1. You are standing on a saucer-shaped sled at rest in the
middle of a frictionless ice rink. Your lab partner throws
you a heavy Frisbee. You take different actions in succes-
sive experimental trials. Rank the following situations
according to your final speed from largest to smallest.
If your final speed is the same in two cases, give them
equal rank. (a)You catch the Frisbee and hold onto it.
(b) You catch the Frisbee and throw it back to your part-
ner. (c) You bobble the catch, just touching the Frisbee
so that it continues in its original direction more slowly.
(d) You catch the Frisbee and throw it so that it moves
vertically upward above your head. (e) You catch the Fris-
bee and set it down so that it remains at rest on the ice.
2. A boxcar at a rail yard is set into motion at the top of
a hump. The car rolls down quietly and without fric-
tion onto a straight, level track where it couples with
a flatcar of smaller mass, originally at rest, so that the
two cars then roll together without friction. Consider
the two cars as a system from the moment of release of
the boxcar until both are rolling together. Answer the
following questions yes or no. (a) Is mechanical energy
of the system conserved? (b) Is momentum of the sys-
tem conserved? Next, consider only the process of the
boxcar gaining speed as it rolls down the hump. For
the boxcar and the Earth as a system, (c) is mechani-
cal energy conserved? (d) Is momentum conserved?
Finally, consider the two cars as a system as the boxcar
is slowing down in the coupling process. (e) Is mechan-
ical energy of this system conserved? (f) Is momentum
of this system conserved?
3. A massive tractor is rolling down a country road. In
a perfectly inelastic collision, a small sports car runs
into the machine from behind. (i) Which vehicle expe-
riences a change in momentum of larger magnitude?
(a) The car does. (b) The tractor does. (c) Their
momentum changes are the same size. (d) It could be
either vehicle. (ii) Which vehicle experiences a larger
change in kinetic energy? (a)The car does. (b) The
tractor does. (c) Their kinetic energy changes are the
same size. (d) It could be either vehicle.
4. A 2-kg object moving to the right with a speed of 4 m/s
makes a head-on, elastic collision with a 1-kg object
that is initially at rest. The velocity of the 1-kg object
after the collision is (a) greater than 4 m/s, (b) less
than 4 m/s, (c)equal to 4 m/s, (d) zero, or (e) impos-
sible to say based on the information provided.
5. A 5-kg cart moving to the right with a speed of 6 m/s
collides with a concrete wall and rebounds with a speed
of 2m/s. What is the change in momentum of the cart?
(a) 0 (b) 40 kg ? m/s (c) 240 kg ? m/s (d) 230 kg ? m/s
(e)210kg ? m/s
6. A 57.0-g tennis ball is traveling straight at a player at
21.0m/s. The player volleys the ball straight back at
25.0m/s. If the ball remains in contact with the racket
for 0.060 0 s, what average force acts on the ball?
(a) 22.6 N (b)32.5 N (c) 43.7 N (d) 72.1 N (e) 102 N
7. The momentum of an object is increased by a factor
of 4 in magnitude. By what factor is its kinetic energy
changed? (a) 16 (b) 8 (c) 4 (d) 2 (e) 1
8. The kinetic energy of an object is increased by a factor
of 4. By what factor is the magnitude of its momentum
changed? (a) 16 (b) 8 (c) 4 (d) 2 (e) 1
9. If two particles have equal momenta, are their kinetic
energies equal? (a) yes, always (b) no, never (c) no,
except when their speeds are the same (d) yes, as long
as they move along parallel lines
10. If two particles have equal kinetic energies, are their
momenta equal? (a) yes, always (b) no, never (c) yes,
as long as their masses are equal (d) yes, if both their
masses and directions of motion are the same (e) yes,
as long as they move along parallel lines
11. A 10.0-g bullet is fired into a 200-g block of wood at rest
on a horizontal surface. After impact, the block slides
8.00 m before coming to rest. If the coefficient of fric-
tion between the block and the surface is 0.400, what
is the speed of the bullet before impact? (a) 106 m/s
(b) 166 m/s (c) 226 m/s (d) 286 m/s (e) none of those
answers is correct
12. Two particles of different mass start from rest. The same
net force acts on both of them as they move over equal
distances. How do their final kinetic energies compare?
(a)The particle of larger mass has more kinetic energy.
(b)The particle of smaller mass has more kinetic
energy. (c) The particles have equal kinetic energies.
(d) Either particle might have more kinetic energy.
