Download If a 0.150 kg baseball has a momentum of p = 6.90 kg.m/s as it is

1
If a 0.150 kg baseball has a momentum of p = 6.90 kg.m/s as it
is thrown from home to second base, what is its velocity?
8
In 1987, Marisa Canofoglia, of Italy, roller-skated at a recordsetting speed of 40.3 km/h. If the magnitude of Canofoglia's
momentum was 6.60 x 102 kg.m/s, what was her mass?
Answer
Answer
46.0 m/s
toward second base
2
What is the momentum of a 0.150 kg baseball thrown with a
velocity of 35 m/s toward home plate?
58.9 kg
9
Answer
5.2 kg.m/s
toward home plate
The largest passenger ship currently in service is the Norway,
which is more than 300 rn long and has a mass of 7.6 x 107 kg.
Its top cruising speed is 33 km/h. Calculate the magnitude of
the ship's momentum.
Answer
6,96 x 108 N.s
3
The world's most massive train ran in South Africa in 1989.
The train, over 7 km long, had a mass of 6.94 x 107 kg and
traveled 861.0 km in 22.67 h. Imagine that the distance was
traveled in a straight line north. Calculate the trains average
momentum.
10
Answer
7.32 x 108 kg.m/s to the north
A 21 kg child is riding a 5.9 kg bike with a velocity of 4.5 m/s
to the northwest.
(a) What is the total momentum of the child and the bike
together?
(b) What is the momentum of the child?
(c) What is the momentum of the bike?
Answer
4
(a) 1.2 x 102 kg-m/s
to the northwest
(b) 94 kg-m/s
to the northwest
(c) 27 kg-m/s
to the northwest
What velocity must a car with a mass of 1,210 kg have in order
to have the same momentum as a 2,250 kg pickup truck with a
velocity of 25 m/s to the east?
Answer
46 m/s
to the east
5
11
An ostrich with a mass of 146 kg is running to the right with a
velocity of 17 m/s. Find the momentum of the ostrich.
Answer
Answer
67 kg
2.5 x 103 kg.m/s
to the right
12
6
In 1994, a tower 22.13 m tall was built of Lego blocks.
Suppose a block with a mass of 2.00 g is dropped from the top
of this tower. Neglecting the air resistance, calculate the
block's momentum at the instant it hits the ground.
(a) 7.60 kg-m/s
(b) .01680 m/s
.06 km/hr
4.17 x 10-2 kg.m/s downward
One of the smallest planes ever flown was the Bumble Bee II,
which had a mass of 1.80 x 102 kg. If the pilot's mass was 70
kg, what was the momentum of both plane and pilot moving
west at 3.00 x 102 km/h?
A 10 g bullet has a speed of 760 m/s.
(a) Calculate the momentum of the bullet.
(b) How fast must a 450-kg deer move to have the same
momentum?
Answer
Answer
7
In 1976, a 53 kg helicopter was built in Denmark. Suppose this
helicopter flew east with a speed of 60.0 m/s and the total
momentum of the helicopter and pilot was 7.20 x 103 kg.m/s to
the east. What was the mass of the pilot?
13
Suppose that your mass is 80 kg. How fast would you have to
run to have the same linear momentum as a 1600 kg car
moving at 1.2 km/h?
Answer
Answer
20,833 N.s West
6.6 m/s
14
15
16
A stream of 40 g bullets fired horizontally with a speed of 1000
m/s strikes a 10 kg wooden block that is free to move on a
horizontal frictionless tabletop. What is the speed of the block
after it has absorbed 15 bullets?
20
Answer
Answers
56.6 m/s
.39 m/s
A 5.2 g bullet moving at 672 m/s strikes a 700 g wooden block
at rest on a very smooth surface. The bullet emerges with its
speed reduced to 428 m/s. Find the resulting speed of the
block.
21
Answer
1.81 m/s
7.o4 m/s
A life raft of mass 180 kg carries two swimmers of mass 50 kg
and 80 kg respectively. The raft is initially floating at rest;
then the swimmers simultaneously dive off opposite ends of
the raft, each with a horizontal velocity of 3 m/sec. With what
velocity and in what direction does the raft start to move?
22
Calculate the recoil velocity of a 5.0-kg rifle that shoots a
0.050-kg bullet at a speed of 120 m/s, see the figure to the left.
3.41 m/s
23
The world's largest guitar was built by a group of high school
students in Indiana. The mass of the instrument is 446 kg.
Suppose that this guitar is placed on a light cart. The cart and
guitar are then pushed with a velocity of 4.0 m/s to the left.
One of the students tries to stop the cart as it passes by her. She
grabs the cart and lets it drag her along for a short distance.
What is the new velocity of the cart, guitar, and student if the
student's mass is 54 kg? Assume the mass of the cart is
negligible and that there is no frictional resistance between the
student and the ground.
Answer
Answer
3.57 m/s
1.2 m/s backward
19
A Chinese giant salamander can reach a mass of 65 kg. If a
salamander of this size chases a 5.0 kg carp with a velocity of
3.5 m/s to the right and the carp moves with a velocity of 2.2
m/s in the same direction (away from the salamander), what
would be the speed of the salamander and carp immediately
after the salamander catches (eats) the carp?
Answer
0.5 m/s in the direction of the 50 kg swimmer
18
A 4800-kg open railroad car coasts along with a constant speed
of 7.50 m/s on a level track. Snow begins to fall vertically and
fills the car at a rate of 3.50 kg/min. Ignoring friction with the
tracks, what is the speed of the car after 90.0 min?
Answer
Answer
17
A 13-g bullet traveling 330 m/s penetrates a 2.0 kg block of
wood and emerges going 270 m/s. If the block is stationary on
a frictionless surface when hit, how fast does it move after the
bullet emerges?
Answer
In 1990, Roger Hickey of California attained a speed of 89
km/h while standing on a skateboard. Suppose Hickey is riding
horizontally at his stand-up speed when he catches up to
another skateboardet, who is moving at 69 km/h in the same
direction. They grab each other's hands and proceed together
with a new velocity. Calculate the final speed assuming that
both skateboarders have equal but unknown masses.
.675 m/s
Answer
A child throws a 5.40-kg package horizontally from a boat
with a speed of 10.0 m/s. Calculate the resulting velocity of the
boat, assuming it was initially at rest. The mass of the child is
25.0 kg and that of the boat is 55.0 kg.
A 10,000-kg boxcar traveling at 15 m/s strikes a second car.
The two stick together and move off with a speed of 4.0 m/s.
What is the mass of the second car?
Answer
27,500 kg
24
21.94 m/s same direction
25
The white shark is the largest carnivorous fish in the world.
The mass of a white shark can be as great as 3.0 x 103 kg. In
spite of (or perhaps because of) the mass and ferocity of the
shark, it is prized by commercial and sports fishermen alike.
Suppose Joe, who is one of these fishermen, goes to a cliff that
overlooks the ocean. To see if the sharks are biting, Joe drops a
2.5 x 102 kg fish as bait into the ocean below. As it so happens,
a 3.0 x 103 kg white shark is prowling the ocean floor just
below the cliff. The shark sees the bait, which is sinking
straight down at a speed of 3.0 m/s. The shark swims upward
with a speed of 1.0 m/s to swallow the bait. What is the shark's
velocity right after it has swallowed the bait?
Answer
29
Answer
q = 44.2o north of east
v' = 14.7 m/s
30
.69 m/s
26
A proton (atomic mass 1 atomic mass unit) with a speed of 500
m/s collides elastically with another proton at rest. The
original proton is scattered 600 from its initial direction. The
target proton moves off at 300 from the original direction.
What are the speeds of the two protons after the collision?
27
A stationary billiard ball, mass 0.17 kg, is struck by an
identical ball moving at 4.0 m/s. After the collision, the second
ball moves off at 60° to the left of its original direction. The
stationary ball moves off at 30° to the right of the second ball's
original direction. What is the velocity of each ball after the
collision?
Answer
v1' = 3.46 m/s
30o to the right
v2' = 2.0 m/s
600 to the left
Answer
(a) 250 m/s
430 m/s
A 1325-kg car moving north at 27.0 m/s collides with a 2165kg car moving east at 17.0 m/s. They stick together.
(a) Draw a vector diagram of the collision.
(b) In what direction does it go?
(c) With what speed do they move after the collision?
