Impulse and Momentum Review Key
1. Which of the following statements are true about momentum?
Answer CFGJ
a. True - Momentum is a vector quantity. Like all vector quantities, the momentum
of an object is not fully described until the direction of the momentum is
identified. Momentum, like other vector quantities, is subject to the rules
of vector operations.
b. False -The Joule is the unit of energy. The kgm is the standard unit of
s
momentum.
c. False - An object has momentum if it is moving. Having mass gives an object
inertia. When that inertia is in motion, the object has momentum.
d. True - This is true. However, one should be quick to note that the object does
not have to have a constant speed in order to have momentum.
e. False - The direction of an object's momentum vector is in the direction that the
object is moving. If an object is traveling eastward, then it has an
eastward momentum. If the object is slowing down, its momentum is still
eastward. Only its acceleration would be westward.
f. False - To say that momentum is a conserved quantity is to say that if a system of
objects can be considered to be isolated from the impact of net external
forces, then the total momentum of that system is conserved. In the
absence of external forces, the total momentum of a system is not altered
by a collision. However, the momentum of an individual object is altered
as momentum is transferred between colliding objects.
g. True - Momentum is calculated as the product of mass and velocity. As the
speed of an object increases, so does its velocity. As a result, an
increasing speed leads to an increasing momentum - a direct relationship.
h. True - For the same speed (and thus velocity), a more massive object has a
greater product of mass and velocity; it therefore has more momentum.
i. False - A less massive object could have a greater momentum owing to a velocity
which is greater than that of the more massive object. Momentum
depends upon two quantities mass and velocity. Both are equally
important.
j. False - When comparing the size of two momentum vectors, the direction is
insignificant. The direction of any vector would never enter into a size
comparison.
k. True - Objects with a changing speed also have a changing velocity. As such,
an object with a changing speed also has a changing momentum.
Impulse & Momentum Review Key
page 2
2. Which of the following are true about the relationship between momentum and
energy?
ANSWER BE
a. False - No. Momentum is momentum and energy is energy. Momentum
is NOT a form of energy; it is simply a quantity which proves to be useful
in the analysis of situations involving forces and impulses.
b. True - If an object has momentum, then it is moving. If it is moving, then it has
kinetic energy. And if an object has kinetic energy, then it definitely has
mechanical energy.
c. False - If an object does NOT have momentum, then it definitely does NOT have
kinetic energy. However, it could have some potential energy and thus
have mechanical energy. For example if the object was held above the
ground it would have gravitational potential energy but no kinetic energy.
d. False - Consider Object A with a mass of 10 kg and a velocity of 3 m and
s
Object B with a mass of 2 kg and a velocity of 10 m . Object A clearly has
s
more momentum. However, Object B has the greatest kinetic energy.
The kinetic energy of A is 45 J and the kinetic energy of B is 100 J.
e. True - When comparing the momentum of two objects to each other, one must
consider both mass and velocity; both are of equal importance when


determining the momentum value of an object. ( p = mv ) When comparing
the kinetic energy of two objects, the velocity of an object is of squared
1


importance.  E k = mv 2  So if two objects of different mass have the
2


same momentum, then the object with the least mass has a greater
velocity. This greater velocity will tip the scales in favor of the least
massive object when a kinetic energy comparison is made.
3. Which of the following statements are true about impulse?
ANSWER BDFGHI
a. False - Impulse is NOT a force. Impulse is a quantity which depends upon both
force and time to change the momentum of an object. Impulse is a force
acting over a time.
b. True - Impulse is a vector quantity like momentum, impulse is not fully described
unless a direction is associated with it.
c. False - An object which is traveling East could encounter a collision from the side,
from behind (by a faster-moving object) or from the front. The direction of
the impulse is dependent upon the direction of the force exerted upon the
object. In each of these scenarios, the direction of the force would be
different.
d. True - In a collision, there is a collision force which endures for some amount of
time. The combination of force and time is what is referred to as an
impulse.
Impulse & Momentum Review Key
page 3
e. False - The Newton is the unit of force. The standard metric unit of impulse is the

Ns since Impulse = F∆t .
f. True - The Ns is the unit of impulse. The Newton can be written as a kgm 2 .
s
kgm
When substituted into the Ns expression, the result is the
.
s
g. True - In a collision, there is a collision force which endures for some amount of
time to cause an impulse. This impulse acts upon the object to change its
velocity and thus its momentum.
f. True - Yes!!! This is the impulse-change in momentum theorem. The impulse
encountered by an object in a collision causes and is equal to the
momentum change experienced by that object.