13. Two particles of different mass start from rest. The
same net force acts on both of them as they move over
equal distances. How do the magnitudes of their final
momenta compare? (a) The particle of larger mass
has more momentum. (b) The particle of smaller
mass has more momentum. (c) The particles have
equal momenta. (d) Either particle might have more
14. A basketball is tossed up into the air, falls freely, and
bounces from the wooden floor. From the moment
after the player releases it until the ball reaches the
top of its bounce, what is the smallest system for which
momentum is conserved? (a) the ball (b) the ball plus
player (c) the ball plus floor (d) the ball plus the Earth
(e) momentum is not conserved for any system
15. A 3-kg object moving to the right on a frictionless,
horizontal surface with a speed of 2 m/s collides head-
on and sticks to a 2-kg object that is initially moving
to the left with a speed of 4 m/s. After the collision,
which statement is true? (a) The kinetic energy of the
system is 20 J. (b) The momentum of the system is
14 kg ? m/s. (c) The kinetic energy of the system is
greater than 5 J but less than 20 J. (d) The momentum
of the system is 22 kg ? m/s. (e) The momentum of the
system is less than the momentum of the system before
denotes answer available in Student Solutions Manual/Study Guide
Chapter 9 Linear Momentum and Collisions
what is the speed of the combined car and truck after
the collision? (a) v (b) v/2 (c) v/3 (d) 2v (e) None of
those answers is correct.
18. A head-on, elastic collision occurs between two billiard
balls of equal mass. If a red ball is traveling to the right
with speed v and a blue ball is traveling to the left with
speed 3v before the collision, what statement is true
concerning their velocities subsequent to the collision?
Neglect any effects of spin. (a) The red ball travels to
the left with speed v, while the blue ball travels to the
right with speed 3v. (b) The red ball travels to the left
with speed v, while the blue ball continues to move to
the left with a speed 2v. (c) The red ball travels to the
left with speed 3v, while the blue ball travels to the
right with speed v. (d) Their final velocities cannot be
determined because momentum is not conserved in
the collision. (e) The velocities cannot be determined
without knowing the mass of each ball.
16. A ball is suspended by a string
that is tied to a fixed point
above a wooden block stand-
ing on end. The ball is pulled
back as shown in Figure
OQ9.16 and released. In trial
A, the ball rebounds elasti-
cally from the block. In trial B,
two-sided tape causes the ball
to stick to the block. In which
case is the ball more likely to
knock the block over? (a) It is
more likely in trial A. (b) It is more likely in trial B.
(c) It makes no difference. (d) It could be either case,
depending on other factors.
17. A car of mass m traveling at speed v crashes into the
rear of a truck of mass 2m that is at rest and in neutral
at an intersection. If the collision is perfectly inelastic,
denotes answer available in Student Solutions Manual/Study Guide
1. An airbag in an automobile inflates when a collision
occurs, which protects the passenger from serious
injury (see the photo on page 254). Why does the air-
bag soften the blow? Discuss the physics involved in
this dramatic photograph.
2. In golf, novice players are often advised to be sure to
“follow through” with their swing. Why does this advice
make the ball travel a longer distance? If a shot is taken
near the green, very little follow-through is required.
3. An open box slides across a frictionless, icy surface of
a frozen lake. What happens to the speed of the box as
water from a rain shower falls vertically downward into
the box? Explain.
4. While in motion, a pitched baseball carries kinetic
energy and momentum. (a) Can we say that it carries a
force that it can exert on any object it strikes? (b) Can
the baseball deliver more kinetic energy to the bat
and batter than the ball carries initially? (c) Can the
baseball deliver to the bat and batter more momentum
than the ball carries initially? Explain each of your
5. You are standing perfectly still and then take a step for-
ward. Before the step, your momentum was zero, but
afterward you have some momentum. Is the principle
of conservation of momentum violated in this case?
Explain your answer.
6. A sharpshooter fires a rifle while standing with the
butt of the gun against her shoulder. If the forward
momentum of a bullet is the same as the backward
momentum of the gun, why isn’t it as dangerous to be
hit by the gun as by the bullet?
7. Two students hold a large bed sheet vertically between
them. A third student, who happens to be the star
pitcher on the school baseball team, throws a raw egg
at the center of the sheet. Explain why the egg does
not break when it hits the sheet, regardless of its initial
8. A juggler juggles three balls in a continuous cycle. Any
one ball is in contact with one of his hands for one
fifth of the time. (a) Describe the motion of the center
of mass of the three balls. (b) What average force does
the juggler exert on one ball while he is touching it?
9. (a) Does the center of mass of a rocket in free space
accelerate? Explain. (b) Can the speed of a rocket
exceed the exhaust speed of the fuel? Explain.
10. On the subject of the following positions, state your
own view and argue to support it. (a) The best theory
of motion is that force causes acceleration. (b) The true
measure of a force’s effectiveness is the work it does, and
the best theory of motion is that work done on an object
changes its energy. (c) The true measure of a force’s
effect is impulse, and the best theory of motion is that
impulse imparted to an object changes its momentum.
11. Does a larger net force exerted on an object always pro-
duce a larger change in the momentum of the object
compared with a smaller net force? Explain.