31
A rocket is fired into the air as shown in the figure to the left.
At the moment it reaches its highest point, a horizontal distance
D from its starting point, a prearranged explosion separates it
into two parts of equal mass. Part I is stopped in mid-air and
falls vertically to Earth. Where does part II land? Assume g =
constant.
A 6.0 kg object, A, moves at a velocity of 3.0 m/s. It collides
with a second 6.0 kg object, B at rest. After the collision, A
moves off in the direction 50.0 degrees to the left of its original
direction and B moves off in the direction 40.0 degrees to the
right of A's original direction.
(a) Draw a vector diagram using momentum.
(b) Determine the momentum of ball A after the collision.
(c) Determine the momentum of ball B after the collision.
(d) What is the velocity and direction of ball A after the
collision?
(e) What is the velocity and direction of ball B after the
collision?
Answer
(a)
(b)
(c)
(d)
(e)
Answer
2d from explosion
3d from the ground
32
28
Ball A, rolling west at 3.0 m/s, has a mass of 1.0 kg. Ball B has
a mass of 2.0 kg and is stationary. After colliding with ball B,
ball A moves south at 2.0 m/s. Calculate the momentum and
velocity of ball B after the collision .
Answer
3.6 kg.m/s at
34 degrees north of west
1.8 m/s at
34 degrees N of west
11.6 kg.m/s
13.8 kg.m/s
1.9 m/s 500 right
2.3 m/s 400 left
A body having a mass of 8 kg explodes into two pieces that fly
out horizontally in opposite directions. One piece is found to
have a mass of 6 kg and the other a mass of 2 kg. What ratio
of the speeds with which the two pieces moved apart
immediately after the explosion occurred?
Answer
3 to 1 the lighter piece has the higher velocity
33
Two opposing hockey players, one of mass 82.0 kg skating
north at 6.0 m/s and the other of mass-70.0 kg skating east at
3.0 m/s, collide and become tangled .
(a) Draw a vector momentum diagram of the collision .
(b) In what direction and with what velocity do they move
after collision?
37
Answer
(a)
(b) 3.5 m/s
67 degrees N of E
23 degrees Bearing
A stationary billiard ball of mass 0.17 kg is struck by a second
identical billiard ball moving at 10.0 m/s. After the collision,
the second ball moves off in a direction 60.0 degrees to the left
of its original direction. The stationary ball moves off in a
direction 30.0 degrees to the right of the second ball's original
direction.
(a) Draw a vector diagram
(b) Determine the momentum of ball A after the collision.
(c) Determine the momentum of ball B after the collision.
(d) What is the velocity and direction of ball A after the
collision?
(e) What is the velocity and direction of ball B after the
collision?
Answer
34
A cue ball, moving with 7.0 N s of momentum strikes the nineball at rest. The nine-ball moves off with 2.0 N s in the original
direction of the cue ball and 2.0 N s perpendicular to that
direction. What is the momentum of the cue ball after the
collision?
a.
(b) 1.5 kgm/s
(c) 85 kgm/s
(d) For first ball: v = 8.8 m/s, 30 degrees to the right of
second ball's original direction.
(e) For second ball: v = 5.0 m/s, 60 degrees to the left of
its original direction.
Answer
5.4 N.s at 22 degrees from original direction
38
35
A 6.0-kg object, A, moving at velocity 3.0 m/s, collides with a
6.0-kg object, B, at rest. After the collision, A moves off in a
direction 40.0° to the left of its original direction. B moves off
in a direction 50.0° to the right of A's original direction.
(a) Draw a vector diagram and determine the momentum of
object A and object B after the collision.
(b) What is the velocity of each object after the collision?
Answer
(a) pa' = 14 kg.m/s
pb' = 12 kg.m/s
(b) va' = 2.3 m/s
40o to the left
vb' = 2.0 m/s
50o to the right
36
Ball A of mass 5.0 kg moves at a speed of 4.0 m/s and collides
with a second stationary ball B, also of mass 5.0 kg. After the
collision Ball A moves off in the direction 45 degrees to the
left of its original direction. Ball B moves off in the direction
45 degrees to the right of ball A's original direction
(a) Draw a vector diagram
(b) Determine the momentum of ball A after the collision.
(c) Determine the momentum of ball B after the collision.
(d) What is the velocity and direction of ball A after the
collision?
(e) What is the velocity and direction of ball B after the
collision?
Answer
(a)
(b) 14.1 kg.m/s
(c) 14,1 kg.m/s fs
(d) 2.8 m/s 45 degrees to the left of its original direction.
(e) 2.8 m/s 45 degrees to the right of its original direction
Body A of mass 4.0 kg and speed 1.0 m/sec collides with a
similar stationary body (b) After the collision A moves in a
direction 30 degrees to the left of its original direction while B
moves in a direction 60 degrees to the right of A's original
direction.
(a) Draw a vector diagram
(b) determine the momentum of ball A
(c) determine the momentum of ball B after the collision.
(d) What is the velocity and direction of ball A after the
collision?
(e) What is the velocity and direction of ball B after the
collision?
Answer
a.
b. 3.46 kg m/sec
c. 2 kg m/sec
d. 875 m/sec .
e. 50 m/sec
39
A cue ball, mass 0.16 kg, rolling at 4.0 m/s, hits a stationary
eight-ball of similar mass. If the cue ball travels 45° above its
original path, and the eight ball at 45° to the left, what is the
velocity of each after collision?
Answer
2.8 m/s
40
The figure at the left shows an overhead view showing six
particles that have emerged from a region in which a twodimensional explosion took place. The explosion was of an
object that had been stationary on a frictionless floor. The
directions of the momenta of the particles are indicated by the
vectors; the numbers give the magnitudes of the momenta (in
kg.m/s).
(a) Will more particles be emerging from the explosion
region?
(b) If so, give their net momentum
(c) If so, give their direction of travel.
43
A stationary billiard ball of mass 0.17 kg is struck by a second
identical billiard ball moving at 10.0 m/s. After the collision,
the second ball moves off in a direction 60.0 degrees to the left
of its original direction. The stationary ball moves off in a
direction 30.0 degrees to the right of the second ball's original
direction.
(a) Draw a vector diagram
(b) Determine the momentum of ball A after the collision.
(c) Determine the momentum of ball B after the collision.
(d) What is the velocity and direction of ball A after the
collision?
(e) What is the velocity and direction of ball B after the
collision?
Answer
a.
(b) 1.5 kgm/s
(c) 85 kgm/s
(d) For first ball: v = 8.8 m/s, 30 degrees to the right of
second ball's original direction.
(e) For second ball: v = 5.0 m/s, 60 degrees to the left of
its original direction.
44
Answer
(a) yes
(b) 6 N.s
(c) Left
41
A 4.0 kg mass sliding on a frictionless surface explodes into
two 2.0 kg masses. After the explosion the velocities of the 2.0
kg masses are 3.0 m/s, due north, and 5.0 m/s, 300 north of
east.
(a) What was the original momentum of the 4 kg ball?
(b) What was the original speed of the 4.0 kg mass?
A stationary billiard ball of mass 0.17 kg is struck by a second
identical billiard ball moving at 10.0 m/s. After the collision,
the second ball moves off in a direction 60.0 degrees to the left
of its original direction. The stationary ball moves off in a
direction 30.0 degrees to the right of the second ball's original
direction.
(a) Draw a vector diagram
(b) Determine the momentum of ball A after the collision.
(c) Determine the momentum of ball B after the collision.
(d) What is the velocity and direction of ball A after the
collision?
(e) What is the velocity and direction of ball B after the
collision?
Answer
Answer
a.
(b) 1.5 kgm/s
(c) 85 kgm/s
(d) For first ball: v = 8.8 m/s, 30 degrees to the right of
second ball's original direction.
(e) For second ball: v = 5.0 m/s, 60 degrees to the left of
its original direction.
(a) 14 kgm/s
(b) 3.5 m/s
51.80 North of east
42
A vessel at rest explodes, breaking into three pieces. Two
pieces, having equal mass, fly off perpendicular to one another
with the same speed of 30 m/s. The third piece has three times
the mass of each other piece. What are the direction and
magnitude of its velocity immediately after the explosion?
