Deck 9: Linear Momentum and Collisions

Question 1

The impulse delivered to an object is equal to the change in the object's velocity.

Answer 1

False

Question 2

Internal forces cannot change the total kinetic energy of a system.

Answer 2

False

Question 3

Two objects of equal mass are traveling with identical speeds v and collide. After the collision they travel together with a speed v/2. What was the angle between the original velocities?

Answer 3

120°

Question 4

When a gun is fired, which has the greater kinetic energy:
the bullet or the recoiling gun?

Question 5

State Newton's second law in terms of momentum.

Question 6

A novice marksman fires a rifle while holding the butt of the rifle a couple of centimeters away from his shoulder. Explain what happens in terms of the physical principles involved.

Question 7

In space there is nothing for the rocket to "push against" so how does it accelerate?

Question 8

State the Conservation of Linear Momentum.

Question 9

When a ball undergoes a one-dimensional elastic collision with a wall, the velocity of the ball is reversed, while the wall remains stationary. Explain why this does not violate conservation of momentum.

Question 10

The net force acting on an object is equal to the rate of change of its momentum.

Question 11

An air track cart with mass m and speed v moving along an air track collides with a stationary cart with a mass m/3. After the collision the first cart has a speed v/2. Is the collision elastic?

Question 12

An air track cart with mass m and speed v moving along an air track collides with a stationary cart with a mass m/3. After the collision the first cart has a speed v/2. What is the speed of the second cart?

Question 13

A particle that has zero momentum must also have zero kinetic energy.

Question 14

Two objects approach each other with velocities such that the total momentum of the masses is zero kg∙m/s, and undergo an elastic collision. Is the sum of the kinetic energies of each object the same before and after the collision?

Question 15

A system that has zero momentum must also have zero kinetic energy.

Question 16

Define an elastic collision in terms of conservation of momentum and energy.

Question 17

In the two-dimensional elastic collision of a particle with a stationary particle that has the same mass, the trajectories of the two particles after the collision are at right angles to each other. Explain why this should be so.

Question 18

Define an inelastic collision in terms of conservation of momentum and energy.

Question 19

State the Conservation of Momentum for a System of Objects

Question 20

Internal forces cannot change the total momentum of a system.

Question 21

In a one-dimensional elastic collision of two identical masses, the masses exchange velocities.

Question 22

An artillery shell explodes in midair and breaks up into many fragments. Which of the following statements are true regarding conditions immediately before and immediately after the explosion:
I. The total momentum of the fragments is equal to the original momentum of the shell.
II. The total kinetic energy of the fragments is equal to the original kinetic energy of the shell.

A) Statement I only
B) Statement II only
C) Both Statement I and Statement II
D) Neither statement is true.

Question 23

The center of mass of a continuous, uniform object is located at the geometric center of the object.

Question 24

In a collision between two unequal masses, how does the impulse imparted to the smaller mass by the larger mass compare with the impulse imparted to the larger mass by the smaller one?

A) It is larger.
B) It is smaller.
C) They are equal.
D) The answer depends on the ratio of the masses.
E) The answer depends on how fast they are moving.

Question 25

The center of mass of an object does not have to be located within the object.

Question 26

A rubber ball and a lump of putty have equal mass. They are thrown with equal speed against a wall. The ball bounces back with nearly the same speed with which it hit. The putty sticks to the wall. Which objects experiences the greater momentum change?

A) the ball
B) the putty
C) Both experience the same non-zero momentum change.
D) Both experience zero momentum change.
E) Cannot be determined from the information given.

Question 27

An inelastic collision of two objects is characterized by the following.

A) Total momentum of the system is conserved.
B) Total kinetic energy of the system remains constant.
C) Both A and B are true.
D) Neither A nor B are true.

Question 28

When objects stick together after colliding, the collision is completely elastic.

Question 29

A railroad car of mass m and speed v collides and sticks to an identical railroad car that is initially at rest. After the collision, the kinetic energy of the system

A) is the same as before.
B) is half as much as before.
C) is one third as much as before.
D) is one fourth as much as before.
E) is one quarter as much as before.

Question 30

A freight car moves along a frictionless level railroad track at constant speed. The freight car is open on top. A large load of coal is suddenly dumped into the car. What happens to the speed of the freight car?

