
A-26
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
33.
35.
37.
39.
41.
ANSWERS
1.99 3 10216 J
1.2 3 105 J
a. 3.6 3 106 m/s b. 2.0 3 103 m/s
a. 1.1 3 10234 m b. 1.7 3 10223 m/s
0.20 nm
a. 121.6 nm, 102.6 nm, 97.3 nm, 95.0 nm b. 91.18 nm c. 31.4 cm
a. 2.0 3 10212 m b. 2.51 3 105
a. 3.14 3 10219 J b. 3.19 3 1015
18.7°, 50.8°, and 71.6°
b. 2.4 nm and 1.2 nm
a. 0.818 mm b. 1.09 3 103 m/s
170 m/s
a. 1.23 3 10219 J, 4.92 3 10219 J, 1.11 3 10218 J
b. 3.69 3 10219 J c. 539 nm
1.35 nm
a. (h/2mL)n b. 1.819 3 106 m/s, 3.64 3 106 m/s, 5.46 3 106 m/s
a. 72.5°, 53.1°, and 25.8° b. 64.9° and 31.9°
c. 19.9° and 76.9°, matching the peaks in Figure 24.7c
b. 7.28 3 104 m/s, 1.46 3 105 m/s, 2.18 3 105 m/s, 2.91 3 105 m/s
a. Electrons removed from glass b. 3.13 3 1010
3.04 3 10211
Right negatively charged, left positively charged
a. 9.0 3 109 N b. 9.0 3 109 m/s2
210 nC
r
r
F B on A 5 4.50 3 1023 j^ N, F A on B 5 24.50 3 1023 j^ N
30 N/kg
a. (9.83 N/kg, toward earth) b. (2.70 3 1023 N/kg, toward earth)
0.111 nC
28.0 nC
(3.27 3 106 N/C, downward)
a. 3.6 3 104 i^ N/C, (21.27 3 104 i^ 1 1.27 3 104 j^ ) N/C,
(21.27 3 104 i^ 2 1.27 3 104 j^ ) N/C
b.
y (cm)
r
EB
B
5.0
r
A EA
10 nC
25.0
r
EC
29.
31.
33.
35.
37.
39.
41.
43.
45.
47.
49.
51.
C
0
q
x (cm)
5.0
25.0
1.36 3 105 C, 21.36 3 105 C
a. Electrons removed from sphere and added to rod b. 2.5 3 1010
2160 nC and 0 nC
a. 498 N b. 2.98 3 1029 m/s2
a. 0.45 N b. 1.0 3 1026 C, 5.0 3 1027 C c. 4.5 m/s2
1.80 3 1024 N to the right
4.74 3 1023 N, 71.6° above 2x-axis
1.74 3 1024 N, 51.75° below 1x-axis
21.02 3 1023 i^ N
(1.02 3 1025 i^ 1 2.16 3 1025 j^ ) N
0.68 nC
22KQqa/(y2 1 a2 ) 3/2
y
r
F2 on q
r
2Q
F1 on q
1q
1
r
F3 on q
2Q
14Q
2
x
3
L
55.
57.
59.
61.
63.
Chapter 25
1.
3.
7.
11.
13.
15.
17.
19.
21.
23.
25.
27.
53. a.
65.
67.
69.
71.
73.
75.
b. (2 2 !2)KQq/L2
a. 243 N b. Yes. Any difference must therefore be smaller than 1 part in 109.
3.2 3 1015
4.42°
1.0 3 105 j^ N/C, (2.88 3 104 i^ 1 2.16 3 104 j^ ) N/C,
5.63 3 104 i^ N/C
(4.02 3 104 i^ 1 8.05 3 104 j^ ) N/C, 4.5 3 105 i^ N/C,
(4.02 3 104 i^ 2 8.05 3 104 j^ ) N/C
a. (21 cm, 2 cm) b. (3 cm, 3 cm) c. (4 cm, 22 cm)
a. (3.20 i^ 1 6.40 j^ ) 3 10217 N b. (23.20 i^ 2 6.40 j^ ) 3 10217 N
c. 4.28 3 1010 m/s2 d. 7.85 3 1013 m/s2
14.3°
b. 22.4 nC
b. 5.13 nC
4.06 g
Chapter 26
(2550 N/C, 0° above horizontal)
(3975 N/C, 9.3° above horizontal)
a. 18.0 N/C b. 36.0 N/C
2.28 3 105 N/C, 1.67 3 105 N/C, 2.28 3 105 N/C
(8.78 3 1024 N, toward rod)
20.056 nC
a. 0 N/C b. 4110 N/C
a. 0 N/C b. 1.49 3 105 N/C
1.39 3 1023 nC
1.41 3 105 N/C
1.86 cm
6.13 3 105 N/C, down
5.93 3 105 N/C
0.185 m
(9.0 3 10213 N, direction opposite pr )
(132,600 i^ 2 12,130 j^ ) N/C; (133,200 N/C, 5.23° below the
1x-axis)
33. (675 i^ 2 78,400 j^ ) N/C; (78,400 N/C, 89.5° below the 1x-axis)
r
r
35. a. E 1 5 3 q/(4pP0 )5 !5a2 4 (23 i^ 1 2 j^ ); E 2 5 3 7q/(4pP0 )9a2 4 i^;
r
2 ^ r
E 3 5 3 17q/(4pP0 )9a 4 i ; E 4 5 3 q/(4pP0 )5 !5 a2 4 (23 i^ 2 2 j^ )
b.
y
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
r
E1 net
2a
1
a
r
2q
2 E2 net
22a
12q
0
2a
2a
22a
r
E4 net
4
a
r
3
2a
E3 net
x
A-27
Answers to Odd-Numbered Exercises and Problems
39. 1.08 3 105 N/C
8ld
41. a.