Answer
45
A 20 kg rocket is fired into the air as shown in the figure to the
left. At the moment it reaches its highest point, a horizontal
distance D from its starting point, a prearranged explosion
separates it into two parts of equal mass. Part I is stopped in
mid-air and falls vertically to Earth. Where does part II land?
Assume g = constant.
14.14 m/s
south of east
Answer
2d from explosion
3d from the ground
46
A 1325-kg car moving north at 27.0 m/s collides with a 2165kg car moving east at 17.0 m/s. They stick together.
(a) Draw a vector diagram of the collision.
(b) In what direction does it go?
(c) With what speed do they move after the collision?
51
Answer
q = 44.2o north of east
v' = 14.7 m/s
47
A brick that weighs 50.0 N is released from rest on a 3.00 m
long, frictionless plane inclined at an angle of 30.0 degrees.
The brick slides down the incline and strikes a second brick
that weighs 40.0 N.
(a) What is the initial velocity of the first brick at the bottom
of the incline before it strikes the second brick
(b) If the two bricks stick together, with what initial speed will
they move along the table?
(c) If the force of friction acting on the two bricks is 5.0 N,
what time will elapse before the bricks come to rest?
(d) How far will the two bricks slide before coming to rest.
Answer
A 1325-kg car moving south at 17.0 m/s collides with a 2165kg car moving east at 17.0 m/s. They stick together.
(a) Draw a vector diagram of the collision.
(b) In what direction does it go?
(c) With what speed do they move after the collision?
(a)
(b)
(c)
(d)
5.42 m/s
3.01 m/s
5.53 s
8.37 m
Answer
(a) Drawing
(b) 31.40
(c) 12.3 m/s
48
A 1325-kg car moving south at 37.0 m/s collides with a 2165kg car moving west at 7.0 m/s. They stick together.
(a) Draw a vector diagram of the collision.
(b) In what direction does it go?
(c) With what speed do they move after the collision?
Answer
49
52
Two 22.7 kg ice sleds are placed a short distance apart, one
directly behind the other, as shown in the figure to the left. A
3.63 kg cat, standing on one sled, jumps across to the other and
immediately back to the first. Both jumps are made at a speed
of 3.05 m/s relative to the ice. Find the final speeds of the two
sleds.
A 15-g bullet strikes and becomes embedded in a 1.1 0-kg
block of wood placed on a horizontal surface just in front of
the gun. If the coefficient of kinetic friction between the block
and the surface is 0.25, and the impact drives the block a
distance of 9.5 m before it comes to rest, what was the muzzle
speed of the bullet?
Answer
507 m/s
53
A block of mass m = 1.20 kg slides down a 30.00 incline which
is 3.60 m high. At the bottom, it strikes a block of mass M =
7.00 kg which is at rest on a horizontal surface, see the figure.
(Assume a smooth transition at the bottom of the incline.)
(a) If the collision is elastic, and friction can be ignored,
determine the speeds of the two blocks after the collision.
(b) If the collision is elastic, and friction can be ignored,
determine how far back up the incline the smaller mass will go.
Answer
Sled 2 = .98 m/s relative to the ground
Sled 1 = .84 m/s relative to the ground.
50
A brick that weighs 30.0 N is released from rest on a 1.00 m
long, frictionless plane inclined at an angle of 20.0 degrees.
The brick slides down the incline and strikes a second brick
that weighs 36.8 N.
(a) What is the initial velocity of the first brick at the bottom
of the incline before it strikes the second brick (b) If the two
bricks stick together, with what initial speed will they move
along the table? (c) If the force of friction acting on the two
bricks is 5.0 N, what time will elapse before the bricks come to
rest? (d) How far will the two bricks slide before coming to
rest.
Answer
(a)
(b)
(c)
(d)
2.59 m/s
1.16 m/s
1.58 s
0.92 m
Answer
54
In a physics lab, a small cube slides down a frictionless incline
as shown in the figure to the left, and elastically strikes a cube
that is only one-half its mass. If the incline is 20 cm high and
the table is 90 cm off the floor, where does each cube land?
(hint: make up a mass)
59
In 1992, Dan Bozich of the United States drove a gasolinepowered go-cart at a speed of 125.5 km/hr. Suppose Bozich
applies the brakes upon reaching this speed. If the combined
mass of the go-cart and driver is 2.00 x 102 kg, the magnitude
of the decelerating force equals 3.60 x 102 N, and the time
during which the deceleration takes place is 10.0 s. What is the
final speed of liozich and the go-cart?
Answer
16.86 m/s
60
Answer
The most powerful tugboats in the world are built in Finland.
These boats can pull with a force of 2.8 x 106 N. Suppose one
of these tugboats is trying to slow a huge barge that has a mass
of 2.0 x 107 kg and is moving with the current at a speed of 3.0
m/s. If the tugboat exerts its maximum force against the
current, what distance will the tugboat and the barge have
moved by the time their net speed is zero?
Answer
55
A 5.00 g bullet is fired with a velocity of 100 m/s toward a
10.00 kg stationary solid block resting on a frictionless surface.
(a) What is the change in momentum of the bullet if it is
embedded in the block?
(b) What is the change in momentum of the bullet if it
ricochets in the opposite direction with a speed of 99 m/s
almost the same speed as it had originally?
61
Answer
Answer
(a) -0.49 kg.m/s
(b) -0.995 kg.m/s
56
A 75 kg man is riding on a 39 kg cart traveling at a speed of
2.3 m/s relative to the ground. He jumps off with zero
horizontal speed. What is the resulting change in the speed of
the cart?
Answer
A 5.00 g bullet is fired with a velocity of 100 m/s toward a
10.00 kg stationary solid block resting on a frictionless surface.
(a) What is the change in momentum of the bullet if it is
embedded in the block?
(b) What is the change in momentum of the bullet if it
ricochets in the opposite direction with a speed of 99 m/s
almost the same speed as it had originally?
(a) -0..49 kg.m/s
(b) -0.995 kg.m/s
62
The figure shows the force exerted by a ball that collided with
a soft wall .
(a) Find the impulse given to the wall by the ball.
(b) If the ball has a mass of 30.0 kg, what velocity did it have
at the beginning of the collision.
4.42 m/s
57
A 0.55 kg ball approaches a wall perpendicularly with a speed
of 17 m/s and rebounds in the opposite direction with a speed
of 15 m/s. What is the impulse exerted on the wall?
Answer
-18 kg.m/s
58
The largest steam-powered locomotive was built in the United
States in 1943. It is still operational and is used for
entertainment purposes. The locomotive's mass is 485 x 103 kg.
Suppose the train is traveling northwest along a straight track
at a speed of 6.00 m/s. What force must the locomotive exert in
order to increase its speed to 8.00 m/s in 1.00 s?
Answer
970, 000 N
Answer
(a) 360 N.s
(b) 12 m/s
63
The figure shows the force exerted by a ball that collided with
a soft wall .
(a) Find the impulse given to the wall by the ball.
(b) If the ball has a mass of 45.0 kg, what velocity did it have
at the beginning of the collision.
66
Answer
64
The figure shows the force exerted by a ball that collided with
a box at rest.
(a) Find the impulse given to the box by the ball.
(b) If the box has a mass of 12.0 kg, what velocity did it have
after the collision.
The figure shows the force exerted by a ball that rebounds
from a wall .
(a) Find the impulse given to the ball by the wall.
(b) If the ball has a mass of 5.3 kg, what velocity did the ball
have as it leaves the wall.
Answer
Approximate
(a) 85 N.s
(b) 16 m/s
67
The figure shows the force exerted by a ball that collided with
a soft wall .
(a) Find the impulse given to the wall by the ball.
(b) If the ball has a mass of 30.0 kg, what velocity did it have
at the beginning of the collision.
Answer
Answer
65
The figure shows the force exerted by a ball that collided with
a soft wall .
(a) Find the impulse given to the wall by the ball.
(b) If the ball has a mass of 2.4 kg, what velocity did it have at
the beginning of the collision.
Answer
Approximate
(a) 24.5 N.s
(b) 10.2 m/s
(a) 120 kgm/s
(b) 4 m/s
68
69
The figure shows the force exerted by a ball that collided with
a box at rest.
(a) Find the impulse given to the box by the ball.
(b) If the box has a mass of 15.0 kg, what velocity did it have
after the collision.
71
The figure to the left shows the force exerted by a ball that
collided with a soft wall .
(a) Find the impulse given to the wall by the ball.