A) It increases.
B) It remains the same.
C) It decreases.
D) It becomes zero.
E) Cannot be determined from the information given.

Question 31

Two different masses have equal, non-zero kinetic energies. The momentum of the smaller mass is

A) smaller than the momentum of the larger mass.
B) larger than momentum of the larger mass.
C) equal to the momentum of the larger mass.
D) zero.
E) There is not enough information to answer the question.

Question 32

A ping-pong ball moving east at a speed of 4 m/s, collides with a stationary bowling ball. The Ping-Pong ball bounces back to the west, and the bowling ball moves very slowly to the east. Which object experiences the greater magnitude impulse during the collision?

A) Neither; both experienced the same magnitude impulse.
B) the Ping-Pong ball
C) the bowling ball
D) It's impossible to tell since the actual mass values are not given.
E) It's impossible to tell since the velocities after the collision are unknown.

Question 33

Identical forces act for the same length of time on two different masses. The change in momentum of the smaller mass is

A) smaller than the change in momentum of the larger mass, but not zero.
B) larger than the change in momentum of the larger mass.
C) equal to the change in momentum of the larger mass.
D) zero.
E) There is not enough information to answer the question.

Question 34

A red ball with a velocity of +3.0 m/s collides head-on with a yellow ball of equal mass moving with a velocity of -2.0 m/s. What is the velocity of the yellow ball after the collision?

A) zero
B) +3.0 m/s
C) -2.0 m/s
D) +2.5 m/s
E) +5.0 m/s

Question 35

A photograph of the two-dimensional elastic collision of two particles shows a particle of mass m₁ approaching a stationary particle of mass m₂. As a result of their interaction, the incident particle moves away along a line that makes an angle of 30° with its original path, and the other particle moves away along a line that makes an angle of 30° to the other side of the original path of the incident particle. What is the ratio of the masses, m₁/m₂?

A) 0.5
B) 1
C) 2
D) 3
E) 4

Question 36

An elastic collision of two objects is characterized by the following.

A) Total momentum of the system is conserved.
B) Total kinetic energy of the system remains constant.
C) Both A and B are true.
D) Neither A nor B are true.

Question 37

A ping-pong ball originally at rest is hit head-on by a bowling ball moving with initial speed v₀. It is given that the mass of the ping-pong ball is as good as negligible in comparison with the mass of the bowling ball. What is the speed of the ping-pong ball after this elastic collision?

A)
B) v₀
C) 2v₀
D) 4v₀
E) 8v₀

Question 38

An object that is initially at rest breaks up into two pieces of unequal masses when a spring-loaded device is released. If you compare the kinetic energy of the larger mass to that of the smaller mass immediately after they separate, which of the following statements is correct?

A) The kinetic energy of the larger mass is greater.
B) The kinetic energy of the smaller mass is greater.
C) The kinetic energies of the two masses are equal.
D) The total kinetic energy is zero J.

Question 39

Jacques and George meet in the middle of a lake while paddling in their canoes. They come to a complete stop and talk for a while. When they are ready to leave, Jacques pushes George's canoe with a force to separate the two canoes. What is correct to say about the final momentum and kinetic energy of the system?

A) The final momentum is in the direction of but the final kinetic energy is zero J.
B) The final momentum is in the direction opposite of but the final kinetic energy is zero J.
C) The final momentum is in the direction of and the final kinetic energy is positive.
D) The final momentum is zero kg∙m/s and the final kinetic energy is zero J.
E) The final momentum is zero kg∙m/s but the final kinetic energy is positive.

Question 40

A tennis ball undergoes an elastic collision when it hits the ground and bounces up. It is given that the speed of the ball just before it hits the ground is -v₀ and immediately after rebounding it is +v₀. Which of the statements below is true?

A) The momentum of the ball changes but the momentum of Earth does not.
B) The momentum of the ball changes and the momentum of Earth also changes by the same amount.
C) The momentum of the ball does not change but the momentum of Earth changes.
D) Neither the momentum of the ball nor the momentum of Earth changes.
E) Additional information is needed to answer this question.

Question 41

A puck with a mass m₁ = 50.0 g moving at 1.00 m/s approaches a stationary puck with a mass m₂ = 100 g on an air table and they undergo a two-dimensional elastic collision. After the collision, both pucks have identical speeds, but travel in different directions. What is the angle between the original and final paths of m₁?