g. True - Since Impulse = F∆t , a force of 100 N for 0.10 s results in an impulse of
10 Ns. This 10 Ns impulse is equivalent to the impulse created by a force of
5 N for 2.0 s.
4. Which of the following statements are true about collisions?
ANSWER ABF
a. True - In any collision between two objects, the colliding objects exert equal and
opposite force upon each other. This is simply Newton's 3rd Law.
b. True - In a collision, there is a collision force which endures for some amount of
time to cause an impulse. This impulse acts upon the object to change its
momentum.
c. False - The impulse encountered by an object is equal to mass multiplied by
velocity change - that is, momentum change.
d. False - Two colliding objects will only experience the same velocity change if they
have the same mass and the collision occurs in an isolated system.
However, their momentum changes will be equal if the system is isolated
from external forces.
e. False - This statement is mistaking the term velocity for momentum. It is
momentum which is conserved by an isolated system of two or more
objects.
f. True - Two colliding objects will always exert equal forces upon each other.
rd
(Newton’s 3 Law) If the objects have different masses, then these equal
forces will produce different accelerations. (Newton’s 2nd Law)
g. False - It the colliding objects have identical masses, the equal force which they
exert upon each other (Newton’s 3rd Law) will lead to identical acceleration
values for the two objects. (Newton’s 2nd Law)
h. False - Total momentum is conserved only if the collision can be considered
isolated from the influence of net external forces.
i. False - In any collision, the colliding objects exert equal and opposite forces upon
each other as the result of the collision interaction. There are no
exceptions to this rule. (Newton’s 3rd Law)
Impulse & Momentum Review Key
page 4
j. False - In any collision, the colliding objects will experience equal (and opposite)
momentum changes, provided that the collision occurs in an isolated
system.
k. False - In any collision, the colliding objects exert equal and opposite forces upon
each other as the result of the collision interaction. There are no
rd
exceptions to this rule. (Newton’s 3 Law)
l. False - In any collision, the colliding objects will experience equal (and opposite)
momentum changes, provided that the collision occurs in an isolated
system.
5. Which of the following statements are true about elastic and inelastic collisions?
a. Perfectly elastic and perfectly inelastic collisions are the two opposite extremes
along a continuum; where a particular collision lies along the continuum is
dependent upon the amount of kinetic energy which is conserved by the two
objects.
ANSWER AEFGI
a. True - A perfectly elastic collision is a collision in which the total kinetic energy of
the system of colliding objects is conserved. Such collisions are typically
characterized by bouncing or repelling from a distance. In a perfectly
inelastic collision (as it is sometimes called), the two colliding objects stick
together and move as a single unit after the collision. Such collisions are
characterized by large losses in the kinetic energy of the system.
b. False - Few collisions are completely elastic. A completely elastic collision occurs
only when the collision force is a non-contact force. Most collisions are
either perfectly inelastic or partially inelastic. Some energy is dissipated in
most collisions
c. False - Momentum can be conserved in both elastic and inelastic collisions
provided that the system of colliding objects is isolated from the influence
of net external forces. It is kinetic energy that is conserved only in a
perfectly elastic collision.
d. False - In a perfectly elastic collision, an individual object may gain or lose kinetic
energy. It is the system of colliding objects which conserves kinetic
energy.
e. True - Kinetic energy is lost from a system of colliding objects because the
collision stores some of the kinetic energy as sound, thermal and light
energy. When the colliding objects don't really collide in the usual sense
(that is when the collision force is a non-contact force), the system of
colliding objects does not lose its kinetic energy. Sound is only produced
when atoms of one object make contact with atoms of another object.
And objects only warm up (storing mechanical energy as thermal energy)
when their surfaces meet and atoms at those surfaces are set into
vibrational motion.
f. True - See above statement.
Impulse & Momentum Review Key
page 5
g. True - If large amounts of kinetic energy are conserved when a ball collides with
the ground, then the post-collision velocity is high compared to the precollision velocity. The ball will thus rise to a height which is nearer to its
initial height.
h. False - This is a perfectly elastic collision. Before the collision, all the kinetic
energy is in the first glider. After the collision, the first glider has no kinetic
energy; yet the second glider has the same mass and velocity as the first
glider. As such, the second glider has the kinetic energy which the first
glider once had.
i. True - There is significant bounce in the collision between a tennis racket and
tennis ball. There is typically little bounce in the collision between a
halfback and a linebacker (though there are certainly exceptions to this
one). Thus, the ball-racket collision tends to be more elastic.
6. Which of the following objects have momentum? Include all that apply.
a. An electron is orbiting the nucleus of an atom.
b. A UPS truck is stopped in front of the school building.
c. A Yugo (a compact car) is moving with a constant speed.
d. A small flea walking with constant speed across Fido's back.
e. The high school building rests in the middle of town.
Answers: ACD