4pP0 (4y2 1 d2 )
b.
24
23
Enet
22
1 l
4pe0 d
8
6
4
2
y/d
21
0
43. 22.29 nC/m
45.
47.
49.
51.
53.
55.
57.
59.
61.
63.
65.
67.
69.
71.
Q
1
4pP0 x"x2 1 L2
i^ 2
Q
4pP0Lx
1
2
1
12
3
5.
7.
9.
11.
13.
15.
17.
19.
21.
No charge
5 N/C, pointing in
21.0 Nm2 /C
a. 6.0 3 1022 N m2/C b. 0 Nm2 /C
1.26 Nm2 /C
a. 0 b. 2pR2E
21.0 Nm2 /C
5.31 nC
2q
4
x
"x2 1 L2
2
2q
2q
2q
j^
b. (1/4pP0 ) (2Q/3 !3 R )
c. (1/4pP0 ) (2Q/pR2 ) ( i^ 1 j^ )
0.9995 cm
1.19 3 107 m/s
a. Positive b. 37,500 N/C c. 2.5 mm
a. 8.84 3 105 N/C b. 60.188 nC
29.89 3 10212 C
18.6 nm
a. mC2 /N or C2 s2 /kg b. ( (1/4pP0 ) 2 (2aq2 /r5 ), toward ion)
b. 1.0 mm
b. z 5 R/ !3
4.16 3 1024 N
a. (h/pP0 ) tan21 (L/2z) k^
c.
E
2q
2
0.5h/e0
2q
(a)
(b)
2q
2q
2q
2q
2q
2q
(c)
(d)
23. 113 Nm2 /C
25. 2.66 3 1025 C/m2
27. a. 20.390 Nm2 /C, 0.225 Nm2 /C, 0.390 Nm2 /C, 20.225 Nm2/C
b. 0 Nm2 /C
29. a. 23.46 Nm2 /C b. 1.15 Nm2 /C
31. 22Q/P0
33. a. 2000 N/C b. 251 Nm2 /C c. 2.22 nC
35. a. 2100 nC b. 150 nC
37. a. 2.39 3 1026 C/m3 b. 1.25 nC, 10.0 nC, 80.0 nC
c. 4500 N/C, 9000 N/C, 18,000 N/C
39. a. 21.068 3 1028 C b. 11.068 3 1028 C c. 4.82 3 1028 C
41.
0.4h/e0
h
E = pe tan21 L
0
2z
0.3h/e0
0.2h/e0
0.1h/e0
z
0
L
2L
3L
43. a. (q/4pP0r2 ) r^ b. 2(q/4pP0r2 ) r^
r
45. a. (2Qr/4pP0a3 ) r^, 2(Q/4pP0r2 ) r^, 0, (Q/4pP0r2 ) r^
b.
E
4L
Q
1
4pe0 c2
73. c. 2.0 3 1012 Hz
0
Chapter 27
2
Q
1
4pe0 b2
2
Q
1
4pe0 a2
r
a
b
c
2c
1.
47. a. r0z/P0 b. r0z0/P0
c.
E
r0 z0
e0
3.
0
r
r
E = 0 N/C
z
z0
2z0
3z0
A-28
49.
51.
53.
55.
ANSWERS
a. 3Q/2AP0, 0, Q/2AP0, 0, 3Q/2AP0 b. 32 Q/A, 2 12 Q/A, 12 Q/A, 32 Q/A
a. (l/2pP0r) r^ b. (lr/2pP0R2 ) r^
b. 0 N/C c. 4.64 3 1013 N/C
a.
55. a. 1.15 3 105 m/s b. 1.5 nm
57. a. (P0I/A) (1/s2 2 1/s1 ) b. 3.68 3 10218 C
Chapter 29
r0
x
22R
2R
0
R
2R
c. (lr2 /2pP0R3 ) r^
Chapter 28
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
31.
33.
35.
37.
39.
41.
43.
45.
7.5 3 1025 m/s
2.62 3 105 s
Aluminum
a. 4.63 3 1021 b. 4.32 3 10212 m
0.31 N/C
9.4 3 1018
3.2 mA
a. 6.25 3 105 A/m2 b. 6.51 3 1025 m/s
a. 1.73 3 107 A/m2 b. 5.31 3 1018 s21
0.141 mA
2.08 3 10214 s, 4.19 3 10215 s
1.68 A
5.01 3 1028 Vm
a. 1.64 3 1023 N/C b. 1.10 3 1025 m/s
a. Doubled b. Unchanged c. Unchanged d. Doubled
a. 3.12 3 1014 b. 398 A/m2 c. 9.11 3 105 N/C d. 0.227 W
22.6 mA
a. 120 C b. 0.449 mm
1/4
10.4 A
a. I/4psr 2 b. 3.32 3 1024 N/C, 5.31 3 1025 N/C
a.