A) 30.0°
B) 60.0°
C) 90.0°
D) 120°
E) 150°

Question 42

Three masses are positioned at the following coordinates:
3.0 kg at (3,2); 4.0 kg at (0,-1); and 5.0 kg at (5,-7).
What are the coordinates of the center of mass of the system?

Question 43

Jennifer hits a stationary 200. gram ball and it leaves the racket at 40. m/s. If time lapse photography shows that the ball was in contact with the racket for 40. ms:
(a) What average force was exerted on the racket?
(b) What is the ratio of this force to the weight of the ball?

Question 44

Three masses are positioned as follows:
2.0 kg at (0, 0); 2.0 kg at (2, 0); and 4.0 kg at (2,1).
Determine the coordinates of the center of mass.

Question 45

An 80. kg man is skating Northward and happens to collide with a 20. kg boy who is ice skating toward the East. Immediately after the collision, the man and boy are seen to be moving together at 2.5 m/s in a direction 60 degrees North of East. How fast was the boy moving before the collision?

Question 46

A batter hits a 0.140-kg baseball that was approaching him at 30.0 m/s and, as a result, the ball leaves the bat at 40.0 m/s in the direction of the pitcher. The ball remains in contact with the bat for 2.0 ms. What is the average force exerted by the bat?

Question 47

A 50-gram ball moving +10 m/s collides head-on with a stationary ball of mass 100.g. The collision is elastic. What is the speed of each ball immediately after the collision?

Question 48

A 900-kg car traveling east at 15.0 m/s collides with a 750-kg car traveling north at 20.0 m/s. The cars stick together.
(a) What is the speed of the wreckage just after the collision?
(b) In what direction does the wreckage move just after the collision?

Question 49

A rope is held from one end in such a way that the lower end just touches a table. The rope is then lowered onto the table with constant velocity. The force that is needed to hold the upper end of the rope is

A) equal to the weight of the portion of the rope that is not on the table.
B) greater than the weight of the portion of the rope that is not on the table.
C) less than the weight of the portion of the rope that is not on the table but not zero N.
D) zero N.
E) Cannot be determined without additional information.

Question 50

A rope is lying on a table. You pick up one end and start raising it with a constant velocity. The force you have to exert on the rope is

A) equal to the weight of the portion of the rope that is not on the table.
B) greater than the weight of the portion of the rope that is not on the table.
C) less than the weight of the portion of the rope that is not on the table but not zero N.
D) zero N.
E) Cannot be determined without additional information.

Question 51

A 14,000-kg boxcar is coasting at 1.50 m/s along a horizontal track when it hits and couples with a stationary 10,000-kg boxcar. What is the speed of the cars after the collision?

Question 52

A 60-kg swimmer dives from a 150-kg raft with a horizontal speed of 1.5 m/s. The raft is initially at rest. What is the speed of the raft immediately after the diver jumps?

Question 53

A rocket develops 10,000 N of thrust at liftoff. If the speed of the ejected fuel is 2000 m/s, at what rate (in kg/s) must the fuel be ejected?

Question 54

A batter applies an average force of 8000 N to a baseball for 1.10 ms. What is the magnitude of the impulse delivered to the baseball?

Question 55

A 2.00-g bullet traveling at 700 m/s hits and becomes embedded in a stationary 5.00-kg wood block. What is the speed of the block immediately after the bullet has stopped moving relative to the block?

Question 56

What is the magnitude of the momentum of a 0.140 kg baseball traveling at 45.0 m/s?

Question 57

A golf club exerts an average force of 1000 N on a 0.045-kg golf ball which is initially at rest. The club is in contact with the ball for 1.8 ms. What is the speed of the golf ball as it leaves the tee?

A) 30 m/s
B) 35 m/s
C) 40 m/s
D) 45 m/s
E) 50 m/s

Question 58

In space, a 4.0 kg metal ball moving 30. m/s has a head-on collision with a stationary 1.0 kg second ball. After the elastic collision, what are the velocities of the balls?

Question 59

A firecracker breaks up into two pieces, one has a mass of 200 g and flies off along the x-axis with a speed of 82.0 m/s and the second has a mass of 300 g and flies off along the y-axis with a speed of 45.0 m/s. What is the total momentum of the two pieces?