(b) If the ball has a mass of 30.0 kg, what velocity did it have
at the beginning of the collision.
Answer
Answer
(a) 82.5 N
(b) 5.5 m/s
(a) 120 kg.m/s
(b) 4 m/s
The graph shows the impulse exerted by a billiard ball
bouncing off a cushion,. What impulse does the ball receive
from the cushion?
72
The figure to the left shows the force exerted by a ball that
collided with a box at rest.
(a) Find the impulse given to the box by the ball.
(b) If the box has a mass of 15.0 kg, what velocity did it have
after the collision.
Answer
1 N.s
70
What impulse is exerted by a collision between a toy car and a
brick wall, if the force time graph of the collision appears as
shown?
Answer
1.75 Ns
Answer
(a) 82.5 N
(b) 5.5 m/s
73
The figure to the left shows the force exerted by a ball that
collided with a soft wall .
(a) Find the impulse given to the wall by the ball.
(b) If the ball has a mass of 2.4 kg, what velocity did it have at
the beginning of the collision.
76
A snowmobile has a mass of 2.50 x 102 kg. A constant force is
exerted on it for 60.0 s. The snowmobile's initial velocity is
6.00 m/s and its final velocity 28.0 m/s.
(a) What is its change in momentum?
(b) What is the magnitude of the force exerted on it?
Answer
(a) 5.5 x 103 kg.m/s
(b) 91.7 N
77
A net force of 2.00 x 103 N acts on a rocket of mass 1.00 x 103
kg. How long does it take this force to increase the rocket's
velocity from 0.0 m/s to 2.00 x 102 m/s?
Answer
1.00 x 102 sec
Answer
Approximate
(a) 24.5 N.s
(b) 10.2 m/s
74
78
Suppose the force acting on a tennis ball (mass 0.060 kg) as a
function of time is given by the graph of the figure to the left.
(a) Use graphical methods to estimate the total impulse given
the ball.
(b) Use graphical methods to estimate the speed of the ball
after being struck, assuming the ball is being served so it is
nearly at rest initially.
The velocity of a 6.00 x 102 kg mass is changed from 10.0 m/s
to 44.0 m/s in 68.0 s by an applied, constant force.
(a) What change in momentum does the force produce?
(b) What is the magnitude of the force?
Answer
a. 2.04 x 104 N.s
b. 3.00 x 102 N
79
What is the final velocity of a rocket of mass 2.0 x 104 kg,
starting from rest, if a net force of 1.5 x 105 N acts upon it for
15.0 s?
Answer
112.5 m/s
80
Answer
Answer
(a) 6.25 N.s
(b) 104.16 m/s
75
The figure gives the linear momentum versus time for a
particle moving along an axis. A force directed along the axis
acts on the particle.
(a) Rank the four regions indicated according to the magnitude
of the force, greatest first.
(b) In which region is the particle slowing?
At 4:40 p.m. the momentum of a speedboat was measured as
20,000 kg m/s, and at 4:42 PM it was 50,000 kg m/s.
Assuming that the boat was moving along a straight course and
that its speed increased steadily (constant force), what forward
force was exerted on the boat?
250 newtons
81
A 845 kg drag race car accelerates from rest to 100 km/h in
0.90 seconds.
(a) What is the change in momentum of the car?
(b) What average force is exerted on the car?
Answer
(a) 2.65 x 104 kg.m/s
(b) 2.6 x 104 N
82
A sprinter with a mass of 76 kg accelerates from 0 to 9.4 m/s in
2.8 s. Find the average force acting on the runner.
Answer
(a) 1, 3, 2 = 4
(b) 3
Answer
2.55 x 102 N
83
Jim strikes a 0.058 kg golf ball with a force of 272 N and gives
it a velocity of 62.0 m/s. How long was the club in contact with
the ball?
89
Answer
The specially designed armored car that was built for Leonid
Brezhnev when he was head of the Soviet Union had a mass of
about 6.0 x 103 kg. Suppose this car is accelerated from rest to
some final speed by a force of 8.0 kN. If the car is displaced to
the east along a horizontal road, what is the final velocity of the
car after 8.0 s?
0.013 s
Answer
84
A 5500 kg freight truck accelerates from 4.2 m/s to 7.8 m/s in
15.0 s by applying a constant force.
(a) What change in momentum occurs?
(b) How large of a force is exerted?
10.66 m/s east
90
Answer
(a) 19,800 kg.m/s
(b) 1,320 N
85
A 2.0 kg skateboard is rolling across a smooth, flat floor when
a small girl kicks it, causing it to speed up to 4.5 m/s in 0.50 s
without changing direction. if the average force exerted by the
girl on the skateboard in its direction of motion was 6.0 N, with
what initial velocity was it moving?
Answer
Answer
219 N upward
91
3.0 m/s [forward]
86
With a height of 296 m, the Yokohama Landmark Tower in
Yokohma, Japan, is one of the tallest buildings in both Japan
and the world. In order for people to reach distant floors
quickly, the building is equipped with elevators that travel at a
speed of 12.5 m/s. Suppose a passenger with a mass of 70.0 kg
enters one of these elevators. The elevator then goes up,
reaching full speed in 4.00 s. Calculate the net force that is
applied to the passenger during the acceleration of the elevator.
A 1.5 x 103 kg car accelerates from rest at 4.0 m/s2 for 6.0 s.
(a) What momentum does it acquire in that time?
(b) What was the impulse exerted on it?
An experimental rocket sled on a level, frictionless track has a
mass of 1.4 x 104 kg. For propulsion, it expels gases from its
rocket engines at a rate of 10 kg/s and at an exhaust speed of
2.5 x 104 m/s relative to the rocket. For how many seconds
must the engines burn in order that the sled acquire a velocity
of 50 m/s starting from rest? You may ignore the small
decrease in mass of the sled and the small speed of the rocket
compared to the exhaust gas.
Answer
Answer
(2.8 s)
(a) 3.6 x 104 kg.mls
(b) 3.6 x 104 N.s
92
87
The average accelerating force exerted on a 5.0 kg shell in a
gun barrel is 5.0 x 104 N, and the muzzle velocity is 200 m/s.
(a) Calculate the impulse on the shell.
(b) Calculate the length of time it takes to move up the heavy
gun barrel.
A compact car, mass 725 kg, is moving at +100 km/h
(a) Find its momentum.
(b) At what velocity is the momentum of a larger car, mass
2175 kg, equal to that of the smaller car?
Answer
(a) 20138 kg m/s
(b) 33.4 km/h (9.3 m/s
Answer
(a) 1.0 x 103 Ns
(b) 2.0 x 10-2 s
88
93
Answer
A football punter accelerates a 0.55 kg football from rest to a
speed of 8.0 m/s in 0.25 s. What constant force does the punter
exert on the ball?
Answer
18 N
Compute the momentum of a golf ball that has a mass of 60 g
and is moving with a velocity of 70 m/sec.
4.2 kg m/sec
94
Jenny has a mass of 35.6 kg and her skateboard has a mass of
1.3 kg. What is the momentum of Jenny and her skateboard
together if they are going 9.50 m/s?
Answer
351 kg.m/s
95
A 2,250 kg pickup truck has a velocity of 25 m/s to the east.
What is the momentum of the truck?
101
Answer
5.6 x 104 kg.m/s
to the east
One of the smallest planes ever flown was the Bumble Bee II,
which had a mass of 1.80 x 102 kg. If the pilot's mass was 7.0 x
101 kg, what was the momentum of both plane and pilot
moving west at 3.00 x 102 km/h?
Answer
2.08 x 104 kg.m/s to the west
96
An astronaut with a mass of 45 kg wears a 32 kg suit and
moves at 5.7 m/s on the moon.
(a) What is the magnitude of the total momentum of the
astronaut and the suit?
(b) What is the magnitude of the astronaut's momentum?
(c) What is the magnitude of the momentum of the same
astronaut jogging at 5.7 m/s on Earth?
102
Answer
0.0 kg.m/s
Answer
(a) 440 kg.m/s
(b) 260 kg.m/s
(c) 260 kg.m/s
97
103
A pitcher claims he can throw a 0.145 kg baseball with as
much momentum as a speeding bullet. Assume that a 3.00 g
bullet moves at a speed of 1.50 x 103 m/s. What must the
baseball's speed be if the pitcher's claim is valid?