Q (C)
1.
3.
5.
7.
9.
11.
13.
15.
19.
21.
23.
25.
27.
29.
31.
33.
1.38 3 105 m/s
7.07 3 104 m/s
2.82 3 1026 J
22.24 3 10219 J
1.61 3 108 N/C
1.87 3 107 m/s
22.09 3 104 V
a. Lower b. 20.712 V
a. 200 V b. 3.54 3 10210 C
a. Right plate b. 1.0 3 105 V/m c. 2.40 3 10217 J
a. 1800 V, 1800 V, 900 V b. 22.88 3 10216 J, 22.88 3 10216 J,
21.44 3 10216 J c. 0 V, 2900 V
4.17 3 10210 C
11410 V
a. 3140 V b. 5.02 3 10216 J
x 5 3 cm and 6 cm
a. qa is positive, qb is negative with the same magnitude
b.
V
a
0
x
b
35. 0 V
37. 1.44 3 1023 N
39. a. x 5 6` b. x 5 6` and 0
c.
E
21.0 cm
0
1.0 cm
x
20
10
0
2t/(2.0 s)
b. (10 A)e
d.
t (s)
5
10
V
c. 10.0 A
I (A)
21.0 cm
10
0
1.0 cm
5
0
47.
49.
51.
53.
2.43 A
5.6 3 1026 m/s
1/2
1.01 3 1023
t (s)
5
10
41. a. 0.720 J b. 14.4 N c. 21.9 m/s and 10.95 m/s
43. 25.3 3 1026 J
45. a. 1000 V b. 1.39 3 1029 C c. 7.0 3 106 m/s
x
A-29
Answers to Odd-Numbered Exercises and Problems
47. a.
23.
25.
27.
29.
31.
33.
35.
V (V)
50
40
30
20
24.0 V
32 mF
200 pF
1414 V
1/2
a. 1.11 3 1027 J b. 0.708 J/m3
a.
E (V/m)
x
10
1000
x (cm)
210 28 26 24 22
49.
51.
53.
55.
57.
59.
61.
63.
65.
67.
69.
71.
73.
75.
77.
0
2
4
6
8
10
b. SHM c. 3.20 3 1027 J d. 2.53 cm/s
1.17 3 106 m/s
Disk
3.99 3 107 m/s
4.07 3 107 m/s
a. 2.09 3 10210 C, 3000 V/m, 15 V b. 2.09 3 10210 C, 3000 V/m,
30 V c. 2.09 3 10210 C, 750 V/m, 3.75 V
a. V0 /R b. 100,000 V/m
b. 8.33 mC c. 0 V/m, 3.33 3 106 V/m
2126 V, point b higher
a. 4q/(4pP0s) 1 16qx2 /(4pP0s3 ) b. SHM
(2qs2 )/(4pP0y3 )
(Q/4pP0L)ln 3 (x 1 L/2)/(x 2 L/2) 4
Q/4pP0R
b. q1 and q2 are 10 nC and 30 nC
b. Q 5 0.35 nC
x (m)
0
21.0
1.0
21000
b. 125 V
37. V0 2 (l/2pP0 )ln(r/R)
39. a.
E (V/m)
1.4 3 10 8
0
1
2
x (cm)
3
–1.4 3 10 8
b.
V (V)
y
140,000
x (cm)
0
1
P (x, y)
2
3
(20.5 cm, 0)
23
22
21
0
1
x
2
3
Q2 = 23.0 nC
Q1 = 1.0 nC
Equipotential
circle
79. vA 5 0.0548 m/s, vB 5 0.110 m/s
83. c. 2.30 3 10213 J
Chapter 30
1. 2200 V
3. 21000 V/m
5.
E (V/m)
2000
x (cm)
0
10
7.
9.
11.
13.
15.
17.
19.
21.
10,000 V/m to the left
220 V
1.5 3 1026 J
12 V
a. 0.087 V b. 3.5 V
3.0 V
2.29 mA
4.75 cm
4
20
30
41.
43.
45.
47.
49.
51.
53.
55.
57.
59.
61.
63.
65.
67.
69.
71.
73.
75.
77.
79.
81.
83.
85.
(Q/2pP0R2 ) 3 1 2 z/(R2 1 z2 ) 1/2 4
Point 1: 3750 V/m, downward; point 2; 7500 V/m, upward
1000 V/m, 53.1° above the 2x-axis
2 nC and 4 nC
1.1 nC
9.1 A
1800 C
a. 63.19 3 10211 C, 9 V b. 63.19 3 10211 C, 18 V
5.90 cm and 6.10 cm
150 mF, in series
37 mF
60 mC on each; 5.0 V, 15.0 V, 10.0 V
45 mC, 9 V; 21.6 mC, 5.4 V; 21.6 mC, 3.6 V
1.67 pF
1.33 3 10212 F 5 1.33 pF
20 mF
2.4 J
0.177 J/m3
179 km 3 179 km; not feasible
b. L 5 4.86 m
b. C 5 2 mF
2rR2/4P0
a.
