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Practice test Impulse and Linear Momentum Solutions
MPC
1) A rubber ball and a lump of clay have equal mass. They are thrown with equal speed against
a wall. The ball bounces back with nearly the same speed with which it hit. The clay sticks to
the wall. Which one of these objects experiences the greater momentum change?
A) the ball
B) the clay
C) Both of them experience the same non-zero momentum change.
D) Both of them experience zero momentum change.
Answer: A
Var: 1
2) A tiger is running in a straight line. If we double both the mass and speed of the tiger, the
magnitude of its momentum will increase by what factor?
A)
B) 2
C) 4
D) 8
E) 16
Answer: C
Var: 1
3) Two friends are standing on opposite ends of a canoe that is initially at rest with respect to a
frictionless lake. The person in the front throws a very massive ball toward the back, and the
person in the back catches it. After the ball is caught, the canoe is
A) moving backward.
B) stationary.
C) moving forward.
Answer: B
Var: 1
4) A small car meshes with a large truck in a head-on collision. Which of the following
statements concerning the magnitude of the momentum change during the collision is correct?
(There could be more than one correct choice.)
A) The truck experiences the greater magnitude momentum change.
B) The small car experiences the greater magnitude momentum change.
C) The small car and the truck experience the same magnitude momentum change.
D) The magnitude of the momentum change experienced by each one is inversely proportional to
its mass.
E) The magnitude of the momentum change experienced by each one is directly proportional to
its mass.
Answer: C
Var: 1
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5) Consider two less-than-desirable options. In the first you are driving 30 mph and crash headon into an identical car also going 30 mph. In the second option you are driving 30 mph and
crash head-on into a stationary brick wall. In neither case does your car bounce back from the
thing it hits, and the collision time is the same in both cases. Which of these two situations would
result in the greater impact force on your car?
A) hitting the other car
B) hitting the brick wall
C) The force would be the same in both cases.
D) None of the above choices are correct.
Answer: C
Var: 1
6) A rocket explodes into two fragments, one 25 times heavier than the other. The magnitude of
the momentum change of the lighter fragment is
A) 25 times as great as the momentum change of the heavier fragment.
B) The same as the momentum change of the heavier fragment.
C) 1/25 as great as the momentum change of the heavier fragment.
D) 5 times as great as the momentum change of the heavier fragment.
E) 1/4 as great as the momentum change of the heavier fragment.
Answer: B
Var: 1
7) Which of the following quantities are units of impulse? (There could be more than one correct
choice.)
A) N · m
B) kg · s/m
C) kg · m/s
D) N · s
E) kg · m2/s2
Answer: C, D
Var: 1
9) During World War I, Germany used a "Big Bertha" cannon to hurl shells into Paris 30 miles
away. This gun also had a very long barrel. What was the reason for using a long barrel in these
guns?
A) to exert a larger force on the shells
B) to reduce frictional losses
C) to allow the force of the expanding gases from the gunpowder to act for a longer time
D) to increase the force exerted on the bullet due to the expanding gases from the gunpowder
E) to reduce the force exerted on the bullet due to the expanding gases from the gunpowder
Answer: C
Var: 1
10) In a collision between two unequal masses, which mass receives a greater magnitude
impulse?
A) the larger mass
B) the smaller mass
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C) They receive equal impulses.
Answer: C
Var: 1
11) A very light ping-pong ball moving east at a speed of 4 m/s collides with a very heavy
stationary bowling ball. The Ping-Pong ball bounces back to the west, and the bowling ball
moves very slowly to the east. Which object experiences the greater magnitude impulse during
the collision?
A) Neither; both experienced the same magnitude impulse.
B) the Ping-Pong ball
C) the bowling ball
D) It is impossible to tell since the actual mass values are not given.
E) It is impossible to tell since the velocities after the collision are unknown.
Answer: A
Var: 1
12) A 2.0-kg ball moving eastward at 3.0 m/s suddenly collides with and sticks to a 4.0-kg ball
moving northward at 2.0 m/s. What is the magnitude of the momentum of this system just after
the collision?