Momentum can be thought of as mass in motion. An object has momentum if it has
its mass in motion. It matters not whether the object is of large mass or small mass,
moving with constant speed or accelerating; if the object is MOVING, then it has
momentum!
7. A truck driving along a highway road has a large quantity of momentum. If it moves
at the same speed but has twice as much mass, its momentum is
________________.
a. zero
b. quadrupled
c. doubled
d. unchanged
Momentum is directly related to the mass of the object. So for the same speed, a
doubling of mass leads to a doubling of momentum.
Impulse & Momentum Review Key
page 6
8. TRUE or FALSE:
A ball is dropped from the same height upon various flat surfaces. For the same
collision time, impulses are smaller when the most bouncing take place.
a. True
b. False
Since being dropped from the same height, the balls will be moving with the same
pre-collision velocity (assuming negligible air resistance). Upon collision with the
ground, the velocity will have to be reduced to zero - that is, the ball will cease
moving downwards. This decrease in velocity constitutes the first portion of the
velocity change. If the ball bounces, then there is an additional velocity change
sending the ball back upwards opposite the original direction. Thus, for the same
collision time, bouncing involves a greater velocity change, a greater momentum
change, and therefore a greater impulse.
9. Consider a karate expert. During a talent show, she executes a swift blow to a
cement block and breaks it with her bare hand. During the collision between her
hand and the block, the ___.
a. time of impact on both the block and the expert's hand is the same
b. force on both the block and the expert's hand have the same magnitude
c. impulse on both the block and the expert's hand have the same magnitude
d. all of the above.
In any collision, there are always four quantities which are the same for both objects
involved in the collision. Each object experiences the same force (Newton's 3rd
Law) for the same amount of time, leading to the same impulse, and subsequently
the same momentum change. Only the acceleration and the velocity change can
differ for the two colliding objects. The lower mass object always receives the
greater velocity change and acceleration.
10. It is NOT possible for a rocket to accelerate in outer space because ____. List all
that apply.
d. ... nonsense! Rockets do accelerate in outer space.
Rockets accelerate in outer space by means of Newton's 3rd Law of Motion. It does
not matter that there is no air outside of the rocket. Rockets produce their own gas
by burning fuels. The combustion of rocket fuels produces gaseous products. The
rocket's thrusters push these gases backwards (or rightwards, or leftwards, or ...)
and the gases push the rocket forwards (or leftwards, or rightwards, or ...). Thus,
rockets indeed can and do accelerate in outer space.
Impulse & Momentum Review Key
page 7
11. In order to catch a ball, a baseball player naturally moves his or her hand backward
in the direction of the ball's motion once the ball contacts the hand. This habit
causes the force of impact on the players hand to be reduced in size principally
because ___.
c. the time of impact is increased
Increasing the time over which the ball's momentum is brought to 0 will decrease the
force required to stop it. Suppose a ball is coming at you with 100-units of
momentum. An impulse of 100-units would be required to stop the ball. Regardless
of how the impulse is accomplished (big F, little t or little F, big t), there must be
100-units of it. Imparting such an impulse over a long time results in a small force.
12. Suppose that Paul D. Trigger fires a bullet from a gun. The speed of the bullet
leaving the muzzle will be the same as the speed of the recoiling gun ____.
d. only if the mass of the bullet equals the mass of the gun
In any collision or explosion involving two objects, the impulse acting on each object
is the same. So both the bullet and the gun encounter the same momentum
change. The momentum change is simply the mass multiplied by the velocity
change. Thus, the velocity change would only be the same if their masses were the
same. Otherwise, the smaller-mass object receives a greater velocity change.
13.Suppose that you're driving down the highway and a moth crashes into the
windshield of your car. Which undergoes the greater change is momentum?
a. the moth
b. your car
c. both the same
In any collision, there are always four quantities which are the same for both objects
involved in the collision. Each object experiences the same force (Newton's Third
Law) for the same amount of time, leading to the same impulse, and subsequently
the same momentum change. Only the acceleration and the velocity change can
differ for the two objects. The object with the least mass always receives the
greatest velocity change and acceleration.
14.Suppose that you're driving down the highway and a moth crashes into the
windshield of your car. Which undergoes the greater force?
a. the moth
b. your car
c. both the same
See #13
15. Suppose that you're driving down the highway and a moth crashes into the
windshield of your car. Which undergoes the greater impulse?
a. the moth
b. your car
c. both the same
See #13
Impulse & Momentum Review Key
page 8
16. Suppose that you're driving down the highway and a moth crashes into the
windshield of your car. Which undergoes the greater acceleration?
b. your car
c. both the same
a. the moth
See #13
17. In a physics experiment, two equal-mass carts roll towards each other on a level,
low-friction track. One cart rolls rightward at 2 m and the other cart rolls leftward at
s
1 m . After the carts collide, they couple (attach together) and roll together with a
s
speed of _____________. Ignore resistive forces.
a. 0.5 m
s