E
1 Q
4pe0 R2
0
r
R
2R
3R
A-30
ANSWERS
b. (Q/4pP0R) 3 3/2 2 r2 /2R2 4 c. 3/2
d.
V
67.
R (V)
1 3Q
4pe0 2R
1 Q
4pe0 R
R
2R
3R
2.0
12.0
0.8
12.0
6
1.2
7.2
4
1.2
4.8
I (A)
DV (V)
R (V)
Chapter 31
1. 5.5 V
3. 2.0 A
5. 0.64 mm
7.
4
2
8
6
4
3
8
8
1
8
24
1
3
2
3
16
24
71.
73.
75.
77.
81.
50 V
75 V
9V
100 V
9. 5 A, toward the junction
11. a. 0.50 A, left to right
b.
V (V)
Battery 2
Wire
0
s
Battery 1
Wire
8
a. 10 A b. 80 W c. 60 V
36.4 V
0.69 ms
a. 80 mC b. 0.23 ms
b. 5140 V
Chapter 32
3
Wire
Wire
–3
–6
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
33.
35.
37.
39.
41.
43.
45.
47.
49.
51.
53.
55.
57.
59.
61.
63.
65.
6
15
69.
r
0
DV (V)
I (A)
9.6 V, 12.5 A
23.6 mm
a. 11.6 A b. 10.4 V
78.4 mV
25 V
93.4 W
3.23%
R/4
12.0 V
24 V
183.3 V
13 V, 9 V, 0 V, 22 V
2 ms
6.93 ms
869 V
A.D5E.B5C
Increase
8.4 3 1028 V
7V
60 V, 10 V
9.00 V, 0.50 V
2.0 V for each
1.0 A, 2.0 A, 15.0 V
3.0 A
a. $14.40 b. 34.7 months
a. 8 A, 8 V b. 9.14 A, 0 V
a. 0.505 V b. 0.50 V
Resistor
Wire
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
33.
35.
37.
39.
41.
43.
45.
47.
49.
Out of the page
(2.0 mT, into the page), (4.0 mT, into the page)
a. 1.60 3 10215 k^ T b. 0 T c. 0 T
1.13 3 10215 k^ T
6.25 3 106 m/s in the 1z-direction
4.0 cm, 0.4 mm, 20 mm to 2 mm, 0.20 mm
a. 20 A b. 1.60 3 1023 m
2.0 3 1024 i^ T, 4.0 3 1024 i^ T, and 2.0 3 1024 i^ T
a. 0.025 Am2 b. 5.0 mT
8.75 3 1025 m2
0.0707 T m
1.0 A
2390 A
a. Into the page b. No deflection
a. In the plane of the paper, 45° cw from straight up
b. In the plane of the paper, 45° ccw from straight down
a. 28.0 3 10213 k^ N b. 5.66 3 10213 (2j^ 2 k^ ) N
1.61 3 1023 T
2.9 3 1028 m23
0.025 N, to the right
3.0 V
7.5 3 1024 N m
a. 1.26 3 10211 N m b. Rotated 90°
a. 1.0 mT b. 2.0% c. 2.0 mT d. 2.0 mT; twice field in (a)
(5.2 3 1025 T, out of the page); 0 T
B (T)
2 3 1024
1 3 1024
0
t (ms)
10
20
30
40
51. 750 A
53. a. 1.13 3 1010 A b. 0.014 A/m2
c. The current density in the earth is much less than
the current density in the wire.
50
Answers to Odd-Numbered Exercises and Problems
55.
57.
59.
61.
63.
65.
67.
69.
71.
73.
75.
77.
81.
83.
#18 gauge; 4.06 A
a. (1.25) 23/2m0NI/R b. 1.80 3 1024 T
m0I/4R
0; (m0I/2pr) 3 (r 2 2 R12 )/(R22 2 R12 ) 4 ; m0I/2pr
2.9 3 1023 T
a. (2.4 3 1010 m/s2, down) b. (2.2 3 1011 m/s2, up)
a. 4.6 3 10213 J b. 2850
2.10 T
2.0 A
(0.00864 T, down)
12.5 T
0.036 mm
a. m0IL/4pd "(L/2) 2 1 d2 b. !2m0I/pR c. 90.0%
a. m0Ir/2pR12, m0I/2pr, 0
b.
B
27. a.
B (T)
1.2
1
0.8
0.6
0.4
0.2
t (s)
0
29.
31.
33.
35.
m0 I
2pR1
0.5
1
1.5
2
2.5
3
3.5
I2 (mA)
t (s)
0.2
0.4
279
r
R2
R1
4.5
b. 0.0628(1 2 12 t) A c. 31.4 mA, 0.0 A, 231.4 mA
41.7 mV
43.9 mA
0.853 mA
i
0
0
4
2R2
Chapter 33
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
37.
39.
41.
43.
45.
47.
49.
51.
53.
55.
57.
59.
61.