A) 14 kg · m/s
B) 2.0 kg · m/s
C) 10 kg · m/s
D) 6.0 kg · m/s
E) 8.0 kg · m/s
Answer: C
Var: 1
13) A 0.14-kg baseball is dropped from rest from a height of 2.0 m above the ground. What is the
magnitude of its momentum just before it hits the ground if we neglect air resistance?
A) 0.28 kg · m/s
B) 0.88 kg · m/s
C) 0.44 kg · m/s
D) 0.62 kg · m/s
E) 1.4 kg · m/s
Answer: B
Var: 1
14) Three objects are moving along a straight line as shown in the figure. Taking the positive
direction to be to the right, what is the total momentum of this system?
A) +106 kg · m/s
B) -106 kg · m/s
C) +14.0 kg · m/s
D) -14.0 kg · m/s
E) 0.00 kg · m/s
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Answer: D
Var: 1
15) A 100-g ball falls from a window that is 12 m above ground level and experiences no
significant air resistance as it falls. What is its momentum when it strikes the ground?
A) 3.3 kg · m/s
B) 4.8 kg · m/s
C) 1.8 kg · m/s
D) 1.5 kg · m/s
E) 2.4 kg · m/s
Answer: D
Var: 1
16) A firecracker breaks up into two pieces, one of which has a mass of 200 g and flies off along
the +x-axis with a speed of 82.0 m/s. The second piece has a mass of 300 g and flies off along
the +y-axis with a speed of 45.0 m/s. What is the total momentum of the two pieces?
A) 361 kg · m/s at 56.3° from the +x-axis
B) 93.5 kg · m/s at 28.8° from the +x-axis
C) 21.2 kg · m/s at 39.5° from the +x-axis
D) 361 kg · m/s at 0.983° from the +x-axis
E) 21.2 kg · m/s at 56.3° from the +x-axis
Answer: C
Var: 1
18) A 0.10-kg ball, traveling horizontally at 25 m/s, strikes a wall and rebounds at 19 m/s. What
is the magnitude of the change in the momentum of the ball during the rebound?
A) 1.2 kg · m/s
B) 1.8 kg · m/s
C) 4.4 kg · m/s
D) 5.4 kg · m/s
E) 72 kg · m/s
Answer: C
Var: 1
19) A 328-kg car moving at 19.1 m/s in the +x direction hits from behind a second car moving at
in the same direction. If the second car has a mass of
and a speed of
right
after the collision, what is the velocity of the first car after this sudden collision?
A) 14.0 m/s
B) 18.2 m/s
C) 24.2 m/s
D) -14.0 m/s
Answer: A
Var: 50+
20) A 1200-kg cannon suddenly fires a
cannonball at
What is the recoil speed of the
cannon? Assume that frictional forces are negligible and the cannon is fired horizontally.
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A) 2.9 m/s
B) 35 m/s
C) 3.5 m/s
D) 3.2 m/s
Answer: A
Var: 50+
21) A dinner plate falls vertically to the floor and breaks up into three pieces, which slide
horizontally along the floor. Immediately after the impact, a 320-g piece moves along the +x-axis
with a speed of 2.00 m/s and a 355-g piece moves along the +y-axis with a speed of 1.50 m/s.
The third piece has a mass of 100 g. In what direction relative to the +x-axis does the third piece
move?
A) 216.9° from the +x-axis
B) 219.8° from the +x-axis
C) 36.9° from the +x-axis
D) 39.9° from the +x-axis
E) 39.8° from the +x-axis
Answer: B
Var: 5
22) Two astronauts, of masses 60 kg and 80 kg, are initially right next to each other and at rest in
outer space. They suddenly push each other apart. What is their separation after the heavier
astronaut has moved 12 m?
A) 9.0 m
B) 16 m
C) 21 m
D) 24 m
E) 28 m
Answer: E
Var: 1
23) Astronaut Jennifer's lifeline to her spaceship comes loose and she finds herself stranded,
"floating" 100 m from the mothership. She suddenly throws her 2.00-kg wrench at 20 m/s in a
direction away from the ship. If she and her spacesuit have a combined mass of 200 kg, how long
does it take her to coast back to her spaceship?