pi = p f



piA + piB = p f



mviA + mviB = (m + m )v f


viA + viB

vf =
2
m
2
+ − 1m

s
s
vf =
2

v f = 0.5 m
s
(
) (
)
18. A physics cart rolls along a low-friction track with considerable momentum. If it rolls
at the same speed but has twice as much mass, its momentum is ____.
a. zero
b. four times as large
d. unchanged
c. twice as large
The momentum of an object is calculated as the product of mass and velocity.
Thus, the momentum is directly proportional to the mass of the object. If the mass
of an object is somehow doubled, the momentum is doubled as well.
19. The firing of a bullet by a rifle causes the rifle to recoil backwards. The speed of the
rifle's recoil is smaller than the bullet's forward speed because the ___.
a. force against the rifle is relatively
b. speed is mainly concentrated in the bullet
small
d. momentum of the rifle is unchanged
c. rifle has lots of mass
Please don't answer A (for it will make Newton roll over in his grave and he's getting
quite tired of that). Perhaps you've heard that "for every action, there is an equal
and opposite ...". Choice B is invalid; speed is not something that becomes
concentrated or squeezed into an object. Choice D is invalid; ask anyone who's
fired a rifle if the rifle is set into motion by the firing of the bullet. (Of course, since it
is set in motion, its momentum is not unchanged.) Because of the large mass of the
rifle, the acceleration and the recoil speed of the rifle is small.
Impulse & Momentum Review Key
page 9
20. Two objects, A and B, have the same size and shape. Object A is twice as massive
as B. The objects are simultaneously dropped from a high window on a tall building.
(Neglect the effect of air resistance.) The objects will reach the ground at the same
time but object A will have a greater ___. Choose all that apply.
a. speed
b. acceleration
c. momentum
The two objects free-fall at the same rate of acceleration, thus giving them the same
speed when they hit the ground. The heavier object however has more momentum
since momentum takes into account both the velcoity and the mass of the object
( p = mv ) .
21. Cars are equipped with padded dashboards. In collisions, the padded dashboards
would be safer than non-padded ones because they ____. List all that apply.
b. decrease an occupant's impulse
a. increase the impact time
d. none of the above
c. decrease the impact force
Both A and C are correct. Padded dashboard serve to increase the time over which
the momentum of a passenger is reduced to zero. With this increase in time, there
is a decrease in force (big t, little F).
The impulse acting upon the passenger is not changed. The passenger still must
have his/her mass slowed down from the pre-impact velocity to zero velocity. This
means the velocity change is the same whether the collision occurs with a padded
dashboard, an air bag or a glass windshield. Since the velocity change is
independent of the collision time, the momentum change and the required impulse
are also independent of the collision time.
22. A 4 kg object has a momentum of 12 kgm . The object's speed is ___ m .
s
s
b. 4
c. 12
d. 48
e. none of these.
a. 3


This is a relatively simple plug-and-chug into the equation p = mv with m = 4 kg and

p = 12 kgm .
s
23. A wad of chewed bubble gum is moving with 1 unit of momentum when it collides
with a heavy box that is initially at rest. The gum sticks to the box and both are set
in motion with a combined momentum that is ___.
a. less than 1 unit
b. 1 unit
c. more than 1 unit
d. not enough information
Before the collision, the total system momentum is 1 unit - all due to the motion of
the wad of gum. Since momentum must be conserved, the total momentum of the
box and gum after the collision must also be 1 unit.
Impulse & Momentum Review Key
page 10
24. A relatively large force acting for a relatively long amount of time on a relatively
small mass will produce a relatively ______. List all that apply.
a. small velocity change
b. large velocity change
c. small momentum change
d. small acceleration

 F
A large force acting upon a small mass will result in a large acceleration  a = 
m

 
and subsequently a large velocity change (∆v = at ) ). This rules out choices A and
D. A large force for a long time will result in a large impulse and therefore a large
momentum change. This rules out choice C.
25. Consider the concepts of work and energy and those of impulse and momentum.
Force and time is related to momentum change in the same manner as force and
displacement pertains to ___________.
a. impulse
d. velocity
e. none of these.
b. work
c. energy change
A force multiplied by a time gives an impulse which will cause (and be equal to) a
momentum change. In the same manner, a force multiplied by a displacement gives
work which will cause (and be equal to) an energy change in a system. Take the
time to reread those two sentences because it relates two big concepts.
26. A 5 N force is applied to a 3 kg ball to change its velocity from + 9 m
to + 3 m .
s
s
This impulse causes the momentum change of the ball to be ____ kgm .
s
a. -2.5
b. -10
d. -45
e. none of these
c. -18
Don't make this harder than it is; the momentum change of an object can be found if


the mass and the velocity change are known. (∆p = m∆v ) In this equation, m = 3 kg
and the velocity change is − 6 m . When finding the velocity change, always
s

 
subtract the initial velocity from the final velocity (∆v = v f − vi ) .
27. A 5 N force is applied to a 3 kg ball to change its velocity from + 9 m
The impulse experienced by the ball is ____ Ns .
a. -2.5
b. -10
d. -45
c. -18
s
to + 3 m .
s
e. none of these
Impulse is defined as a force acting upon an object for a given amount of time.
 
