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Name:______________________________Class:__________________ Date:__________________
Assessment
Chapter Test B
Teacher Notes and Answers
Momentum and Collisions
CHAPTER TEST B (ADVANCED)
1. a
Given
a: m = 275 kg
11. Yes, a spaceship traveling with constant
velocity could experience a change in
momentum if its mass changed, for example,
by burning fuel.
12. 10.5 m/s
13. Stopping a falling egg requires changing the
momentum of the egg from its value at the
time of first impact to zero. If the egg hits
the concrete, the time interval over which
this happens is very small, so the force is
large. If the egg lands on grass, the time
interval over which the momentum changes
is larger, so the force on the egg is smaller.
14. Producing sound requires energy. Because
the system of objects loses some energy as
sound is produced in the collision, the total
kinetic energy cannot be conserved, so the
collision cannot be perfectly elastic.
15. 30 m/s to the west
Given
v = 0.55 m/s
b: m = 2.7 kg
v = 7.5 m/s
c: m = 91 kg
v = 1.4 m/s
d: m = 1.8 kg
v = 6.7 m/s
Solution
p = mv
pa = (275 kg)(0.55 m/s) = 1.5 102 kg • m/s
p b = (2.7 kg)(7.5 m/s) = 2.0 101 kg • m/s
pc = (91 kg)(1.4 m/s) = 1.3 102 kg • m/s
pd = (1.8 kg)(6.7 m/s) = 1.2 101 kg • m/s
pa > pc > p b > pd
2. a
3. d
Given
m = 2.0 kg
m1 = 2680 kg
v 1 = 15 m/s to the west
m 2 = 1340 kg
Solution
v i = 40 m/s
4.
5.
6.
7.
8.
9.
10.
v f = 60 m/s
Solution
p = m(vf vi) =
(0.2 kg)(60 m/s 40 m/s) = 20 kg•m/s
b
a
b
b
d
b
The first pitch is harder to stop. The first
pitch has greater momentum because it has a
greater velocity.
m1 v 1 = m2 v 2
v2 =
m1 v 1 (2.68 103 kg)(15 m/s)
=
m2
(1.34 103 kg)
= 3.0 101 m/s
16. 1.8 kg • m/s
Given
m = 6.0 10 2 kg
v i = 12 m/s
v f = 18 m/s
Solution
p = m( v f v i ) =
(6.0 10 2 kg)(18 m/s 12 m/s)
= 1.8 kg • m/s
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Chapter Tests
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17. 77 s; 5.8 102 m
Given
20. 10 m/s to the north
Given
m1 = 90 kg
m = 1.8 105 kg
v i = 15 m/s
m2 = 120 kg
v f = 0 m/s
v 2, i = 4 m/s to the south = 4 m/s
F = 3.5 10 4 N
v f = 2 m/s to the north = 2 m/s
Solution
Ft = p
p m( v f v i )
t =
=
=
F
F
(1.8 105 kg )(0 m/s 15 m/s)
3.5 10 4 N
= 77 s
v 2, f = 2.0 m/s
Solution
m1 v 1, i + m2 v 2, i = (m1 + m2 )v f
v 1, i = 1
x = ( v i + v f )t =
2
(90 kg + 120 kg)(2 m/s) (120 kg)(4 m/s)
90 kg
=
1 101 m/s
v 1, i = 10 m/s to the north
2
1
(m1 + m2 )v f m2 v 2, i
=
m1
(15 m/s + 0 m/s)(77 s) =
5.8 10 2 m
18. 0.33 m/s
Given
m1 = 85 kg
m2 = 2.0 kg
v 1, i = v 2, i = 0 m/s
v 2, f = 14 m/s
Solution
m1 v 1,i + m2 v 2,i = m1 v 1,f + m2 v 2,f = 0
m1 v 1,f = m2 v 2,f
v 1,f = m2 v 2,f
m1
=
(2.0 kg)(14 m/s)
85 kg
= 0.33 m/s
19. 0.20 m/s
Given
m1 = 0.10 kg
m2 = 0.15 kg
v 2, i = 0 m/s
v 1, f = 0.045 m/s
v 2, f = 0.16 m/s
Solution
m1 v 1,i + m2 v 2,i
v 1,i =
=
m1 v 1,f + m2 v 2,f
m1 v 1,f + m2 v 2,f m2 v 2,i
m1
v 1,i = [(0.10 kg )(0.045 m/s) + (0.15 kg)(0.16 m/s)
(0.15 kg)(0 m/s)] ÷ 0.10 kg = 0.20 m/s
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Chapter Tests
Name:______________________________Class:__________________ Date:__________________
Assessment
Momentum and Collisions
Chapter Test B
MULTIPLE CHOICE
In the space provided, write the letter of the term or phrase that best completes
each statement or best answers each question.