A) 361 kg∙m/s at 56.3° from the x-axis
B) 93.5 kg∙m/s at 28.8° from the x-axis
C) 21.2 kg∙m/s at 39.5° from the x-axis
D) 361 kg∙m/s at 0.983° from the x-axis
E) 21.2 kg∙m/s at 56.3° from the x-axis

Question 60

Two air track carts move along an air track towards each other. Cart A has a mass of 450 g and moves toward the right with a speed of 0.850 m/s and air track cart B has a mass of 300 g and moves toward the left with a speed of 1.12 m/s. What is the total momentum of the system?

A) 0.047 kg∙m/s toward the right
B) 0.719 kg∙m/s toward the right
C) 0.719 kg∙m/s toward the left
D) 0.750 kg∙m/s toward the right
E) 0.750 kg∙m/s toward the left

Question 61

A plate falls vertically to the floor and breaks up into three pieces, which slide along the floor. Immediately after the impact, a 320-g piece moves along the x-axis with a speed of 2.00 m/s and a 355-g piece moves along the y-axis with a speed of 1.50 m/s. The third piece has a mass of 100 g. In what direction does the third piece move?

A) 216.9° from the x-axis
B) 219.8° from the x-axis
C) 36.9° from the x-axis
D) 39.9° from the x-axis
E) 39.8° from the x-axis

Question 62

A plate falls vertically to the floor and breaks up into three pieces, which slide along the floor. Immediately after the impact, a 200-g piece moves along the x-axis with a speed of 2.00 m/s, a 235-g piece moves along the y-axis with a speed of 1.50 m/s. The third piece has a mass of 100 g. What is its speed?

A) 2.51 m/s
B) 2.57 m/s
C) 3.50 m/s
D) 5.33 m/s
E) 6.83 m/s

Question 63

A 50.0-kg person stands on a 200-kg raft, which is at rest. She starts to walk on the raft with a speed of 3.00 m/s with respect to the raft. What is the speed of the person relative to the water?

A) 2.40 m/s
B) 0.225 m/s
C) 0.500 m/s
D) 0.750 m/s
E) 1.20 m/s

Question 64

A 0.140-kg baseball is dropped from rest from a height of 2.00 m above the ground. What is the magnitude of its momentum just before it hits the ground?

A) 0.280 kg∙m/s
B) 0.877 kg∙m/s
C) 0.439 kg∙m/s
D) 0.620 kg∙m/s
E) 1.37 kg∙m/s

Question 65

A 500-kg cannon fires a 4.0-kg projectile with a velocity of 500 m/s relative to the ground. What is the recoil speed of the cannon?

A) 1.0 m/s
B) 2.0 m/s
C) 4.0 m/s
D) 6.0 m/s
E) 8.0 m/s

Question 66

A 0.330-kg volleyball is thrown vertically downward with a speed of 0.150 m/s. It takes it 0.0655 s to reach the ground. What is the magnitude of its momentum just before it hits the ground?

A) 0.212 kg∙m/s
B) 0.262 kg∙m/s
C) 0.163 kg∙m/s
D) 0.0216 kg∙m/s
E) 0.0418 kg∙m/s

Question 67

A batter hits a 0.140-kg baseball that was approaching him at 40.0 m/s and, as a result, the ball leaves the bat at 30.0 m/s in the direction of the pitcher. What is the magnitude of the impulse delivered to the baseball?

A) 9.80 Ns
B) 1.40 Ns
C) 5.60 Ns
D) 4.90 Ns
E) 7.00 Ns

Question 68

A 0.140-kg baseball is dropped from rest. It has a speed of 1.20 m/s just before it hits the ground. It rebounds with a speed of 1.00 m/s. The ball is in contact with the ground for 0.0140 s. What is the average force exerted by the ground on the ball during that time?

A) 2.00 N upwards
B) 2.00 N downwards
C) 22.0 N upwards
D) 22.0 N downwards
E) 0 N

Question 69

A 0.140-kg baseball is dropped from rest from a height of 2.2 m above the ground. It rebounds to a height of 1.6 m. What change in the ball's momentum occurs when the ball hits the ground?