Impulse can be computed by multiplying force*time J = F∆t . But in this problem,
the time is not known. Never fear - the impulse also equals the momentum change.
The momentum change in this problem is − 18 kgm (see question #26). Thus, the
s
impulse is also − 18 Ns .
(
)
Impulse & Momentum Review Key
page 11
28. A 5 N force is applied to a 3 kg ball to change its velocity from + 9 m
s
to + 3 m .
s
The impulse is encountered by the ball for a time of ____ seconds.
a. 1.8
b. 2.5
d. 10
e. none of these
c. 3.6

Use the impulse momentum change theorem with F = 5 N , m = 3 kg and

∆v = −6 m .
s


F∆t = ∆p


F∆t = m∆v



F∆t = m(v f − vi )


m(v f − vi )

∆t =
F
3 kg 3 m − 9 m
s
s
∆t =
5N
∆t = 3.6 s
(
)

29. When a mass M experiences a velocity change of ∆v in a time of ∆t , it


experiences a force of F . Assuming the same velocity change of ∆v , the force
1
experienced by a mass of 2 M in a time of ∆t is ____.
2


1
1
c. F
d. F
e. none of these
a. 2 F
b. 4 F
4
2


The impulse – change in momentum theorem states that F∆t = m∆v . This equation

can be rearranged to locate the F by itself on one side of the equation; rearranging
yields
 m∆v
F=
∆t
The equation shows that force is directly related to the mass, directly related to the
change in velocity, and inversely related to the time. In this case, doubling the mass
1
(from M to 2M) will double the force and halving the time (from ∆t to ∆t ) will
2
double the force. The combined effect of these two changes will make the new
force four times bigger than the old force. This is a case of where equations can be
a guide to thinking about how a change in one variable (or two variables) impacts
other dependent variables.




2 M∆v
 M∆v 
Fnew =
= (2 ∗ 2 )
 = 4F
1
 ∆t 
∆t
2
Impulse & Momentum Review Key
page 12

30. When a mass M experiences a velocity change of ∆v in a time of ∆t , it


experiences a force of F . Assuming the same velocity change of ∆v , the force
1
experienced by a mass of 2 M in a time of ∆t is ____.
4


1
1
c. F
d. F
e. none of these
b. 8 F
a. 2 F
2
8




2 M∆v
 M∆v 
Fnew =
= (2 ∗ 4)
 = 8F
1
 ∆t 
∆t
4

31. When a mass M experiences a velocity change of ∆v in a time of ∆t , it


experiences a force of F . Assuming the same velocity change of ∆v , the force
1
1
experienced by a mass of M in a time of ∆t is ____.
2
2


1
1
c. F
d. F
e. none of these
a. 2 F
b. 4 F
4
2
1


M∆v

 1  M∆v  
=  ∗ 2 
Fnew = 2
=F
1
2  ∆t 

∆t
2

32. When a mass M experiences a velocity change of ∆v in a time of ∆t , it


experiences a force of F . Assuming the same velocity change of ∆v , the force
1
experienced by a mass of M in a time of 4∆t is ____.
2


1
1
c. F
d. F
e. none of these
b. 8 F
a. 2 F
2
8
1


M∆v

 1 1  M∆v  1 
2
Fnew =
=  ∗ 
= F
4∆t
 2 4  ∆t  8
Impulse & Momentum Review Key
page 13
33. A 0.5 kg ball moving at 5 m
strikes a wall and rebounds in the opposite direction
s
with a speed of 2 m . If the impulse occurs for a time duration of 0.01 s, then the
s
average force (magnitude only) acting upon the ball is ____ Newtons.
a. 0.14
b. 150
d. 500
e. none of these
c. 350
This is a relatively simple plug-and-chug into the Impulse – change in momentum

equation with m = 0.5 kg , ∆t = 0.01 s and ∆v = −7 m . Using these numbers and
s
solving for force yields − 350 N . The magnitude of the force is 350 N and the "-"
sign indicates the direction of the force.

F∆t = ∆p


F∆t = m∆v



F∆t = m(v f − vi )


 m(v f − vi )
F=
∆t
 0.5 kg − 2 m s − 5 m s
F=
0.01 s

F = −350 N
(
)
34. If mass and collision time are equal, then impulses are greater on objects which
rebound (or bounce).
b. FALSE
a. TRUE
The impulse is equal to the momentum change. When there is a rebound, the
momentum change is larger since there is a larger velocity change. For instance, a
ball thrown at a wall at 5 m may rebound at − 3 m yielding a velocity change of
s
s
m
. An egg thrown at the same wall at the same speed of 5 m hits and stops,
−8
s
s
m
thus yielding a velocity change of only − 5
. More velocity change means more
s
momentum change and thus more impulse.
Impulse & Momentum Review Key
page 14
35. Consider the head-on collision between a lady bug and the windshield of a high
speed bus. Which of the following statements are true? List all that apply.
d. The magnitude of the velocity change encountered by the bug is greater
than that of the bus.
e. The magnitude of the acceleration encountered by the bug is greater than
that of the bus.
In any collision between two objects, the force, impulse, and momentum change are
the same for each object. Hence, statements A, B, and C are false. However, the
smaller mass object encounters a greater acceleration and velocity change.