(7.44 mA)cos(2pft)
a. 12,500 b. 2.0 A
39.5 nA
a. 0.20 A b. 4.0 3 1023 N c. 11°C
a. (4.93 3 1023 )fsin(2pft) A b. 405 Hz; not feasible
a. (vlBcos u)/R b. (mgRtanu)/(l2B2 cos u)
a. (mgR)/(l2B2 ) b. 0.98 m/s
12 V
500
a. 0.0637 J/m3 b. 0.628 J/m3
a. 1.0 3 1016 J b. 0.25%
3.0 s
(0.10 T, out of the page)
a. 4.0 m/s b. 2.24 T
6.28 3 1025 Wb in both cases
a. Right to left b. No
cw
3.14 V
Increasing at 2.34 T/s
100 V, increase
9.47 3 1025 J
0.253 mH
900 V
3.54 3 1024 Wb
a.
t (s)
B (T)
E (V)
I (A)
20
0.0
0.00
0.16
1.6
10
0.5
1.50
0.08
0.8
1.0
2.00
0.00
0.0
1.5
1.50
20.08
20.8
2.0
2.00
20.16
21.6
DVL (V)
t (ms)
0
b.
3
210
63.
B (T)
2
6
I (A)
0.4
1
0.2
0
t (s)
1
2
t (ms)
0
20
I (A)
20.2
1.6
20.4
t (s)
0
1
21.6
2
40
A-31
A-32
ANSWERS
65. a. (LI0/t)e2t/t b. 1.0 V, 0.37 V, 0.13 V, 0.05 V
c.
DV (V)
43. b. 1.48 3 10213 A
45. a. (2.83 3 103t 2 ) Vm
b.
L
r
1.2
B
1
0.8
0.6
0.4
0.2
R
0
67.
69.
71.
73.
75.
t (ms)
0.5
1
1.5
2
2.5
3
r
E
3.5
a. 0.628 ms b. 25 V
0.707Q0
a. 76 mA b. 0.50 ms
a. 1.0 A b. 2.0 A
a. DVbat/R b. I0 (1 2 e2t/(L/R) )
c.
I
47.
49.
51.
53.
55.
57.
59.
I0
c. 1.11 3 1029rt T; 4.44 3 10212 T
d. 1.00 3 10214 t/r T; 5.0 3 10212 T
a. 3.85 3 1026 W b. 589 W/m2
Yes
73.5 W
0.408 m/s
I0/8
b. 6.67 3 1026 J/m3
a. IR/L; m0I/2pr b. (I2R/2prL, radially inward)
t
0
Chapter 35
77. (m0vI/2p)ln 3 (d 1 l)/d 4
79. a. v0 exp 3 2(l2B2 /mR)t 4
b. v (m/s)
1. a. 175 rad/s b. 28.66 V
3.
12
Phasor at
t = 3.0 ms
E0
10
8
608
6
E
0
4
2
0
t (s)
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
81. a. (m0/2p)ln(r2/r1 ) b. 0.36 mH/m
Chapter 34
1.
3.
5.
7.
9.
11.
13.
17.
19.
21.
23.
27.
29.
31.
33.
35.
37.
39.
41.
(2.0 T, into the face)
(23.2 i^ 2 4.8 j^ ) 3 10214 N
(1.73 3 106 V/m, left)
a. (2.0 3 106 m/s, 45° from the y-axis)
b. (1.47 3 106 m/s, 16.2° from the yr-axis )
21.0 3 106 j^ V/m, 1.11 3 1025 k^ T
16.3°
a. 0 V/m b. 0.040 V/m
1.0 3 106 V/s
22.1 mA
6.0 3 105 V/m
a. 1.00 3 10 28 m b. 3.0 3 1016 Hz c. 6.67 3 10 28 T
1.2 3 10210 W/m2
a. 2.21 3 1026 W/m2 b. 0.041 V/m
3.3 3 1026 N
60°
131 W/m2
a. (0.10 T, into the page) b. 0 V/m, (0.10 T, into the page)
1.0 3 107 m/s parallel to the current
(R2 /2r) (dB/dt)
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
33.
35.
37.
a. 50 mA b. 50 mA
a. 1.88 mA b. 1.88 A
a. 79.6 kHz b. 0 V
125 V
6.02 V, 7.99 V
1.59 mF
a. 0.796 A b. 0.796 mA
a. 3.18 3 104 Hz b. 0 V
80 V
1.27 mF
a. 200 kHz b. 141 kHz
a. 227.2° b. 126.3°
9.6 V
43.5 V
395 W
a. 1/ !3RC b. ( !3/2)E0 c. 3630 rad/s
a. 9.95 V, 9.57 V, 7.05 V, 3.15 V, 0.990 V
b.
V (V)
C
10
5
0
0
20
40
60
80
100
f (kHz)
Answers to Odd-Numbered Exercises and Problems
41.
43.
45.
47.
49.
51.
53.
55.
59.
61.
63.