Answer
-12.0 kg.m/s
104
The largest passenger ship currently in service is the Norway,
which is more than 300 m long and has a mass of 7.6 x 107 kg.
Its top cruising speed is 33 km/h. Calculate the magnitude of
the ship's momentum.
Answer
2.7 s
105
(a) 14.24 m/s
52/hr
(b) 49.41 m/s
77.8 km/hr
14.l8 m/s
53.3 km/hr
A 0.40 kg soccer ball approaches a player horizontally with a
velocity of 18 m/s to the north. The player strikes the ball and
causes it to move in the opposite direction with a velocity of 22
m/s. What impulse was delivered to the ball by the player?
Answer
A 2650 kg Cadillac is traveling at a speed of 16 km/h.
(a) How fast must an 816-kg Volkswagen travel to have the
same momentum as the Cadillac?
(b) Make the same calculations using a 9080 kg truck instead
of a Cadillac.
Answer
A 0.45 kg ball is thrown upward with an initial speed of 13
m/s. The ball is caught when it has a downward speed of 13
m/s. Using the weight of the ball as the impulse force,
determine how long the ball is in the air.
Answer
7.0 x 108 kg.m/s
99
A 0.40 kg ball approaches a wall perpendicularly at 15 m/s. It
collides with the wall and rebounds with an equal speed in the
opposite direction. Calculate the impulse exerted on the wall.
Answer
31.0 m/s
98
A 0.10 kg ball of dough is thrown straight up into the air with
an initial velocity of 15 m/s. Find the momentum of the ball of
dough at its maximum height.
16.0 kg-m/s
to the south
106
A 0.50 kg object is at rest. A 3.00 N force to the right acts on
the object during a time interval of 1.50 s.
(a) What is the velocity of the object at the end of this
interval?
(b) At the end of this interval, a constant force of 4.00 N to the
left is applied for 3.00 s. What is the velocity at the end of the
3.00 s?
Answer
100
A 10 g bullet has a speed of 760 m/s.
(a) Calculate the momentum of the bullet.
(b) How fast must a 450 kg deer move to have the same
momentum?
Answer
(a) 7.60 kg-m/s
(b) .01680 m/s
.06 km/hr
(a) 9.0 m/s
to the right
(b) 15 m/s
to the left
107
A 2.5 kg ball strikes a wall with a velocity of 8.5 m/s to the
left. The ball bounces off with a velocity of 7.5 m/s to the right.
If the ball is in contact with the wall for 0.25 s, what is the
constant force exerted on the ball by the wall?
112
A 15-kg object with a speed of 30 m/s strikes a steel plate an
angle of 50 degree and rebounds at the same speed and angle
shown in the figure. What is the change (magnitude and
direction ) of the linear momentum of the object?
Answer
160 N
to the right
108
A constant force of 2.5 N to the right acts on a 1.5 kg mass for
0.50 s.
(a) Find the final velocity of the mass if it is initially at rest.
(b) Find the final velocity of the mass if it is initially moving
along the x-axis.
Answer
Answer
689.4 kg.m/s
straight up
113
(a) 0.83 m/s
to the right
(b) 1.2 m/s
to the left
109
A 25-kg object with a speed of 15 m/s strikes a steel plate an
angle of 40 degree and rebounds at the same speed and angle
shown in the figure. What is the change (magnitude and
direction ) of the linear momentum of the object?
A frictionless disc of mass 0.50 kg is moving in a straight line
across an air table at a speed of 2.4 m/s when it bumps into an
elastic band stretched between two fixed posts. if the elastic
band exerts an average opposing force of 1.4 N on the disc for
1.5 s, what will be the final velocity of the disc?
Answer
Answer
482 N.s
Perpendicular to the surface
- 1.8 m/s[forward]
or
1.8 m/s[backward]
114
110
A 300 g ball is struck by a bat with an impact that lasts 0.020 s.
If the ball moves through the air towards the bat at 50 m/s and
leaves at 100 m/s in the opposite direction, calculate the
average force exerted by the bat on the ball.
A 25-kg object with a speed of 40 m/s strikes a steel plate an
angle of 35 degree and rebounds at the same speed and angle
shown in the figure. What is the change (magnitude and
direction ) of the linear momentum of the object?
Answer
2.3 x 103 N
111
Answer
A 5-kg object with a speed of 30 m/s strikes a steel plate an
angle of 40 degree and rebounds at the same speed and angle
shown in the figure. What is the change (magnitude and
direction ) of the linear momentum of the object?
1,147 N.s
straight up
115
A 5-kg object with a speed of 30 m/s strikes a steel plate an
angle of 15 degree and rebounds at the same speed and angle
shown in the figure. What is the change (magnitude and
direction ) of the linear momentum of the object?
Answer
192.8 kg.m/s up and perpendicular to the plate
Answer
77.64 N.s
straight up
116
What is the impulse given to a golf ball by a club if they are in
contact for 0.0050 s, during which the club exerts an average
force of 500 N on the ball?
123
Answer
2.5 N.s
117
With a height of 296 m, the Yokohama Landmark Tower in
Yokohama, Japan, is one of the tallest buildings in both Japan
and the world. In order for people to reach distant floors
quickly, the building is equipped with elevators that travel at a
speed of 12.5 m/s. Suppose a passenger with a mass of 70.0 kg
enters one of these elevators. The elevator then goes up,
reaching full speed in 4.00 s. Calculate the net force that is
applied to the passenger during the acceleration of the elevator.
Answer
What impulse is exerted by a force of 25 N on a dynamics cart
for 3.2 s
Answer
80 N.s
118
124
What impulse is exerted by a hockey stick exerting a force of
120 N on a puck during the 0.05 s they are in contact
Answer
The "human cannonball" has long been a popular andextremely
dangerous-circus stunt. The record speed at which a person has
been shot from a circus cannon is about 24 m/s.
(a) Calculate the magnitude of the impulse that the cannon
must impart to a human cannonball with a mass of 45 kg.
(b) What is the magnitude of the force if it accelerates the
human cannonball in 0.70 s?
Answer
6.0 N.s
119
What impulse is exerted by the Earth pulling down on a 12 kg
rock during the 3.0 s it takes to fall from a cliff
125
Answer
352.8 N.s
120
Answer
2.1 x 104 kg m/s2
What average force will stop a 1000 kg car in 1.5 s, if the car is
moving at 22 m/s?
Answer
A golf ball has a mass of 60 g and is moving with a velocity of
70 m/s after it is hit with a golf club. The impact between the
golf club and the ball lasts for 2 x 10-4 s, what was the average
force applied to the ball?
126
14,666 N
A Force of 6.00 N acts on a 3.00 kg object for 10.0 s.
(a) What is the object's change in momentum?
(b) What is the object's change in velocity?
Answer
121
Describe the beneficial effects of "air bags" used in modern
cars to cushion passengers from collisions with the dashboard
during an accident. Explain from the point of view of impulse
and momentum.
Answer
122
(a) 60.0 N.s
(b) 20.0 m/s
127
In 1991, a Swedish company, Kalmar LMV, constructed a
forklift truck capable of raising 9.0 x 104 kg to a height of
about 2 m. Suppose a mass this size is lifted with an upward
velocity of 12 cm/s. If it takes the forklift 1.8 s to accelerate the
load to this upward velocity, what is the net force exerted on
the load during the acceleration?
Answer
A hockey player makes a slap shot, exerting a force of 30.0 N
on the hockey puck for 0.16 s.
(a) What impulse is given to the puck?
(b) The hockey puck has a mass of 0.115 kg and was at rest
before the shot. With what speed does the hockey puck head
toward the goal?
Answer
(a) 4.8 kg.m/s
(b) 42 m/s
128
The velocity of a 600-kg auto is changed from + 10.0 m/s to
+44.0 m/s in 68.0 s by an applied, constant force.
(a) What change in momentum does the force produce?
(b) What is the magnitude of the force?
Answer
(a) 2.04 x 104 Ns
(b) 300 N
129
130
What velocity will a 40 kg child sitting on a 40 kg wagon
acquire if pushed from rest by a force of 75 N for 2.0 s?
Answer
The head of a 1.0-kg hammer, moving at 3.6 m/s, strikes a nail
and drives it into hardwood.
(a) The head stays in contact 0.002 s and rebounds with
negligible velocity. What is the average force exerted on the
nail?