  Fnet 
a =
 Hence, statements D and E are true.

m 

36. An object with a mass M and a velocity v has a momentum of 32 kgm
s
. An object
with a mass of ...
a. ... 2 M and a velocity of 2v would have a momentum of ____ kgm
s
.
Momentum is the product of mass and velocity. As such, the momentum of an
object is directly proportional to the mass and directly proportional to the velocity. If
the mass of an object is altered by some factor, then the momentum of the object is
altered by that same factor. If the velocity of an object is altered by some factor,
then the momentum of the object is altered by that same factor.



p new = 2 M (2v ) = 4(Mv ) = 4 32 kgm  = 128 kgm
s
s

b. ... 2 M and a velocity of 0.5v would have a momentum of ____ kgm



p new = 2 M (0.5v ) = 1(Mv ) = 32 kgm
.
s
c. ... 0.5M and a velocity of 2v would have a momentum of ____ kgm



p new = 0.5M (2v ) = 1(Mv ) = 32 kgm
s
s
.
s
d. ... 0.5M and a velocity of 0.5v would have a momentum of ____ kgm



p new = 0.5M (0.5v ) = 0.25(Mv ) = 0.25 32 kgm  = 8 kgm
s
s

s
.
Impulse & Momentum Review Key
e. ... 4 M and a velocity of v would have a momentum of ____ kgm
page 15
s
.


p new = 4 M (v ) = 4 32 kgm  = 128 kgm
s
s

f. ... 4 M and a velocity of 0.5v would have a momentum of ____ kgm
s
.



p new = 4 M (0.5v ) = 2(Mv ) = 2 32 kgm  = 64 kgm
s
s

g. ... 0.5M and a velocity of 4v would have a momentum of ____ kgm
s
.



p new = 0.5M (4v ) = 2(Mv ) = 2 32 kgm  = 64 kgm
s
s

37. A cart with a mass of M is moving along a low-friction track with a speed of
60 cm . A brick is gently dropped from rest upon the cart. After the collision the cart
s
and brick move together.
a. If the brick has a mass of 2 M , then the post-collision speed of the two objects
will be ____ cm .
s
This is a special case of a perfectly inelastic collision. The total system momentum
before the collision is possessed solely by the moving cart. After the collision, the
total system momentum is the combined momentum of the brick and the cart. Since
the brick and cart travel at the same velocity after the collision, the momentum is
simply the sum of their masses multiplied by their velocity. In effect, the total mass
which is in motion is increased by some factor as a result of the subsequent motion
of the brick. For momentum to be conserved, the velocity of the cart (and the brick
which is on top of it) must be decreased by that same factor. This principle is used
to reason towards the answers to these questions.
Adding a brick with a mass of 2 M will increase the total mass in motion from M
(the cart's mass) to 3M . This threefold increase in mass is accompanied by a
threefold decrease in velocity to conserve the total amount of momentum. The new
velocity is one-third the original value. The cart and brick move forward with a
velocity of 20 cm .
s


pi = p f


Mvi = (M + 2 M )v f


Mvi = 3Mv f
1

v f = vi
3
Impulse & Momentum Review Key
page 16
b. If the brick has a mass of 4 M , then the post-collision speed of the two objects
will be ____ cm .
s
Adding a brick with a mass of 4 M will increase the total mass in motion from M
(the cart's mass) to 5M . This fivefold increase in mass is accompanied by a fivefold
decrease in velocity. The new velocity is one-fifth the original value. The cart and
brick move forward with a velocity of 12 cm .
s
c. If the brick has a mass of 0.5M , then the post-collision speed of the two
objects will be ____ cm .
s
Adding a brick with a mass of 0.5M will increase the total mass in motion from M
(the cart's mass) to 1.5M . This increases the mass by a factor of 1.5 and is
accompanied by a decrease in velocity by a factor of 1.5 . The new velocity is
 1
1
2
two-thirds 
=
=  the original value. The cart and brick move forward with a
3
 1.5 3
2


cm
velocity of 40
.
s
d. If the brick has a mass of 0.25M , then the post-collision speed of the two
objects will be ____ cm .
s
Adding a brick with a mass of 0.25M will increase the total mass in motion from
M (the cart's mass) to 1.25M . This increases the mass by a factor of 1.25 and is
accompanied by a decrease in velocity by a factor of 1.25 . The new velocity is
 1
1
4
four-fifths 
=
=  the original value. The cart and brick move forward with
5
 1.25 5
4


