Question 1

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

Accepted Answer

In an elastic collision, both the momentum and kinetic energy are conserved. Since both masses have the same velocity before the collision and the collision is elastic, they will exchange velocities after the collision while conserving momentum and kinetic energy. Therefore, the statement is true.

Question 2

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.

Accepted Answer

Conservation of momentum states that in the absence of external forces, the total momentum of a system remains constant. Therefore, immediately before the explosion, the momentum of the shell must be equal to the momentum of all of its fragments after the explosion. Thus, statement I is true.

However, the total kinetic energy is not necessarily conserved in an explosion. Some of the original kinetic energy of the shell may be converted into other forms of energy, such as thermal or potential energy. Therefore, statement II is not necessarily true.

Question 3

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

Accepted Answer

This statement is true for objects with uniform density distribution. However, if the density is not uniform, the center of mass may not coincide with the geometric center.

Question 4

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.

Accepted Answer

According to Newton's third law of motion, the force exerted by one object on another is always equal and opposite to the force exerted by the second object on the first. This means that the impulse imparted on one object by the other is also equal and opposite. Therefore, the impulse imparted to the smaller mass by the larger mass is equal in magnitude and opposite in direction to the impulse imparted to the larger mass by the smaller one.

Question 5

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

Accepted Answer

The center of mass can be located outside of the object if there is a non-uniform distribution of mass within the object.

Question 6

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.

Accepted Answer

The momentum change of an object is given by the expression:
Δp = mΔv
where Δp is the momentum change, m is the mass of the object, and Δv is the change in velocity.
Since both the ball and the putty have the same mass and are thrown with the same initial velocity, the only difference in their momentum change will be due to the change in velocity upon hitting the wall.
The ball bounces back with nearly the same speed, so its change in velocity is large in magnitude but in the opposite direction. This means that the ball experiences a large momentum change.
The putty, on the other hand, sticks to the wall and thus experiences zero change in velocity. Therefore, the putty experiences zero momentum change. 
Thus, the ball experiences the greater momentum change.

Question 7

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.

Accepted Answer

In an inelastic collision, total momentum of the system is conserved (A), but the total kinetic energy of the system is not conserved (B) due to some energy being transferred as internal energy, like deformation, sound, or heat.

Question 8

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

Accepted Answer

When objects stick together after colliding, the collision is completely inelastic. In an elastic collision, the objects bounce off each other and separate.

Question 9

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.

Accepted Answer

The initial kinetic energy is (1/2)mv^2. After the collision, the combined mass is 2m and the velocity is v/2, so the kinetic energy is (1/2)(2m)(v/2)^2 = (1/2)mv^2/2, which is half the initial kinetic energy.

Question 10

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.

Accepted Answer

The speed of the freight car decreases because the mass of the system increases while the momentum is conserved. Since momentum (mass x velocity) is conserved and the mass increases, the velocity must decrease to keep the momentum constant.

Question 11

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.

Accepted Answer

The answer of Two different masses have equal, non-zero kinetic...

Question 12

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.

Accepted Answer

According to Newton's third law, the forces between two colliding objects are equal and opposite, so the magnitude of the impulse experienced by both objects is the same.

Question 13

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.

Accepted Answer

According to Newton's second law, the change in momentum is equal to the force applied times the length of time it acts. Since the forces are identical, the change in momentum is directly proportional to the mass. Therefore, the change in momentum of the smaller mass is equal to the change in momentum of the larger mass.

Question 14

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

Accepted Answer

In an elastic collision between two objects of equal mass, they exchange velocities. Thus, the yellow ball will have the velocity of the red ball, which is +3.0 m/s.

Question 15

A photograph of the two-dimensional elastic collision of two particles shows a particle of mass m₁approaching 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

Accepted Answer

Momentum is conserved in both the x and y directions. In the x direction, the initial momentum is m1vi, and the final momentum is m1v1cos30° + m2v2cos30°. In the y direction, the initial momentum is 0, and the final momentum is m1v1sin30° + m2v2sin30°. Since the collision is elastic, the total kinetic energy is conserved, so 1/2m1v1^2 = 1/2m1v1^2cos^230° + 1/2m2v2^2cos^230° + 1/2m1v1^2sin^230° + 1/2m2v2^2sin^230°. Solving for m1/m2, we get m1/m2 = 2.

Question 16

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.

Accepted Answer

In an elastic collision, both total momentum and total kinetic energy of the system are conserved. Therefore, both options A and B are true, making choice C the correct answer.

Question 17

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

Accepted Answer

Since momentum is conserved in the collision, we have:

mS1U1B10S1U1B0vS1U1B10S1U1B0 + mS1U1B20S1U1B0(0) = mS1U1B10S1U1B00vS1U1B00 + mS1U1B20S1U1B0vS1U1B20S1U1B0

Simplifying this equation and using the fact that mS1U1B20S1U1B0 is negligible compared to mS1U1B10S1U1B0, we get:

vS1U1B20S1U1B0 = 2vS1U1B10S1U1B0

Therefore, the speed of the ping-pong ball after the collision is twice the speed of the bowling ball before the collision.

Question 18

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.

Accepted Answer

When an object breaks up into two pieces, the total kinetic energy remains the same, but it is divided among the two pieces. Since the masses are unequal, the velocity of the larger mass will be smaller than that of the smaller mass, because the larger mass will experience a smaller force than the smaller mass. Thus, the kinetic energy of the smaller mass will be greater than the kinetic energy of the larger mass.

Question 19

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.

Accepted Answer

The answer of Jacques and George meet in the middle...

Question 20

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.

Accepted Answer

In an elastic collision, both the momentum and the energy of the objects involved are conserved. Therefore, the momentum of the tennis ball changes from -mv to +mv, and by Newton's third law, the momentum of the Earth changes by an equal and opposite amount, i.e., the total momentum of the system (ball + Earth) remains zero, so the momentum of Earth changes by the same amount as the momentum of the ball. Therefore, option B is correct.

Quiz 9: Linear Momentum and Collisions

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

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

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?

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

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?

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

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

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 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?

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

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?

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

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?

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

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?

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 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 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 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?