(b) When the same hammer hits a springy nail, it rebounds
with its initial speed, 3.6 m/s. The contact time is the same.
What force is exerted this time?
A toy rocket develops an average forward thrust of 4.0 N when
the velocity of the exhaust gases is 30 m/s. Calculate the mass
of gases ejected per second.
Answer
135
(a) 1.8 x 103 N
(b) 3.6 x 103 N
Answer
0.13 kg/s
131
136
A bronze statue of Buddha was completed in Tokyo in 1993.
The statue is 35 m tall and has a mass of 1.00 x 106 kg.
Suppose this statue were to be moved to a different location.
(a) What is the magnitude of the impulse that must act on the
statue in order for the speed to increase from 0.00 m/s to 0.20
m/s?
(b) If the magnitude of the net force of the impulse is 12.5 kN,
how long would it take for the final speed to be reached?
In 1990, Gary Stewart of California made 177,737 jumps on a
pogo stick. Suppose the pogo stick reaches a height of 12.0 cm
with each jump and that the time of contact with the ground
between the jumps is 0.60 s. Find the average net force acting
on the pogo stick during the contact with the ground. Assume
the total mass of Stewart and the pogo stick is 65 kg. (Hint:
The difference between the initial and final velocities is one of
direction rather than magnitude.)
Answer
330 N upward
Answer
2.0 x 105 kg.m/s
132
137
What force, acting for 0.001 sec, will change the velocity of a
100 g baseball from 30 m/sec eastward to 40 m/sec westward?
(do not find the acceleration.)
A force that averages 1000 N is applied to a 0.40 kg steel ball
moving at 14 m/s by a collision lasting 27 ms. If the force is in
a direction opposite to the initial velocity of the ball, find the
final speed of the ball.
Answer
53.5 m/s
Answer
7000 newtons
Small rockets are used to make small adjustments in the speed
of satellites. One such rocket has a thrust of 35 N. If it is fired
to change the velocity of a 72 000 kg spacecraft by 63 cm/s,
how long should it be fired?
A billiard ball of mass 200 g rolls towards the right-hand
cushion of a billiard table at 2.0 m/s and rebounds straight back
at 2.0 m/s.
(a) What is its change in momentum as a result of hitting the
cushion?
(b) What impulse is given to the ball by the cushion?
Answer
Answer
1275 s
- 0.80 kg.m/s[R],
+0.80 kg.m/s[L]
138
133
134
Before a collision, a 25 kg object is moving at +12 m/s.
(a) Find the impulse that acted on this object if after the
collision it moves at +8 m/s.
(b) Find the impulse that acted on this object if after the
collision it moves at -8 m/s.
Answer
(a) -1.0 x 102 kg.m/s
(b) -5.0 x 102 kg.m/s
139
A pellet gun fires ten 2.0 g pellets per second with a speed of
500 m/s. The pellets are stopped by a rigid wall
(a) What is the momentum of each pellet?
(b) What is the average force exerted by the stream of pellets
on the wall?
(c) If each pellet is in contact with the wall for 0.6 ms what is
the average force exerted on the wall by each pellet while in
contact?
Answer
(a) 1.0 kg-m/s
(b) 10 N
(c) 1,667 N
140
A movie set machine gun fires 50 g bullets at a speed of 1000
m/s. The gunner, holding the machine gun in his hands, can
exert an average force of 180 N against the gun. determine the
maximum number of bullets he can fire per minute?
145
Answer
216 bullets
141
Answer the following questions using the figure to the left:
(a) Calculate the impulse experienced when a 70-kg person
moving at 7 m/s lands on firm ground after jumping from a
height of 3.0 m.
(b) Estimate the average force exerted on the person's feet by
the ground if the landing is stiff-legged. Assume the body
moves 1.0 cm during impact,
(c) Estimate the average force exerted on the person's feet by
the ground if the landing is with bent legs. Assume the body
moves 50 cm during impact.
A 150 g (weight = 5.3 oz) baseball pitched at 40 m/s (=130
ft/s) is hit straight back to the pitcher at 60 m/s (=200 ft/s).
What average force was exerted by the bat if it was in contact
with the ball for 5.0 ms?
Answer
3000 N
142
A force that averages 1000 N is applied to a 0.40 kg steel ball
moving at 14 m/s by a collision lasting 27 ms. If the force is in
a direction opposite to the initial velocity of the ball, find the
final speed of the ball.
Answer
Answer
(a) -490 N.s
(b) 171,500 N
(c) 3,430 N
53.5 m/s
143
A force that averages 1000 N is applied to a 0.40 kg steel ball
moving at 14 m/s by a collision lasting 27 ms. If the force is in
a direction opposite to the initial velocity of the ball, find the
final speed of the ball.
146
A tennis ball may leave the racket of a top player on the serve
with a speed of 65.0 m/s.
(a) If the ball's mass is 0.0600 kg and it is in contact with the
racket for 0.0300 s, what is the average force on the ball?
(b) Would this force be large enough to lift a 60-kg person?
Answer
Answer
53.5 m/s
144
Water leaves a hose at a rate of 1.5 kg/s with a speed of 20 m/s
and strikes a wall, which stops it, see the figure to the left.
(That is, we ignore any splashing back.) What is the force
exerted by the water on the wall?
(a) 260 N
(b) No
147
A 115-kg fullback is running at 4.0 m/s to the east and is
stopped in 0.75 s by a head-on tackle by a tackler running due
west.
(a) Calculate the original momentum of the' fullback.
(b) Calculate the impulse exerted on the fullback.
(c) Calculate the impulse exerted on the tackler.
(d) Calculate the average force exerted on the tackler.
Answer
Answer
-30 N
148
A tennis ball of mass m = 0.060 kg and speed v = 25 m/s
strikes a wall at a 450 angle and rebounds with the same speed
at 450 (see the figure to the left). What is the impulse given the
wall?
152
A force of 6.00 N acts on a 3.00 kg object for 10.0 s.
(a) What is the object's change in momentum?
(b) What is its change in velocity?
Answer
(a) 60.0 N.s
(b) 20.0 m/s
153
A truck loaded with sand is moving down the highway in a
straight path. What happens to the momentum of the truck if
sand leaks at a constant rate through a hole in the truck bed
while the truck maintains a constant velocity?
Answer
momentum decreases
Answer
2.12 kg.m/sr
149
154
A 0.145-kg pitched baseball moving horizontally at 35.0 m/s
strikes a bat and is popped straight up to a height of 55.6 m
before turning around. If the contact time is 0.50 ms, calculate
the average force on the ball during the contact.
A glass ball of mass 5.0 g moves with a velocity of 20 m/s.
The ball collides with a second glass ball of mass 10.0 g, which
is moving along the same line with a velocity of 10.0 m/s.
After the collision, the 5.0 g ball is still moving at a velocity of
8.0 m/s.
(a) What is the change of momentum of the 5.0 g ball?
(b) What is the change of momentum of the 10.0 g ball?
Answer
Answer
150
The figure shows a 2.0 kg toy race car before and after taking a
turn on a track. Its speed is 0.50 m/s before the turn and 0.40
m/s after the turn. What is the change ∆P in the linear
momentum of the car?
(a) -.06 kg.m/s
(b) +.06 kg.m/s
155
A 0.165 kg cue ball with an initial speed of 2.00 m/s bounces
off the rail in a game of pool, as shown from overhead in the
figure at the left. For x and y axes located as shown, the
bounce reverses the y component of the ball's velocity but does
not alter the x component.
(a) What is θ in the figure at the left?
(b) What is the change in the ball's linear momentum in unitvector notation? (The fact that the ball rolls is not relevant to
either question.)
Answer
1.28 kgm/s
51.380 degrees above the x axis
Answer
151
A 0.70 kg mass is moving horizontally with a speed of 5.0 m/s
when it strikes a vertical wall. The mass rebounds with a speed
of 2.0 m/s. What is the magnitude of the change in linear
momentum of the mass?
Answer
156
A 2,500 kg car traveling to the north is slowed down uniformly
from an initial velocity of 20.0 m/s by 6,250 N braking force
acting opposite to the car's motion. Use the
impulse_momentum theorem to answer the following
questions:
(a) What is the car's velocity after 2.50 s?
(b) How far does the car move during 2.50 s?
(c) How long does it take the car to come to a complete stop?