cm
a velocity of 48
.
s
Impulse & Momentum Review Key
page 17
38. Two carts each of mass M are placed next to each other on a low-friction track.
The carts are equipped with a spring-loaded mechanism which allows them to
impart an impulse to each other. The spring-loaded mechanism is engaged and
released. The impulse causes Cart A to be propelled forward with a velocity of
40 cm .
s
a. Cart B will be propelled backward with a velocity of ___ cm .
s
Cart A and Cart B begin at rest. The original momentum of the system is 0 units . If
momentum is to be conserved, the final total momentum of the system of two carts
must also be 0 units . This means that the momentum of Cart A must have the
same magnitude as the momentum of Cart B and be in the opposite direction. That
is, after the spring is released, the product of mass and velocity for Cart A must
equal the product of mass and velocity for Cart B and be in the opposite direction.
This principle is illustrated in the reasoning below.


pi = p f


0 = p Af + p Bf


p Bf = − p Af


Mv Bf = − Mv Af


v Bf = −v Af
Since the two carts have the same mass, they must also have the same velocity in
order to have the same magnitude of momentum. The post-explosion velocity of
Cart B is − 40 cm .
s
b. If Cart B had a mass of 2 M then it would be propelled backwards with a velocity
of ___ cm .
s
If Cart B has twice the mass as Cart A, then it must be propelled backwards with
one-half the velocity. The post-explosion velocity of Cart B is − 20 cm .
s
c. If Cart B had a mass of 0.5M then it would be propelled backwards with a
velocity of ___ cm .
s
If Cart B has one-half the mass of Cart A, then it must be propelled backwards with
two times the velocity. The post-explosion velocity of Cart B is − 80 cm .
s
Impulse & Momentum Review Key
page 18
d. If Cart B has a mass of 2 M then it would be propelled backwards with a
momentum which is ____ (two times the, one-half the, the same as the) original
momentum.
Changing the mass of either one of the carts does not alter the impulse or the
momentum change which it experiences. An alteration in the mass merely alters the
velocity with which the cart is propelled. A twice-as-massive cart acquires one-half
the original velocity but the momentum change is the same as the original
momentum change.
e. If Cart B has a mass of 2 M then it would encounter an impulse which is ____
(two times the, one-half the, the same as the) original impulse.
Changing the mass of either one of the carts does not alter the impulse or the
momentum change which it experiences. An alteration in the mass merely alters the
velocity with which the cart is propelled. A twice-as-massive cart acquires one-half
the original velocity but the impulse is the same as the original impulse.
39. A 0.530 kg basketball hits a wall head-on with a forward speed of 18.0 m . It
s
m
rebounds with a speed of 13.5
. The contact time is 0.100 s.
s
a. Determine the impulse with the
b. Determine the force of the wall on the
wall.
ball.


Impulse = ∆p
Impulse = F∆t

 Impulse
Impulse = m∆v
F=


Impulse = m(v f − vi )
∆t

− 16.7 Ns
Impulse = 0.530 kg − 13.5 m − 18.0 m
F=
s
s
0.100 s

Impulse = −16.7 Ns
F = −167 N
(
)
40. A 4.0 kg object has a forward momentum of 20. kgm
. A 60. Ns impulse acts upon
s
it in the direction of motion for 5.0 seconds. Determine the final velocity of the object.


J = ∆p
 

J = p f − pi
60. Ns + 20. kgm

s
 
vf =

4
.
0
kg
p f = J + pi



mv f = J + pi
v f = 20. m
s

+
J
p

i
vf =
m
Impulse & Momentum Review Key
page 19
41. A 3.0 kg object is moving forward with a speed of 6.0 m . The object then collides
s
head-on with a wall and heads in the opposite direction with a speed of 4.0 m .
s
Determine the impulse delivered by the wall to the object.


J = ∆p

J = m∆v



J = m(v f − vi )

J = 3.0 kg − 4.0 m − 6.0 m
s
s

J = 3.0 kg − 10. m
s

J = −30. Ns
(
(
)
)
For Questions 42 – 45 complete the momentum bar graphs quantitatively, and then
use it to calculate the requested quantity.
A
B
42. A 2.0 kg box is attached by a string to a 5.0 kg box. A compressed spring is placed
between them. The two boxes are initially at rest on a friction-free track. The string is
cut and the spring applies an impulse to both boxes, setting them in motion. The
2.0 kg box is propelled backwards at 2.4 m . Determine the velocity of the 5.0 kg box
s
after the “explosion.”
Final
Initial
Object / Mass / Velocity
Object / Mass / Velocity
A / 2.0 kg / 0 m/s
A / 2.0 kg / -2.4 m/s
B / 5.0 kg / 0 m/s
B / 5.0 kg / ?
-
0
Momentum
-4.8 kgm/s
+4.8 kgm/s
-
+