A) 0.117 kg∙m/s upwards
B) 0.117 kg∙m/s downwards
C) 1.70 kg∙m/s upwards
D) 0.350 kg∙m/s upwards
E) 0.350 kg∙m/s downwards

Question 70

A 900-kg car traveling 30.0° south of east at 12.0 m/s collides with a 750-kg car traveling north at 17.0 m/s. The cars stick together. What is the speed of the wreckage just after the collision?

A) 7.21 m/s
B) 12.2 m/s
C) 20.4 m/s
D) 25.0 m/s
E) 17.3 m/s

Question 71

A 0.140-kg baseball is dropped and reaches a speed of 1.20 m/s just before it hits the ground. It rebounds with a speed of 1.00 m/s. What is the change of the ball's momentum?

A) 0.0280 kg∙m/s upwards
B) 0.0280 kg∙m/s downwards
C) 0.308 kg∙m/s upwards
D) 0.308 kg∙m/s downwards
E) 0 kg∙m/s

Question 72

Two ice skaters, one with a mass of 45 kg and the other with a mass of 60 kg, push off against one another starting from a stationary position. After they have pushed off, the relative speed at which they separate is 0.600 m/s. What is the speed of the 60-kg skater?

A) 0.343 m/s
B) 0.257 m/s
C) 0.375 m/s
D) 0.750 m/s
E) 0.225 m/s

Question 73

A 900-kg car traveling east at 15.0 m/s collides with a 750-kg car traveling north at 20.0 m/s. The cars stick together. In what direction does the wreckage move just after the collision?

A) 36.9° N of E
B) 42.0° N of E
C) 45.0° N of E
D) 53.1° N of E
E) 48.0° N of E

Question 74

A 900-kg car traveling east at 15.0 m/s collides with a 750-kg car traveling north at 20.0 m/s. The cars stick together. What is the speed of the wreckage just after the collision?

A) 6.10 m/s
B) 12.2 m/s
C) 25.0 m/s
D) 35.0 m/s
E) 17.3 m/s

Question 75

A batter hits a foul ball. The 0.140-kg baseball that was approaching him at 40.0 m/s leaves the bat at 30.0 m/s in a direction perpendicular to the line between the batter and the pitcher. What is the magnitude of the impulse delivered to the baseball?

A) 9.80 Ns
B) 1.40 Ns
C) 3.50 Ns
D) 5.60 Ns
E) 7.00 Ns

Question 76

A 600-kg car makes a 90° turn. Its speed before the turn is 21.0 m/s and after the turn it is 24.0 m/s. What is the magnitude of the change in the car's momentum?

A) 19.1 × 10³ kg∙m/s
B) 10.2 × 10³ kg∙m/s
C) 9.55 × 10³ kg∙m/s
D) 12.0 × 10³ kg∙m/s
E) 22.2 × 10³ kg∙m/s

Question 77

A 0.330-kg volleyball is dropped from rest. It takes it 1.30 s to reach the ground. What is the magnitude of its momentum just before it hits the ground?

A) 4.21 kg∙m/s
B) 0.429 kg∙m/s
C) 3.24 kg∙m/s
D) 2.11 kg∙m/s
E) 1.18 kg∙m/s

Question 78

Two ice skaters push off against one another starting from a stationary position. The 45-kg skater acquires a speed of 0.375 m/s. What speed does the 60-kg skater acquire?

A) 0.500 m/s
B) 0.281 m/s
C) 0.375 m/s
D) 0.750 m/s
E) 0 m/s

Question 79

A 3.0-kg object moves to the right at 4.0 m/s. It collides head-on with a 6.0-kg object moving to the left at 2.0 m/s. Which statement is correct?

A) The total momentum both before and after the collision is 24 kg ∙ m/s.
B) The total momentum before the collision is 24 kg ∙ m/s, and after the collision is 0 kg ∙ m/s.
C) The total momentum before the collision is 0 kg ∙ m/s, and after the collision is 24 kg ∙ m/s.
D) The total momentum both before and after the collision is zero.
E) None of the above is true.

Question 80

A 2.00-g bullet hits and becomes embedded in a 5.00-kg wood block which is hanging from a 1.20-m long string. This causes the block to swing through an arc of 3.50°. What was the speed of the bullet before it hit the block?

A) 16.7 m/s
B) 524 m/s
C) 25.3 m/s
D) 262 m/s
E) 789 m/s