162
Answer
Answer
(a) 14 m/s
to the north
(b) 42 m
(c) 8.0 s
157
-390 N
0.13 m
163
In running a ballistics test at the police department, officer
Spears fires a 6.0g bullet at 350 m/s into a container that stops
it in 0.30 m. What average force stops the bullet?
(a) F = -8.45 x 103 N
to the west
F = 8.45 x 103 N
to the east
(b) Dx = 50.0 m
to the west
-1.2 x 103 N
A 1,400 kg car moving westward with a velocity of 15 m/s
collides with a utility pole and is brought to rest in 0.30 s. Find
the magnitude of the force exerted on the car during the
collision.
164
Answer
F = -7.0 x 104 kg.m/s2
to the west
F = 7.0 x 104 km/s2
to the east
159
Air bags are designed to protect passengers during collisions.
Compare the magnitude of the force required to stop a moving
passenger in 0.75 s (by a deployed air bag) with the magnitude
of the force required to stop the same passenger at the same
speed in 0.026 s (by the dashboard).
A 2,250 kg car traveling to the west is slowed down uniformly
from 20.0 m/s to 5.00 m/s in 4.00 s.
(a) What constant force acted on the car during this time?
(b) How far did the car travel during the deceleration?
Answer
Answer
158
A 0. 150 kg baseball moving at +26 m/s is slowed to a stop by
a catcher in 0.010 s.
(a) What constant force did the catcher exert on the ball during
this time?
(b) How far did the ball travel before stopping?
A 2,500 kg car traveling to the north is slowed down uniformly
from an initial velocity of 20.0 m/s by 6,250 N braking force
acting opposite to the car's motion. Use the impulse
Answer
(a) 13.75 m/s
to the north
(b) 34.37 m
(c) 8.8 s
165
Answer
Fdashboard = 29(Fair bag)
The largest nuts (and presumably, the largest bolts) are
manufactured in England. The nuts have a mass of 4.74 x 103
kg each, which is greater than any passenger car currently in
production. Suppose one of these nuts slides along a rough
horizontal surface with an initial velocity of 2.4 m/s to the
right. How great is the change in the nut's momentum if its
final velocity is 0.8 m/s to the right?
Answer
160
A 0.50 kg football is thrown with a velocity of 15 m/s to the
right. A stationary receiver catches the ball and brings it to rest
in 0.020 s. What is the force exerted on the receiver?
-7.6 x 103 kg.m/s to the right
Answer
An 82 kg man drops from rest on a diving board 3.0 m above
the surface of the water and comes to rest 0.55 s after reaching
the water. What force does the water exert on him?
The record for the smallest dog in the world belongs to a terrier
who had a mass of only 113 g. Suppose this dog runs to the
right with a speed of 2.00 m/s when it suddenly sees a mouse.
The dog becomes scared and uses its paws to bring itself to
rest. After sliding 80.0 cm during this deceleration, the dog
turns and runs in the opposite direction. Use this data to
calculate the magnitudes of change in the dog's momentum and
the average frictional force that brings about that change.
Answer
Answer
1.1 x 103
upward
0.226 kg.m/s
0.282 N
3.8 x 102 N
to the right
161
166
167
In 1920, a 6.5 x 104 kg meteorite was found in Africa. Suppose
a meteorite with this mass enters Earth's atmosphere with a
speed of 1.0 km/s. After passing through the upper layers of
the atmosphere, its velocity is decreased to 0.20 km/s. If the
meteorite travels 18 km during the deceleration process, what
is the magnitude of the average net force acting on the
meteorite?
171
Answer
-1.7 x 106 N
168
Steel Phantom is a roller coaster in Pennsylvania that, like the
Desperado in Nevada, has a vertical drop of 68.6 m. Suppose a
roller distance of 30.0 m along this horizontal track before the
car comes to rest, what is the magnitude of its change in
momentum? Assume the car's speed at the peak of the drop is
zero. What is the magnitude of the average force acting on the
car during its deceleration?
Answer
Answer
(a)
(b)
(c)
(d)
172
-2.24 x 104 N
169
In 1992, an ice palace estimated to be 4.90 x 106 kg was built
in Minnesota. Despite this sizable mass, this structure could be
moved at a constant velocity because of the small force of
friction between the ice blocks of its base and the ice of the
lake upon which it was constructed. Imagine moving the entire
palace with a speed of 0.200 m/s on this very smooth, icy
surface. Once the palace is no longer being pushed, it coasts to
a stop in 10.0 s.
(a) What is the average force of sliding friction acting on the
palace?
(b) What is the palace's stopping distance?
Answer
9.80 x 104 N opposite the palace’s direction of motion
1.00 m
170
The longest canoe in the world was constructed in New
Zealand. The combined mass of the canoe and its crew of more
than 70 people was 20.3 x 103 kg. Suppose this canoe is sped
up to a velocity of 5.00 m/s to the west, at which point the crew
takes a break for 20.0 s.
(a) If the average retarding force acting on the canoe is 1.200 x
103 N, what is the final velocity of the canoe and crew after the
20.0 s coasting interval?
(b) What is the displacement of the canoe during that time?
Answer
3.8 m/s to the west
88.0 m to the west
When a person parachutes, the impact velocity is equal to that
attained in free fall from a height of 4.5 m. After contacting the
ground, the jumper's momentum is quickly brought to zero by
the Earth.
(a) What is the impact velocity?
(b) What is the impulse of the ground on the jumper, assuming
a mass of 80 kg?
(c) What is the average force on the jumper's feet if he lands
stiff-legged and the impulse only lasts 0.019 s? extended over a
time interval of 0.050 s?
d What is the average force on the jumper's feet if he lands
with his knees flexed, so that the impulse is extended over a
time interval of 0.050 s?
- 9.4 m/s
7.5 x 102 N-s
3.9 x 104 N
1.5 x 104 N
A girl on skis (total mass 60 kg including skis) reaches the
bottom of a hill moving at 20 m/s.
(a) What is her momentum?
(b) She encounters deeper snow and stops in 3.0 s. What
average force does the deeper snow exert on the girl?
(c) How far into the deeper snow does she penetrate, assuming
that the snow exerts a constant force on her?
Answer
(a) 1.2 x 103 kg.m/s
(b) -4.0 x 102 N
(c) 30 m
173
A bullet of mass 0.050 kg, moving with a velocity of 400 m/s,
penetrates a distance of 0.10 m into a wooden block firmly
attached to the Earth.
(a) If the resisting force is assumed constant, calculate the
acceleration of the bullet
(b) If the resisting force is assumed constant, calculate the
average force exerted on the bullet
(c) If the resisting force is assumed constant, calculate the time
required for it to stop
(d) If the resisting force is assumed constant, calculate the
impulse of the collision
(e) If the resisting force is assumed constant, calculate the
original momentum of the bullet
Answer
(a) -8.0 x 105 m/s2
(b) -4.0 x 10- N
(c) 5.0 x 10-4 S
(d) -20 N.s
(e) 20 kg.m/s
174
A hockey puck of mass 0.20 kg is sliding along a smooth, flat
section of ice at 18 m/s when it encounters some snow. After
15 s of sliding through the snow, it returns to smooth ice,
continuing at a speed of 10 m/s.
(a) What is the change in momentum of the puck?
(b) What impulse does the snow exert on the puck?
(c) What average frictional force does the snow exert on the
puck?
Answer
180
Answer
30.0 s
181
1.6 kg.m/s [forward],
1.6 kg-m/s [backward],
0.64 N[backward])
175
A 0.25-kg soccer ball is rolling at 6.0 m/s toward a player. The
player kicks the ball back in the opposite direction and gives it
a velocity of 14 m/s. What is the average force during the
interaction between the player's foot and the ball if the
interaction lasts 2.0 x 10-2 s.
(a) 5.0 x 10-2s
(b) --4.0 x 103 N
(c) 4.1 x 102 kg
no
(d) Holding child is dangerous to child
-2.5 x 102 N
A 0.145 kg baseball is pitched at 42 m/s. The batter hits it
horizontally to the pitcher at 58 m/s.
(a) Find the change in momentum of the ball.
(b) If the ball and bat were in contact 4.6 x 10-4 seconds, what
would be the average force while they touched?
182
Answer
(a) 14.5 kg.m/s
(b) 3.2 x 104 N
177
The brakes exert a 6.40 x 102 N force on a car weighing 15,680
N and moving at 20.0 m/s. The car finally stops.