A) 1000 s
B) 750 s
C) 500 s
D) 250 s
E) 2.50 min
Answer: C
Var: 1
24) The graph in the figure shows the x component F of the net force that acts for 10 s on a 100kg crate. What is the change in the momentum of the crate during the 10 s that this force acts?
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A) -100 kg · m/s
B) -25 kg · m/s
C) 75 kg · m/s
D) -75 kg · m/s
E) 25 kg · m/s
Answer: D
Var: 1
25) A golf club exerts an average horizontal force of 1000 N on a 0.045-kg golf ball that is
initially at rest on the tee. The club is in contact with the ball for 1.8 ms. What is the speed of the
golf ball just as it leaves the tee?
A) 30 m/s
B) 35 m/s
C) 40 m/s
D) 45 m/s
E) 50 m/s
Answer: C
Var: 1
26) Calculate the impulse due to a force of
A) 6.3 kg· m/s
B) 5.0 kg· m/s
C) 5.7 kg· m/s
D) 6.9 kg· m/s
Answer: A
Var: 50+
that lasts for
27) A 0.140 kg baseball is thrown horizontally with a velocity of 28.9 m/s. It is struck with a
constant horizontal force that lasts for 1.85 ms, which results in a velocity of 37.0 m/s in the
opposite direction. What was the magnitude of the horizontal force?
A) 0.613 kN
B) 2.19 kN
C) 2.80 kN
D) 4.99 kN
Answer: D
Var: 1
28) A 0.24 kg blob of clay is thrown at a wall with an initial horizontal velocity of
If the
clay comes to a stop in
what is the average horizontal force on the clay due to the wall?
A) 42 N
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B) 26 N
C) 35 N
D) 51 N
Answer: A
Var: 14
29) A block of mass m = 34 kg and speed V is behind a block of mass M = 81 kg and speed of
as shown in the figure. The surface is frictionless and the blocks collide and couple.
After the collision, the blocks have a common speed of
What is the magnitude of the
impulse on the 34-kg block due to the collision?
A) 32 N · s
B) 14 N · s
C) 41 N · s
D) 57 N · s
E) 73 N · s
Answer: A
Var: 50+
30) A 0.140-kg baseball is dropped from rest. It has a speed of 1.20 m/s just before it hits the
ground, and it rebounds with an upward speed of 1.00 m/s. The ball is in contact with the ground
for 0.0140 s. What is the average force exerted by the ground on the ball during the time of
contact?
A) 2.00 N upwards
B) 2.00 N downwards
C) 22.0 N upwards
D) 22.0 N downwards
E) 0.00 N
Answer: C
Var: 1
31) A block of mass m = 5.6 kg, moving on a frictionless surface with a velocity of
to
the right, collides with a block of mass M at rest, as shown in the figure. After the collision, the
5.6-kg block recoils with a velocity of
to the left. If the blocks are in contact for 0.20
s, what is the magnitude of the average force on the 5.6-kg block, while the two blocks are in
contact?
A) 202 N
B) 192 N
C) 182 N
D) 0 N
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E) 0 N
Answer: A
Var: 50+
32) A 1200-kg car moving at
suddenly collides with a stationary car of mass
If
the two vehicles lock together, what is their combined velocity immediately after the collision?
A) 6.9 m/s
B) 8.6 m/s
C) 12.1 m/s
D) 5.5 m/s
Answer: A
Var: 50+
33) A 1000-kg whale swims horizontally to the right at a speed of 6.0 m/s. It suddenly collides
directly with a stationary seal of mass 200 kg. The seal grabs onto the whale and holds fast. What
is the speed of these two sea creatures just after their collision? You can neglect any drag effects
of the water during the collision.
A) 0.00 m/s
B) 3.0 m/s
C) 4.0 m/s
D) 5.0 m/s
E) 6.0 m/s
Answer: D
Var: 1
34) Two vehicles approach a right angle intersection and then suddenly collide. After the
collision, they become entangled. If their mass ratios were 1:4 and their respective speeds as they
approached the intersection were both 13 m/s, find the magnitude and direction of the final
velocity of the wreck.