65.
a. 10.0 Hz b. 4.47 V, 3.45 V, 2.24 V
a. 25.1 mA b. 6.67 V
44.1 Hz
a. E 0 /"R2 1 v2L2, E 0R/"R2 1 v2L2 , E 0vL/"R2 1 v2L2
c. Low d. R/L
a. 1.62 A b. 217.7° c. 137 W
a. 3.16 3 104 rad/s 5 5.03 3 103 Hz b. 10.0 V, 31.6 V
a. 69.53 V, 0.072 A, 244.0° b. 50.0 V, 0.100 A, 0°
c. 62.42 V, 0.080 A, 36.8°
a. 3.60 V b. 3.47 V c. 23.60 V
a. 11.6 pF b. 1.5 3 1023 V
40 W: 14.4 W; 60 W: 9.6 W; 100 W: 100 W
a. 0.833 b. 100 V c. 12.5 V d. 320 mF
C = 100 mF
7.8 V
12.0 V
18.7 V
45.
47.
49.
51.
53.
55.
57.
59.
61.
63.
65.
67.
69.
71.
73.
75.
77.
79.
81.
A-33
1st ball: 4.0 m/s to the right; 2nd ball: 2.0 m/s to the left
11.2 hr
a. No b. 67.1 y
a. 0.9965c b. 59.8 ly
4600 kg/m3
a. 8.50 ly, 17 y b. 7.36 ly, 14.7 y
0.96c
0.9997c
a. 0.98c b. 8.49 3 10211 J
b. Lengths perpendicular to the motion are not affected.
a. uyr 5 uy/g(1 2 uxv/c2 ) b. 0.877c
3.87mc
0.786c
a. 7.56 3 1016 J b. 0.84 kg
7.5 3 10213 J
1.06 3 10212 m
22 m
0.845c
Yes
6.0 V
Chapter 37
67. b. 10.0 V, 11.55 V
69. c. !1/LC
d.
I
3.
5.
7.
9.
11.
15.
17.
19.
E0
R
0
v0
v
21.
23.
25.
27.
29.
31.
33.
35.
37.
39.
Chapter 36
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
33.
35.
37.
39.
41.
43.
5 m, 1 s; 25 m, 5 s
345 m/s, 15 m/s
a. 15 m/s b. 5 m/s c. 11.2 m/s
3.00 3 108 m/s
167 ns
2 ms
Bolt 2 first, by 20 ms
Simultaneously
0.866c
a. 0.8c b. 16 y
4.8 ns
Yes
0.78 m
9.5 3 104 m/s
(8.25 3 1010 m, 325 s)
0.36c
0.71c
0.8c
0.71c
a. 1.8 3 1016 J b. 9.0 3 109
0.943c
50 g ball: 1.33 m/s to the right; 100 g ball: 3.33 m/s to the right
41.
43.
45.
47.
6.25 3 1010
(5.0 3 1023 T, out of page)
0.521 mm
a. 71.2 eV b. 214.4 eV c. 5.0 keV
a. 5.93 3 106 m/s b. 3.10 3 107 m/s c. Alpha particle
a. 3, 4, and 5 b. 6, 6, and 6 c. 4, 7, and 8
a. 2H b. 14N11
a. 82 protons, 82 electrons, 125 neutrons
b. 1.66 3 107 V, 2.34 3 1021 V/m
a. 2 and 3; 2 and 4; 2 and 5; 2 and 6 b. 397.1 nm
121.6 nm, 102.6 nm, 97.3 nm, 95.0 nm
a. 6.66 GeV b. 3.63 MeV
0.512 MeV and 939 MeV
173 MeV
(0.0457 T, into page)
a. 7.2 3 1013 b. 1.16 mA
0.000000000058% occupied, 99.999999999942% empty
a. 50,000 kg/m3 b. 3.2 3 10210 m c. 1.7 3 1017 kg/m3
a. 57.6 N b. 4.65 3 10235 N
c. Very strong, very short range, independent of charge
1.77 3 107 V
a. 3.43 3 107 m/s b. 6.14 3 106 V
2.52 3 105 m/s, 65° below the 1x-axis
a. mg/E0 b. mg/b d. 2.40 3 10218 C e. 15
Chapter 38
3.
Photoelectron current I
Intense light
Larger stopping
voltage
5.
7.
9.
11.
13.
15.
17.
19.
Weak light
0
DV
6.25 3 1013
3.20 eV
1.78 eV
a. Aluminum b. 1.93 V
a. 4140 nm; infrared b. 414 nm; visible c. 41.4 nm; ultraviolet
497 nm
6.0 3 1026 V
0.427 nm
A-34
21.
23.
25.
27.
29.
33.
35.
ANSWERS
19.
21.
23.
25.
27.
29.
31.
0.354 nm
a. Yes b. 0.5 eV
Yes to n 5 2, no to n 5 3
a. 69 b. 3.2 3 104 m/s, 20.0029 eV
3.40 eV
91.18 nm
a.
rn (nm)
vn (m/s)
1
2
3
n
25 ns
100,000
18 mm
0 m/s # v # 2.5 3 107 m/s
85 m
1.0 3 105 pulses/s
a.
