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Chap9
1. *Chapter 9, Problem 4
In Fig. 9-37, three uniform thin rods, each of length L = 10 cm, form an inverted U. The vertical rods each have a mass
of 15 g; the horizontal rod has a mass of 37 g. What are (a) the x coordinate and (b) the y coordinate of the system's
center of mass? (Give your answer in cm)
Fig. 9-37
Problem 4.
(a) Number
5
Units cm
(b) Number
-2.238805970149
Units cm
2. *Chapter 9, Problem 114
Figure 9-82 shows a uniform square plate of edge length 6d = 6.0 m from which a square piece of edge length 2d has
been removed. What are (a) the x coordinate and (b) the y coordinate of the center of mass of the remaining piece?
Fig. 9-82
Problem 114.
(a) Number
-0.25
(b) Number
0
Units m
Units m
3. Test Bank, Question 20
A large wedge with a mass of 10 kg rests on a horizontal frictionless surface, as shown. A block with a mass of 5.0 kg
starts from rest and slides down the inclined surface of the wedge, which is rough. At one instant the vertical component
of the block's velocity is of 3.0 m/s and the horizontal component is 6.0 m/s. At that instant the velocity of the wedge is:
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3.0 m/s left
3.0 m/s, right
6.0 m/s, right
6.0 m/s, left
17 m/s, right
4. *Chapter 9, Problem 12
Two skaters, one with mass 61 kg and the other with mass 47 kg, stand on an ice rink holding a pole of length 12 m and
negligible mass. Starting from the ends of the pole, the skaters pull themselves along the pole until they meet. How far
does the 47 kg skater move?
Number
6.777777777778
Units m
Significant digits are disabled; the tolerance is +/-2%
5. *Chapter 9, Problem 14
In Figure 9-43, two particles are launched from the origin of the coordinate system at time t = 0. Particle 1 of mass m1
= 3.70 g is shot directly along the x axis (on a frictionless floor), where it moves with a constant speed of 12.0 m/s.
Particle 2 of mass m2 = 4.10 g is shot with a velocity of magnitude 15.7 m/s, at an upward angle such that it always
stays directly above particle 1 during its flight. (a) What is the maximum height Hmax reached by the com of the twoparticle system? In unit-vector notation, what are the (b) velocity and (c) acceleration of the com when the com
reaches Hmax?
Fig. 9-43
Problem 14.
(a) Number
2.748619832548
(b) Number
12
(c) Number
0
i+
i+
0
Units m
j Units m/s
-5.151282051282
j Units m/s^2
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6. *Chapter 9, Problem 17
In Fig. 9-45a, a 4.1 kg dog stands on a 13 kg flatboat at a distance D = 7.2 m from the shore. He walks 2.3 m along the
boat toward shore and then stops. Assuming no friction between the boat and the water, find how far the dog is then
from the shore. (Hint: See Fig. 9-45b. The dog moves leftward and the boat moves rightward, but does the center of
mass of the boat + dog system move?)
Fig. 9-45
Problem 17.
Number
5.451461988304
Units m
Significant digits are disabled; the tolerance is +/-2%
7. Test Bank, Question 68
A block moves at 5 m/s in the positive x direction and hits an identical block, initially at rest. A small amount of
gunpowder had been placed on one of the blocks. The explosion does not harm the blocks but it doubles their total
kinetic energy. After the explosion the blocks move along the x axis and the incident block has a speed of:
1.8 m/s
5.0 m/s
6.8 m/s
7.1 m/s
11.8 m/s
8. Test Bank, Question 66
A 2-kg cart, traveling on a horizontal air track with a speed of 3 m/s, collides with a stationary 4-kg cart. The carts
stick together. The impulse exerted by one cart on the other has a magnitude of:
4N
12 N
s
s
0
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6N
s
9N
s
9. Test Bank, Question 42
A uniform narrow bar, resting on ice, is given a transverse horizontal impulse
at one end as shown. The center of
mass of the bar COM will then:
remain at rest
move in a circle
move in a straight line
move in a parabola
move along some other curve
10. *Chapter 9, Problem 37
A soccer player kicks a soccer ball of mass 0.45 kg that is initially at rest. The player's foot is in contact with the ball for
1.7 x 10-3 s, and the force of the kick is given by
F(t) = [(6.9 x 104)t - (2.3 x 106)t2] N
for 0
t
1.7 x 10-3s, where t is in seconds. Find the magnitudes of the following: (a) the impulse on the ball due to
the kick, (b) the average force on the ball from the player's foot during the period of contact, (c) the maximum force on
the ball from the player's foot during the period of contact, and (d) the ball's speed immediately after it loses contact
with the player's foot.