12. Does a larger net force always produce a larger change
in kinetic energy than a smaller net force? Explain.
13. A bomb, initially at rest, explodes into several pieces.
(a)Is linear momentum of the system (the bomb
before the explosion, the pieces after the explosion)
conserved? Explain. (b) Is kinetic energy of the system
energy of the boy–girl system? (c) Is the momentum
of the boy–girl system conserved in the pushing-apart
process? If so, explain how that is possible consider-
ing (d) there are large forces acting and (e) there is no
motion beforehand and plenty of motion afterward.
9. In research in cardiology and exercise physiology, it is
often important to know the mass of blood pumped by
a person’s heart in one stroke. This information can be
obtained by means of a ballistocardiograph. The instru-
ment works as follows. The subject lies on a horizontal
pallet floating on a film of air. Friction on the pallet is
negligible. Initially, the momentum of the system is zero.
When the heart beats, it expels a mass m of blood into
the aorta with speed v, and the body and platform move
in the opposite direction with speed V. The blood veloc-
ity can be determined independently (e.g., by observ-
ing the Doppler shift of ultrasound). Assume that it is
50.0 cm/s in one typical trial. The mass of the subject
plus the pallet is 54.0 kg. The pallet moves 6.00 3 10–5 m
in 0.160 s after one heartbeat. Calculate the mass of
blood that leaves the heart. Assume that the mass of
blood is negligible compared with the total mass of the
person. (This simplified example illustrates the prin-
ciple of ballistocardiography, but in practice a more
sophisticated model of heart function is used.)
10. When you jump straight up as high as you can, what is
the order of magnitude of the maximum recoil speed
that you give to the Earth? Model the Earth as a per-
fectly solid object. In your solution, state the physical
quantities you take as data and the values you measure
or estimate for them.
11. Two blocks of masses m and
3m are placed on a friction-
less, horizontal surface. A
light spring is attached to the
more massive block, and the
blocks are pushed together
with the spring between
them (Fig. P9.11). A cord
initially holding the blocks
together is burned; after that
happens, the block of mass
3m moves to the right with a
speed of 2.00 m/s. (a) What
is the velocity of the block of
mass m? (b)Find the system’s original elastic potential
energy, taking m 5 0.350 kg. (c) Is the original energy
Section 9.1 linear Momentum
1. A particle of mass m moves with momentum of magni-
tude p. (a) Show that the kinetic energy of the particle
is K 5 p2/2m. (b) Express the magnitude of the parti-
cle’s momentum in terms of its kinetic energy and mass.
2. An object has a kinetic energy of 275 J and a momen-
tum of magnitude 25.0 kg ? m/s. Find the speed and
mass of the object.
3. At one instant, a 17.5-kg sled is moving over a horizontal
surface of snow at 3.50 m/s. After 8.75 s has elapsed, the
sled stops. Use a momentum approach to find the aver-
age friction force acting on the sled while it was moving.
4. A 3.00-kg particle has a velocity of
(a) Find its x and y components of momentum. (b) Find
the magnitude and direction of its momentum.
5. A baseball approaches home plate at a speed of 45.0 m/s,
moving horizontally just before being hit by a bat. The
batter hits a pop-up such that after hitting the bat, the
baseball is moving at 55.0 m/s straight up. The ball has
a mass of 145 g and is in contact with the bat for 2.00 ms.
What is the average vector force the ball exerts on the
bat during their interaction?
Section 9.2 analysis Model: Isolated System (Momentum)
6. A 45.0-kg girl is standing on a 150-kg plank. Both are
originally at rest on a frozen lake that constitutes a fric-
tionless, flat surface. The girl begins to walk along the
plank at a constant velocity of 1.50
m/s relative to the
plank. (a)What is the velocity of the plank relative to
the ice surface? (b)What is the girl’s velocity relative to
the ice surface?
7. A girl of mass m
is standing on a plank of mass m
are originally at rest on a frozen lake that constitutes a
frictionless, flat surface. The girl begins to walk along
the plank at a constant velocity v
to the right relative to
the plank. (The subscript gp denotes the girl relative to
plank.) (a) What is the velocity v
of the plank relative
to the surface of the ice? (b) What is the girl’s velocity
relative to the ice surface?
8. A 65.0-kg boy and his 40.0-kg sister, both wearing roller
blades, face each other at rest. The girl pushes the boy
hard, sending him backward with velocity 2.90 m/s
toward the west. Ignore friction. (a) Describe the sub-
sequent motion of the girl. (b) How much potential
energy in the girl’s body is converted into mechanical
The problems found in this
chapter may be assigned
online in Enhanced WebAssign
full solution available in the Student
Solutions Manual/Study Guide
Analysis Model tutorial available in
Master It tutorial available in Enhanced
Watch It video solution available in
Chapter 9 Linear Momentum and Collisions
(c) what is the acceleration of the car? Express the accel-
eration as a multiple of the acceleration due to gravity.