0 c(x) 0 2
0.5 cm21
En (eV)
0.026
4.38 3 10
6
254.4
0.106
2.19 3 106
213.6
0.238
1.46 3 106
26.0
37. 1.44
39. a. 1.74 3 1018 b. 1.74 3 1026 photons/s
41. Potassium: a. 5.56 3 1014 Hz b. 540 nm c. 1.08 3 106 m/s d. 3.35V;
Gold: a. 1.23 3 1015 Hz b. 244 nm c. 4.4 3 105 m/s d. 0.55 V
43. Sodium
I (mA)
45.
x (cm)
0
b. 1.0% c. 104 d. 0.50 cm21
33. a. Yes b.
1
2
c(x)
1
21
x (cm)
1
21
0.3
c. 0.000, 0.0050, 0.0010 d. 900
35. a. "3/8 mm21/2
b.
0 c(x)0 2 (mm21)
0.1
DV (V)
23 22 21
0
1
2
3/8
3
47. a. p 5 E/c b. l 5 h/p c. l 5 h/mv
49. a. 2.09 3 1024 eV b. 1.985 nm c. 3.5 m
51. 0.427 nm
53.
63.
65.
67.
69.
71.
a. 6.5 eV b. 355 nm, 276 nm c. Both ultraviolet d. 6.16 3 105 m/s
20.278 eV
1876 nm
a. n 5 99: 518 nm, 2.21 3 104 m/s; n 5 100: 529 nm, 2.19 3 104 m/s
b. 6.79 3 109 Hz, 6.59 3 109 Hz c. 6.68 3 109 Hz d. 0.15%
10.28 nm, 7.62 nm, 6.80 nm; ultraviolet
4.16 eV
a. PN b. 2.4 mA c. 4.5 3 106 d. 3.0
a. 1.518 3 10216 s b. 1.32 3 106
a. 4.26 3 1025 nm, 1.31 3 107 m/s b. 0.0164 nm c. X ray
d. 7.3 3 1013 orbits
20%, 10%
a. 7.7% b. 25%
a. 1/6 b. 1/6 c. 5/18
2.0 3 107
a. 3333 b. 1111
a. 5.0 3 1023 b. 2.5 3 1023 c. 0 d. 2.5 3 1023
c(x)
a. 0.25 mm21 b.
c. 0.25
1
c.
21
1 cm21
0
1
2
43.
45.
47.
49.
21
1
1
2
2
1
2
|c(x)|2
4c
16c2
3c
12c2
2c
8c2
4
4c2
x (mm)
x (mm)
c. 0.25
0 c 0 2 (mm21)
c2
22
0
x (mm)
0
c. Both 0.838 d. 58.1%
No; 1.4 3 10227 m
a. 0 # v # 1.8 3 1010 m/s b. Not possible
a. 1.5 3 10213 m; no b. 4.4 3 1011 m
a. b 5 c
c(x)
b.
22
24
2221
P(x)
a
20.5
17. a. 0.354 mm21/2 b.
x (cm)
22
2
d. 3440
41. a. a 5 b b.
x (mm)
0
|c(x)|2
x (cm)
22
0.5
22
4
cm21/2
22
24
2
d. 0.125
37. a. 0.27% b. 31.8%
39. a. 0.866 cm21/2
b.
c(x)
Chapter 39
1.
3.
5.
7.
11.
13.
15.
x (mm)
0
c.
Increasing l
55.
57.
59.
61.
22
24
x (cm)
0
2
4
c. 91%
21
0
1
2
22
21
0
Answers to Odd-Numbered Exercises and Problems
39. a. 4.95 eV b. 4.80 eV c. 4.55 eV
43. b. 0.0091 eV, 0.0272 eV, 0.0453 eV, 0.0634 eV c. 69 mm; infrared
232
45. 101.17310 or 102117000000000000000000000000000000
Chapter 40
1.
3.
7.
9.
11.
0.739 nm
0.752 nm
0.135
0.038 eV
Chapter 41
`
`
1.
3.
5.
7.
11.
E6
x
0
13. a.
L
13.
15.
19.
21.
23.
25.
27.
U (eV)
Turning points
E6
2
1
0
E3
x (nm)
0
1
2
3
a. !2U b. !12U
a. f b. 20.85 eV
20.378 eV; !12U
a. 2 b. 1
Si: 1s22s22p63s23p2; Ge: 1s22s22p63s23p64s23d104p2;
Pb: 1s22s22p63s23p64s23d104p65s24d105p66s24f 145d106p2.
a. Fluorine; excited state b. Nickel; ground state
1s23s1
a. Yes; 2.21 mm b. No; Dl 2 1
0.020
a. 9.0 3 105 b. 8.7 ns
5.3 3 1022
a. 1.48 3 10234 J s b. 21, 0, 1
c.
z-axis
Circle of radius
S 5 !2 U
b.
U (eV)
Sz 5 U
E6
2
0
1
0
15.
17.
19.
21.
25.
29.
E3
x (nm)
0
1
2
2U
3
150 nm
a. 0.49 eV, 1.46 eV, 2.43 eV b. 640 nm
1.35 N/m
1.22%
a. l 5 8mcL2 /3h b. 0.795 nm
a.
29. !6U
31. a. 3.68 3 1023 b. 5.41 3 1023 c. 2.93 3 1023
37. a.