(a) What is the car's mass?
(b) What is its initial momentum?
(c) What is the change in the car's momentum?
(d) How long does the braking force act on the car to bring it
to a halt?
178
(a)
(b)
(c)
(d)
183
1.6 x 103 kg
3.20 x 104 kg.m/s
-3.20 x 104 kg.m/s
50 s
What force is needed to bring a rocket of mass 1.00 x 103 kg
moving at 22.0 m/s to a halt in 20.0 s
Answer
A 10-kg lead brick falls from a height of 2.0 m.
(a) Find its momentum as it reaches the ground.
(b) What impulse is needed to bring the brick to rest?
(c) The brick falls onto a carpet, 1.0 cm thick. Assuming the
force stopping it is constant, find the average force the carpet
exerts on the brick.
(d) If the brick falls onto a 5.0 cm foam rubber pad, what
constant force is needed to bring it to rest?
Answer
Answer
(a)
(b)
(c)
(d)
A car moving at 10 m/s crashes into a barrier and stops in 0.25
m.
(a) Find the time required to stop the car.
(b) If a 20 kg child were to be stopped in the same time as the
car, what average force must be exerted?
(c) Approximately what is the mass of an object whose weight
equals the force from part b? Could you lift such a mass with
your arm?
(d) What does your answer to part c say about holding an
infant on your lap instead of using a separate infant restraint?
Answer
Answer
176
A 10 000-kg freight car is rolling along a track at 3.00 m/s.
Calculate the time needed for a force of 1000 N to stop the car.
63 kg.m/s
63 N.s
2.0 x 104 N
4.0 x 103 N
A 0.145 kg baseball is pitched at 42 m/s. The batter hits it
horizontally to the pitcher at 58 m/s.
(a) Find the change in momentum of the ball.
(b) If the ball and bat were in contact 4.6 x 10-4 seconds, what
would be the average force while they touched?
Answer
(a) 14.5 kg.m/s
(b) 3.2 x 104 N
184
A 0.450-kg block, moving with a speed of 3.00 m/s, has a
head-on collision with a 0.900-kg block initially at rest.
Assuming a perfectly elastic collision, what will be the speed
and direction of each block after the collision?
1.10 x 103 N
Answer
179
A force of 1.21 x 103 N is needed to bring a car moving at
+22.0 m/s to a halt in 20.0 s? What is the mass of the car?
Answer
1.0 x 103 kg
185
A gun is fired vertically into a 1.40-kg block of wood at rest
directly above it. If the bullet has a mass of 21.0 g and a speed
of 310 m/s, how high will the block rise into the air after the
bullet becomes imbedded in it?
190
The bird perched on the swing in the figure below has a mass
of 52.0 g, and the base of the swing has a mass of 153 g. The
swing and bird are originally at rest, and then the bird takes off
horizontally at 2.00 m/s. How high will the base of the swing
rise above its original level? Disregard friction.
Answer
1.07 m
186
A 2100 kg truck traveling north at 41 km/h turns east and
accelerates to 51 km/h.
(a) What is the change in the kinetic energy of the truck?
(b) What are the magnitude and direction of the change in the
linear momentum of the truck?
Answer
Answer
187
A 16.0 kg canoe moving to the left at 12 m/s makes an elastic
head-on collision with a 4.0 kg raft moving to the right at 6.0
m/s. After the collision, the raft moves to the left at 22.7 m/s.
(a) Find the velocity of the canoe after the collision.
(b) Verify your answer by calculating the total kinetic energy
before and after the collision.
.0236 m
191
An 8.0 g bullet is fired into a 2.5 kg pendulum bob initially at
rest and becomes embedded in it. If the pendulum rises a
vertical distance of 6.0 cm, calculate the initial speed of the
bullet.
Answer
(a) 5 m/s
to the left
(b) KEi 1.3 x 103 J
KEf 1.2 x 103 J,
so KEi = KEf
188
Answer
340 m/s
192
A 4.0 kg bowling ball moving to the right at 8.0 m/s has an
elastic head on collision with another 4.0 kg bowling ball
initially at rest. The first ball stops after the collision.
(a) Find the velocity of the second ball after the collision.
(b) Verify your answer by calculating the total kinetic energy
before and after the collision.
The heaviest wild lion ever measured had a mass of 313 kg.
Suppose this lion is walking by a lake when it sees an empty
boat floating at rest near the shore. The curious lion jumps into
the boat with a speed of 6.00 m/s, causing the boat with the
lion in it to move away from the shore with a speed of 2.50
m/s. Find the amount of kinetic energy dissipated in this
inelastic collision.
Answer
-3,280 J
Answer
(a) 8.0 m/s
to the right
(b) KEi = 1.3 x 102 J = KEf
189
A railroad car with a mass of 2.00 x 104 kg moving at 3.00 m/s
collides and joins with two railroad cars already joined
together, each with the same mass as the single car and initially
moving in the same direction at 1.20 m/s.
(a) What is the speed of the three joined cars after the
collision?
(b) What is the decrease in kinetic energy during the collision?
Answer
(a) 1.80 m/s
(b) 2.16 x 104 J
193
The cheapest car ever commercially produced was the Red Bug
Backboard, which sold in 1922 in the United States for about
$250. The car had a mass of only 111 kg. Suppose two of these
cars are used in a production of an action movie. A movie stunt
involves the two cars crashing into each other head-on. If one
car's speed before the crash is 9.00 m/s and the other car's
speed is 5.00 m/s, how much kinetic energy is dissipated in the
crash if the collision is perfectly inelastic?
Answer
-5,450 J
194
The Arctic snow train, built for the U.S. Army, has a mass of
4.00 x 105 kg and a top speed of 32.0 km/h. Suppose such a
train moving at its top speed is hit from behind by another
snow train with a mass of 1.60 x 105 kg and a velocity of 45.0
km/h in the same direction. What is the change in kinetic
energy after the trains' inelastic collision?
199
Answer
The cheapest car ever commercially produced was the Red Bug
Backboard, which sold in 1922 in the United States for about
$250. The car had a mass of only 111 kg. Suppose two of these
cars are used in a production of an action movie. A movie stunt
involves the two cars crashing into each other head-on. If one
car's speed before the crash is 9.00 m/s and the other car's
speed is 5.00 m/s, how much kinetic energy is dissipated in the
crash if the collision is perfectly inelastic?
Answer
-7 x 105 J
195
Two clay balls collide head-on in a perfectly inelastic collision.
The first ball has a mass of 0.500 kg and an initial velocity of
4.00 m/s to the right. The mass of the second ball is 0.250 kg,
and it has an initial velocity of 3.00 m/s to the left.
(a) What is the final velocity of the composite ball of clay after
the collision?
(b) What is the decrease in kinetic energy during the collision?
200
The Arctic snow train, built for the U.S. Army, has a mass of
4.00 x 105 kg and a top speed of 32.0 km/h. Suppose such a
train moving at its top speed is hit from behind by another
snow train with a mass of 1.60 x 105 kg and a velocity of 45.0
km/h in the same direction. What is the change in kinetic
energy after the trains'inelastic collision?
Answer
Answer
(a) vf = 1.67 m/s
to the right
(b) 4.07 J
196
A 0.25 kg arrow with a velocity of 12 m/s to the west strikes
and pierces the center of a 6.8 kg target.
(a) What is the final velocity of the combined mass?
(b) What is the decrease in kinetic energy during the collision?
Answer
(a) 0.43 m/s
to the west
(b) 17 j
197
Alaskan moose can be as massive as 8.00 x 102 kg. Suppose
two feuding moose, both of which have a mass of 8.00 x 102
kg, back away and then ran toward each other. If one of them
runs to the right with a speed of 8.0 m/s and the other runs to
the left with a speed of 6.0 m/s, what amount of kinetic energy
will be dissipated after their inelastic collision?
Answer
39,200 N.m
198
The heaviest wild lion ever measured had a mass of 313 kg.
Suppose this lion is walking by a lake when it sees an empty
boat floating at rest near the shore. The curious lion jumps into
the boat with a speed of 6.00 m/s, causing the boat with the
lion in it to move away from the shore with a speed of 2.50
m/s. Find the amount of kinetic energy dissipated in this
inelastic collision.
Answer