_____ 1. Which of the following has the greatest momentum?
a. a tortoise with a mass of 275 kg moving at a velocity of 0.55 m/s
b. a hare with a mass of 2.7 kg moving at a velocity of 7.5 m/s
c. a turtle with a mass of 91 kg moving at a velocity of 1.4 m/s
d. a roadrunner with a mass of 1.8 kg moving at a velocity of 6.7 m/s
_____ 2. A person sitting in a chair with wheels stands up, causing the chair to
roll backward across the floor. The momentum of the chair
a. was zero while stationary and increased when the person stood.
b. was greatest while the person sat in the chair.
c. remained the same.
d. was zero when the person got out of the chair and increased while
the person sat.
_____ 3. A 0.2 kg baseball is pitched with a velocity of 40 m/s and is then batted
to the pitcher with a velocity of 60 m/s. What is the magnitude of
change in the ball’s momentum?
a. 2 kg•m/s
c. 8 kg•m/s
b. 4 kg•m/s
d. 20 kg•m/s
_____ 4. Which of the following statements properly relates the variables in the
equation Ft = p?
a. A large constant force changes an object’s momentum over a long
time interval.
b. A large constant force acting over a long time interval causes a large
change in momentum.
c. A large constant force changes an object’s momentum at various
time intervals.
d. A large constant force does not necessarily cause a change in an
object’s momentum.
_____ 5. Two objects with different masses collide and bounce back after an
elastic collision. Before the collision, the two objects were moving at
velocities equal in magnitude but opposite in direction. After the
collision,
a. the less massive object had gained momentum.
b. the more massive object had gained momentum.
c. both objects had the same momentum.
d. both objects lost momentum.
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Chapter Test B continued
_____ 6. Two swimmers relax close together on air mattresses in a pool. One
swimmer’s mass is 48 kg, and the other’s mass is 55 kg. If the
swimmers push away from each other,
a. their total momentum triples.
b. their momenta are equal but opposite.
c. their total momentum doubles.
d. their total momentum decreases.
_____ 7. Which of the following statements about the conservation of
momentum is not correct?
a. Momentum is conserved for a system of objects pushing away from
each other.
b. Momentum is not conserved for a system of objects in a head-on
collision.
c. Momentum is conserved when two or more interacting objects push
away from each other.
d. The total momentum of a system of interacting objects remains
constant regardless of forces between the objects.
_____ 8. Two balls of dough collide and stick together. Identify the type of
collision.
a. elastic
c. inelastic
b. perfectly elastic
d. perfectly inelastic
_____ 9. Which of the following best describes the momentum of two bodies
after a two-body collision if the kinetic energy of the system is
conserved?
a. must be less
c. might also be conserved
b. must also be conserved
d. is doubled in value
SHORT ANSWER
10. A baseball pitcher’s first pitch is a fastball, moving at high speed. The
pitcher’s second pitch—with the same ball—is a changeup, moving more
slowly. Which pitch is harder for the catcher to stop? Explain your answer in
terms of momentum.
_________________________________________________________________
_________________________________________________________________
11. Is it possible for a spaceship traveling with constant velocity to experience a
change in momentum? Explain your answer.
_________________________________________________________________
_________________________________________________________________
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Chapter Tests
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Chapter Test B continued
12. Each croquet ball in a set has a mass of 0.50 kg. The green ball travels at
10.5 m/s and strikes a stationary red ball. If the green ball stops moving, what
is the final speed of the red ball after the collision?
_________________________________________________________________
13. A moderate force will break an egg. Using the concepts of momentum, force,
and time interval, explain why an egg is more likely to break when it is
dropped on concrete than if it is dropped on grass.
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
14. Why is the sound produced by a collision evidence that the collision is not
perfectly elastic?
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
PROBLEM
15. What velocity must a 1340 kg car have in order to have the same momentum
as a 2680 kg truck traveling at a velocity of 15 m/s to the west?
16. A 6.0 102 kg tennis ball moves at a velocity of 12 m/s. The ball is struck by
a racket, causing it to rebound in the opposite direction at a speed of 18 m/s.
What is the change in the ball’s momentum?
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Chapter Tests
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Chapter Test B continued
17. A train with a mass of 1.8 103 kg is moving at 15 m/s when the engineer
applies the brakes. If the braking force is constant at 3.5 104 N, how long
does it take the train to stop? How far does the train travel during this time?
18. An astronaut with a mass of 85 kg is outside a space capsule when the tether
line breaks. To return to the capsule, the astronaut throws a 2.0 kg wrench
away from the capsule at a speed of 14 m/s. At what speed does the astronaut
move toward the capsule?
19. A 0.10 kg object makes an elastic head-on collision with a 0.15 kg stationary
object. The final velocity of the 0.10 kg object after the collision is
0.045 m/s, and the final velocity of the 0.15 kg object after the collision is
0.16 m/s. What was the initial velocity of the 0.10 kg object?
20. A 90 kg halfback runs north and is tackled by a 120 kg opponent running
south at 4 m/s. The collision is perfectly inelastic. Just after the tackle, both
players move at a velocity of 2 m/s north. Calculate the velocity of the 90 kg
player just before the tackle.
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Chapter Tests