18. A tennis player receives a shot with the ball (0.060 0 kg)
traveling horizontally at 20.0 m/s and returns the shot
with the ball traveling horizontally at 40.0 m/s in the
opposite direction. (a) What is the impulse delivered
to the ball by the tennis racket? (b) Some work is done
on the system of the ball and some energy appears in
the ball as an increase in internal energy during the
collision between the ball and the racket. What is the
sum W 2 DE
for the ball?
19. The magnitude of the net
force exerted in the x direc-
tion on a 2.50-kg particle
varies in time as shown in
Figure P9.19. Find (a) the
impulse of the force over
the 5.00-s time interval,
(b) the final velocity the
particle attains if it is origi-
nally at rest, (c) its final
velocity if its original veloc-
ity is 22.00
m/s, and (d) the average force exerted on
the particle for the time interval between 0 and 5.00 s.
20. Review. A force platform is a tool used to analyze the per-
formance of athletes by measuring the vertical force
the athlete exerts on the ground as a function of time.
Starting from rest, a 65.0-kg athlete jumps down onto
the platform from a height of 0.600 m. While she is in
contact with the platform during the time interval 0 ,
t , 0.800 s, the force she exerts on it is described by the
F 5 9 200t 2 11 500t2
where F is in newtons and t is in seconds. (a) What im-
pulse did the athlete receive from the platform? (b) With
what speed did she reach the platform? (c) With what
speed did she leave it? (d) To what height did she jump
upon leaving the platform?
21. Water falls without splashing at a rate of 0.250 L/s from
a height of 2.60 m into a 0.750-kg bucket on a scale. If
the bucket is originally empty, what does the scale read
in newtons 3.00 s after water starts to accumulate in it?
Section 9.4 Collisions in one Dimension
22. A 1 200-kg car traveling initially at v
5 25.0 m/s in an
easterly direction crashes into the back of a 9 000-kg
truck moving in the same direction at v
5 20.0 m/s
(Fig. P9.22). The velocity of the car immediately after
the collision is v
5 18.0 m/s to the east. (a) What is
the velocity of the truck immediately after the colli-
in the spring or in the cord? (d) Explain your answer
to part (c). (e) Is the momentum of the system con-
served in the bursting-apart process? Explain how that
is possible considering (f) there are large forces acting
and (g) there is no motion beforehand and plenty of
Section 9.3 analysis Model: Nonisolated System
12. A man claims that he can hold onto a 12.0-kg child in a
head-on collision as long as he has his seat belt on.
Consider this man in a collision in which he is in one
of two identical cars each traveling toward the other at
60.0 mi/h relative to the ground. The car in which he
rides is brought to rest in 0.10 s. (a) Find the magni-
tude of the average force needed to hold onto the
child. (b) Based on your result to part (a), is the man’s
claim valid? (c) What does the answer to this problem
say about laws requiring the use of proper safety
devices such as seat belts and special toddler seats?
13. An estimated force–
time curve for a baseball
struck by a bat is shown
in Figure P9.13. From
this curve, determine
(a) the magnitude of the
impulse delivered to the
ball and (b) the average
force exerted on the ball.
14. Review. After a 0.300-kg rubber ball is dropped from
a height of 1.75 m, it bounces off a concrete floor and
rebounds to a height of 1.50 m. (a) Determine the
magnitude and direction of the impulse delivered to
the ball by the floor. (b) Estimate the time the ball is
in contact with the floor and use this estimate to calcu-
late the average force the floor exerts on the ball.
15. A glider of mass m is free to slide along a horizontal
air track. It is pushed against a launcher at one end
of the track. Model the launcher as a light spring of
force constant k compressed by a distance x. The glider
is released from rest. (a) Show that the glider attains a
speed of v 5 x(k/m)1/2. (b) Show that the magnitude
of the impulse imparted to the glider is given by the
expression I5 x(km)1/2. (c) Is more work done on a cart
with a large or a small mass?
16. In a slow-pitch softball game, a 0.200-kg softball crosses
the plate at 15.0 m/s at an angle of 45.0° below the hor-
izontal. The batter hits the ball toward center field, giv-
ing it a velocity of 40.0 m/s at 30.0° above the horizontal.
(a) Determine the impulse delivered to the ball. (b) If
the force on the ball increases linearly for 4.00 ms,
holds constant for 20.0 ms, and then decreases linearly
to zero in another 4.00 ms, what is the maximum force
on the ball?
17. The front 1.20 m of a 1 400-kg car is designed as a
“crumple zone” that collapses to absorb the shock of a
collision. If a car traveling 25.0 m/s stops uniformly in
1.20 m, (a) how long does the collision last, (b) what
is the magnitude of the average force on the car, and
= 18000 N
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