A) 11 m/s at 14° with respect to the original direction of the lighter car
B) 16 m/s at 76° with respect to the original direction of the lighter car
C) 11 m/s at 76° with respect to the original direction of the lighter car
D) 26 m/s at 76° with respect to the original direction of the lighter car
E) 16 m/s at 14° with respect to the original direction of the lighter car
Answer: C
Var: 1
35) A puck with a mass m1 = 50 g moving at 1.0 m/s approaches a stationary puck with a mass
m2 = 100 g on a frictionless air table, and they undergo a sudden two-dimensional elastic
collision. After the collision, both pucks have identical speeds, but travel in different directions.
What is the angle between the original and final paths of puck with mass m1?
A) 30°
B) 60°
C) 90°
D) 120°
E) 150°
Answer: C
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Var: 1
36) A 900-kg car traveling east at 15.0 m/s suddenly collides with a 750-kg car traveling north at
20.0 m/s. The cars stick together after the collision. In what direction does the wreckage move
just after the collision?
A) 36.9° N of E
B) 42.0° N of E
C) 45.0° N of E
D) 53.1° N of E
E) 48.0° N of E
Answer: E
Var: 1
37) A 1500-kg car traveling at 90 km/h toward the east suddenly collides with a 3000-kg car
traveling at 60 km/h toward the south. The two cars stick together after the collision. What is the
speed of the cars after collision?
A) 8.3 m/s
B) 14 m/s
C) 17 m/s
D) 22 m/s
Answer: B
Var: 1
38) Two dogs, Rover and Fido, run on a level frictionless surface. Rover runs eastward with a
momentum of 24 kg . m/s, and Fido runs northward with momentum 10 kg . m/s. They make a
sudden perfectly inelastic collision. What is the magnitude of their combined momentum after
the collision?
A) 14 kg . m/s
B) 26 kg . m/s
C) 34 kg . m/s
D) It cannot be determined without knowing the masses and velocities of the dogs.
Answer: B
Var: 1
Free Response
1) What is the magnitude of the momentum of a 0.140 kg baseball traveling at 45.0 m/s?
Answer: 6.30 kg · m/s
Var: 1
2) A 60-kg swimmer suddenly dives horizontally from a 150-kg raft with a speed of 1.5 m/s. The
raft is initially at rest. What is the speed of the raft immediately after the diver jumps if the water
has negligible effect on the raft?
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Answer: 0.60 m/s
Var: 1
3) A 14,000-kg boxcar is coasting at 1.50 m/s along a horizontal track when it suddenly hits and
couples with a stationary 10,000-kg boxcar. What is the speed of the cars just after the collision?
Answer: 0.875 m/s
Var: 1
4) A batter applies an average force of 8000 N to a baseball for 1.1 ms. What is the magnitude of
the impulse delivered to the baseball by the bat?
Answer: 8.8 N · s
Var: 1
5) A batter hits a 0.140-kg baseball that was approaching him at 30 m/s and, as a result, the ball
leaves the bat at 40 m/s in the reverse of its original direction. The ball remains in contact with
the bat for 2.0 ms. What is the magnitude of the average force exerted by the bat on the ball?
Answer: 4900 N
Var: 1
6) A force of 5.3 N is needed to hold on to an umbrella in a strong wind. If the air molecules
each have a mass of 4.7 ×10-26 kg, and each one strikes the umbrella (without rebounding) with
a speed of 2.0 m/s in the same direction, how many atoms strike the umbrella each second?
Assume that the wind blows horizontally so that the gravity can be neglected.
Answer: 5.6 ×1025 per second
Var: 1
7) A car (of mass 1500 kg) and a small truck (of mass 2000 kg) collide suddenly at right angles
at an icy intersection. The car was originally traveling eastward at 20.0 m/s and the truck was
traveling northward at 20.0 m/s just before the collision took place. What is the speed of the
combined wreck just after the collision if the vehicles become enmeshed?
Answer: 14.3 m/s
Var: 1
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