Lz
U
0 c1(x) 0 2
U
0
x
0
L
0
2U
0 c2(x) 0 2
2U
x
0
b.
L
39.
0 c3(x) 0 2
Sz
Jz
mj
1
2U
2 12 U
1
2U
2 12 U
1
2U
2 12 U
3
2U
1
2U
1
2U
2 12 U
2 12 U
2 32 U
3
2
1
2
1
2
1
22
2 12
2 32
1 3
2, 2
4p
4s
4s
3p
3s
2p
2p
2s
2s
x
0
L
1s
n
b. Most
c. Least
d. Probability
e. Probability
1
1
2L
1
3
L,
4
4L
1
3
5
L,
L,
6
6
6L
0 and L
, 13
0.195
0, 21 L, L
, 13
0.402
2
1
3 L, 3 L,
5 13
3
0,
L
0.333
31. 4.77 3 107 m/s
`
35. a. (pb2 ) 21/4 b. 2(pb2 ) 21/2 eb exp(2x2 /b2 ) dx c. 15.7%
37. a.
1
b.
2h !1 2 (y/h)
3d
3p
3s
2
A-35
1s
K
(1s 2 2s2 2p6 3s2 3p6 4s1)
3d
4s
3p
4s
3s
2p
2s
1s
Ti
(1s 2 2s 2 2p 6 3s 2 3p6 4s 2 3d 2)
3d
3p
3s
8
2p
2s
4
1s
2
(y/h)
0
0
0.2 0.4 0.6 0.8 1.0
3d
3s
2s
4s
6
4p
3p
2p
Pclass(y)/(1/h)
10
Ge
(1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d10 4p2)
Fe
(1s 2 2s 2 2p 6 3s 2 3p6 4s 2 3d 6)
1s
Br
(1s 2 2s2 2p 6 3s 2 3p6 4s2 3d10 4p5)
A-36
ANSWERS
41. a. 6s S 5p, 6s S 4p, and 6s S 3p b. 7290 nm; 1630 nm; 515 nm
43. a.
Energy
13.6 eV
15.
17.
19.
21.
20.179 u
8000 N
2.3 3 10238
a.
14
C
n=3
2
n=2
4
n=1
2
2
4
2
Neutrons Protons
14
N
n=3
2
n=2
4
n=1
2
2
4
6.0 eV
2
Neutrons Protons
1.5 eV
0 eV
14
n=3
2
n=2
4
n=1
2
2
4
b. 21.7 eV
45. 1.13 3 106 m/s
47.
49.
51.
53.
55.
57.
61.
O
2
Neutrons Protons
Transition
a. Wavelength
b. Type
c. Absorption
2p S 2s
670 nm
VIS
Yes
3s S 2p
816 nm
IR
No
3p S 2s
324 nm
UV
Yes
No
3p S 3s
2696 nm
IR
3d S 2p
611 nm
VIS
No
3d S 3p
25 mm
IR
No
4s S 2p
498 nm
VIS
No
4s S 3p
2430 nm
IR
No
a. 6.25 3 108 s21 b. 0.17 ns
5.72 ns
5.0 3 1016 s21
a. 1.06 mm b. 1.87 W
0.677
1.5aB; 5aB
Chapter 42
1. a. 1 proton; 2 neutrons b. 18 protons; 22 neutrons
c. 20 protons; 20 neutrons d. 94 protons; 145 neutrons
3. a. 3.8 fm b. 8.2 fm c. 14.5 fm
5. 3.6 3 1026 protons; 3.6 3 1026 neutrons
7. 1.2 3 1011 kg
9. a. 36S and 36Ar b. 5, 8
11. 40Ar: 344 MeV, 8.59 MeV/nucleon; 40Ca: 342 MeV,
8.55 MeV/nucleon
13. 12C: 7.68 MeV/nucleon; 13C: 7.47 MeV/nucleon; 12C
23.
25.
27.
29.
31.
33.
35.
37.
39.
41.
43.
45.
47.
51.
53.
55.
57.
59.
61.
63.
65.
67.
69.
71.
b. 14N stable; 14C beta-minus decay; 14O beta-plus decay
a. 9.3 3 1011 b. 4.7 3 1011 c. 5.5 3 108
a. 3.32 b. 6.64
80.2 days
a. 228Th b. 207Tl c. 7Li d. 60Ni
5.52 MeV
4.82 MeV
60 mrem
0.225 J
a. 3.50 3 107 m/s b. 25.6 MeV
a. 12.7 km b. 780 ms
a. 1.46 3 1028 u; 1.45 3 1026% b. 0.0304 u; 0.76%
6.0 MeV
a. 17N, 17O, 17F b. 17O
c. 17N S 17O by beta-minus; 17F S 17O by EC
7.16 3 1011 Bq or 19.4 Ci
2.73 3 1017
a. 18.9 s b. No
1.19 hr
210 million years
69.7 mrem
3.31 3 1012
a. 2.61 3 1010 b. 0.0239 Bq c. 1.436 3 107 rem/year
d. Yes; <50 million times the natural background.
15 cm
<6 billion years
a. 65.0 MeV; 5.0 MeV b. 3.7 3 1021 s21 c. 6.6 3 10239
d. 650 million years