p B f = mB v B f

pB f

vB f =
mB
4.8 kgm

s
vB f =
5.0 kg

v B f = 0.96 m
s
0
Momentum
+
Impulse & Momentum Review Key
page 20
A
43. Two children are at rest on ice skates on a frozen pond. The 33 kg child pushes off
B
against a 28 kg child, imparting a horizontal speed of 5.0 m to the 28 kg child.
s
Assuming negligible friction, what is the final velocity of the 33 kg child?
Final
Initial
Object / Mass / Velocity
Object / Mass / Velocity
A / 33 kg / 0 m/s
A / 33 kg / ?
B / 28 kg / 0 m/s
B / 28 kg / 5.0 m/s
-
0
Momentum
+
Momentum Conservation Equation:


p A f = mAv A f

pA f

vA f =
mA
-140 kgm/s
+140 kgm/s
-
0
Momentum
+
− 140 kgm

s
vA f =
33 kg

v A f = −4.2 m
s
A
44. Two ice skaters collide on the ice. A 39.6 kg skater moving South at - 6.21 m
s
B
collides with a 52.1 kg skater moving North at + 4.33 m . The two skaters entangle
s
and move together across the ice. Determine the magnitude and direction of their
post-collision velocity.
Final
Initial
Object / Mass / Velocity
Object / Mass / Velocity
-246 kgm/s
A / 39.6 kg / -6.21 m/s
-20.3 kgm/s
combo / 91.7 kg / ?
B / 52.1 kg / +4.33 m/s +226 kgm/s
-
0
Momentum
Momentum Conservation Equation:
-
+


p f = (m A + m B )v f

pf

vf =
m A + mB

vf =
− 20.3 kgm
s
39.6 kg + 52.1 kg

v f = −0.22 m
s
0
Momentum
+
Impulse & Momentum Review Key
page 21
45. At an amusement park, twin brothers Tubby (m = 50 kg) and Chubby (m = 62 kg)
occupy separate 36 kg bumper cars. Tubby gets his car cruising at 3.6 m/s and
collides head-on with Chubby who is moving the opposite direction at 1.6 m/s. After
the collision, Tubby bounces backwards at 0.50 m . Assuming an isolated system,
s
determine Chubby's post-collision velocity.
Final
Initial
Object / Mass / Velocity
Object / Mass / Velocity
Tubby / 86 kg / 3.6 m/s +309.6 kgm/s
-156.8 kgm/s
Chubby / 98 kg / -1.6 m/s
-
-43 kgm/s
Tubby / 86 kg / -0.50 m/s
0
Momentum
Momentum Conservation Equation:
Chubby / 98 kg / ? +195.8 kgm/s
-
+
0
Momentum
C
C
p C f = mC v C f
C
pC f
C
vC f =
mC
195.8 kgm
C
s
vC f =
98 kg
C
vC f = 2.0 m
s
For Questions 46 – 48 write the momentum conservation equation and calculate the
answer.
0.046 kg
46. A 46 gram tennis ball is launched from a 1.35 kg homemade cannon. If the cannon
recoils with a speed of - 2.1 m , determine the muzzle speed of the tennis ball.
s
C
C
pi = p f
C
C
0 = p B f + pC f
C
C
p B f = − pC f
C
C
m B v B f = − mC v C f
m C
C
v B f = − C vC f
mB
(
1.35 kg
C
vB f = −
− 2.1 m
s
0.046 kg
C
v B f = +62 m
s
)
+
Impulse & Momentum Review Key
page 22
47. A 2.8 kg physics cart is moving forward with a speed of 45 cm . A 1.9 kg brick is
s
dropped from rest and lands on the cart. The cart and brick move together across
the horizontal surface. Assume an isolated system. Determine the post-collision
speed of the cart and the brick.

vf =
C
C
pi = p f
C
C
pC i = p f
C
C
mC vC i = (mC + m B )v f
C
vf =
(
2.8 kg
45 cm
s
2.8 kg + 1.9 kg

v f = 27 cm
s
)
mC
C
vC i
mC + m B
A
48. In a physics lab, a 0.500 kg cart moving at 36.4 cm collides inelastically with a
s
B
second cart which is initially at rest. The two carts stick together and move with a
speed of 21.8 cm after the collision. Determine the mass of the second cart.(mB = ?)
s

mAv A i


pi = p f


pAi = p f


m A v A i = (m A + m B )v f



m A v A i = m A v f + mB v f


− m A v f = mB v f


m A (v A i − v f )
mB =

vf
(
0.500 kg 36.4 m − 21.8 m
s
s
m
21.8
s
m B = 0.335 kg
mB =
)