(a) Number
0.095938366667
(b) Number
56.434333333333
(c) Number
110.653
(d) Number
0.213196370370
Units kg·m/s or N·s
Units N
Units N
Units m/s
11. Test Bank, Question 51
A projectile in flight explodes into several fragments. The total momentum of the fragments immediately after this
explosion:
is the same as the momentum of the projectile immediately before the explosion
has been changed into kinetic energy of the fragments
is less than the momentum of the projectile immediately before the explosion
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is more than the momentum of the projectile immediately before the explosion
has been changed into radiant energy
12. Test Bank, Question 76
Two objects, X and Y, are held at rest on a horizontal frictionless surface and a spring is compressed between them.
The mass of X is 2/5 times the mass of Y. Immediately after the spring is released, X has a kinectic energy of 50 J and
Y has a kinetic erengy of:
20 J
8J
310 J
125 J
50 J
13. *Chapter 9, Problem X32
In Fig. 9-65, block 1 (mass 7.4 kg) is moving rightward at 8.2 m/s and block 2 (mass 4.7 kg) is moving rightward at 3.1
m/s. The surface is frictionless, and a spring with a spring constant of 6700 N/m is fixed to block 2. Eventually block 1
overtakes block 2. At the instant block 1 is moving rightward at 6.9 m/s, what are (a) the speed of block 2 and (b) the
elastic potential energy of the spring?
Figure 9-65
(a) Number
5.146808510638
(b) Number
32.963851063830
Units m/s
Units J
14. *Chapter 9, Problem 59
In Fig. 9-63, block 1 (mass 1.5 kg) is moving rightward at 10 m/s and block 2 (mass 4.2 kg) is moving rightward at 3.1
m/s. The surface is frictionless, and a spring with a spring constant of k = 1200 N/m is fixed to block 2. When the blocks
collide, the compression of the spring is maximum at the instant the blocks have the same velocity. Find the maximum
compression.
Fig. 9-63
Problem 59.
Number
0.209407057640
Units m
Significant digits are disabled; the tolerance is +/-2%
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15. *Chapter 9, Problem X40
Figure 9-86 shows two 22.1 kg ice sleds that are placed a short distance apart, one directly behind the other. A 3.88 kg
cat initially standing on one sled jumps to the other one and then back to the first. Both jumps are made at a speed of
2.11 m/s relative to the ice. What are the final speeds of (a) the first sled and (b) the other sled?
Fig. 9-86
Problem X40.
(a) Number
0.630238645112
Units m/s
(b) Number
0.740886877828
Units m/s
16. *Chapter 9, Problem 52
In the figure here, a 13.7 g bullet moving directly upward at 1040 m/s strikes and passes through the center of mass of
a 7.4 kg block initially at rest. The bullet emerges from the block moving directly upward at 590 m/s. To what maximum
height does the block then rise above its initial position?
Number
0.035411689785
Unit m
Significant digits are disabled; the tolerance is +/-2%
17. *Chapter 9, Problem 63
Block 1 of mass m1 slides along a frictionless floor and into a one-dimensional elastic collision with stationary block 2 of
mass m2 = 5.0m1. Prior to the collision, the center of mass of the two-block system had a speed of 2.0 m/s. Afterward,
what are the speeds of (a) the center of mass and (b) block 2?
(a) Number
2
Units m/s
(b) Number
4
Units m/s
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18. *Chapter 9, Problem 74
Two 5.3 kg bodies, A and B, collide. The velocities before the collision are
2.4 ) m/s. After the collision,
′A = (-11
A
= (49
+ 38 ) m/s and
B
= (-18
+
+ 3.6 ) m/s. What are (a) the x-component and (b) the y-component of
the final velocity of B? (c) What is the change in the total kinetic energy (including sign)?
(a) Number
42
(b) Number
36.8
Units m/s
(c) Number
-2444.784
Units m/s
Units J
19. Test Bank, Question 81
A 1000-kg space probe is motionless in space. To start moving, its main engine is fired for 5 s during which time it ejects
exhaust gases at 5000 m/s. At the end of this process it is moving at 20 m/s. The approximate mass of the ejected gas
is:
0.8 kg
4 kg
5 kg
20 kg
25 kg
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