Question 1

Three masses are moving along the x-axis. Their masses and velocities are:  with  ,  with  , and  with  (the minus sign indicating this velocity is in the negative x-direction). The three masses collide and stick together in a completely inelastic collision. What is the resultant velocity of the combined mass?

Accepted Answer

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Question 2

Two skaters, both of mass 75 kg, are initially at rest on skates on a frictionless ice pond. One skater throws a 0.3-kg ball at 10 m/s to his friend, who catches it and throws it back at 10 m/s. When the first skater has caught the returned ball, what is the velocity of each of the two skaters?

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Question 3

In a completely inelastic collision between two objects where the mass of one is double that of the other, which of the following statements is always true?

Accepted Answer

In a completely inelastic collision, both objects stick together and move with a common velocity after the collision. The kinetic energy is not conserved, but the total momentum is conserved. The changes in kinetic energy and momentum depend on the initial velocities, so none of the statements A, B, or C are always true.

Question 4

A neutron in a nuclear reactor makes an elastic head-on collision with a carbon atom initially at rest. (The mass of the carbon atom is 12 times that of the neutron.) What fraction of the neutron's original kinetic energy is retained by the neutron?

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Question 5

A 7.0-kg bowling ball strikes a 2.0-kg pin. The pin flies forward with a velocity of 6.0 m/s; the ball continues forward at 5.0 m/s. What was the original velocity of the ball?

Accepted Answer

Conservation of momentum can be applied in this situation since there are no external forces acting on the system. Using the equation:
(m1)(v1) + (m2)(v2) = (m1)(v1f) + (m2)(v2f)
where m1 and v1 are the mass and velocity of the ball, m2 and v2 are the mass and velocity of the pin, and v1f and v2f are the final velocities of the ball and pin, respectively. Plugging in the values given, we get:
(7.0 kg)(v1) + (2.0 kg)(0 m/s) = (7.0 kg)(5.0 m/s) + (2.0 kg)(6.0 m/s)
Solving for v1, we get:
v1 = 6.7 m/s
Therefore, the original velocity of the ball was 6.7 m/s, which is choice C.

Question 6

When a collision is completely inelastic, then:

Accepted Answer

In a completely inelastic collision, the colliding objects stick together after the collision, maximizing the loss of kinetic energy while conserving momentum.

Question 7

In a system with two moving objects, when a collision occurs between the objects:

Accepted Answer

The total momentum of the system is always conserved in a collision between two objects, regardless of whether the collision is elastic or inelastic. The kinetic energy, however, may not be conserved depending on the type of collision. In an elastic collision, the kinetic energy is conserved, whereas in an inelastic collision, some of the kinetic energy is lost as heat, sound, or deformation of the objects involved. Therefore, option A and C are incorrect. Option D is also incorrect as momentum is always conserved.

Question 8

Two masses collide and stick together. Before the collision, one of the masses was at rest. Is there a situation in which the kinetic energy is conserved in such a collision?

Accepted Answer

In a collision where two masses stick together, the collision is inelastic, meaning kinetic energy is not conserved. This is due to the fact that some of the kinetic energy is converted into other forms of energy, such as heat or internal energy, during the collision.

Question 9

A billiard ball (Ball #1) moving at 5.00 m/s strikes a stationary ball (Ball #2) of the same mass. After the elastic collision, Ball #1 moves at a speed of 3.50 m/s. Find the speed of Ball #2 after the collision.

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Question 10

Two billiard balls have velocities of 2.0 m/s and -1.0 m/s when they meet in an elastic head-on collision. What is the final velocity of the second ball after collision?

Accepted Answer

Explanation:In an elastic head-on collision, the total momentum and kinetic energy of the system are conserved. The total momentum before the collision is:$$P_i = m_1v_1 + m_2v_2$$where m_1 and m_2 are the masses of the two balls, and v_1 and v_2 are their velocities.The total momentum after the collision is:$$P_f = m_1v_1' + m_2v_2'$$where v_1' and v_2' are the velocities of the two balls after the collision.Since the collision is elastic, the total kinetic energy of the system is also conserved:$$K_i = \frac{1}{2}m_1v_1^2 + \frac{1}{2}m_2v_2^2$$$$K_f = \frac{1}{2}m_1v_1'^2 + \frac{1}{2}m_2v_2'^2$$Using the conservation of momentum and kinetic energy, we can solve for the final velocities of the two balls. We find that:$$v_1' = \frac{m_1 - m_2}{m_1 + m_2}v_1 + \frac{2m_2}{m_1 + m_2}v_2$$$$v_2' = \frac{2m_1}{m_1 + m_2}v_1 + \frac{m_2 - m_1}{m_1 + m_2}v_2$$In this case, the masses of the two balls are equal, so we have:$$v_1' = -v_1$$$$v_2' = v_2$$Therefore, the final velocity of the second ball is 1.0 m/s.

Question 11

A 1000-kg vehicle is moving in the positive y-direction along the y-axis at 10 m/s. A 2000-kg vehicle is moving in the positive x-direction at along the x-axis at 20 m/s. The vehicles collide and stick together. They move as a single object in a direction  as measured counterclockwise from the x-axis immediately after the collision. What is the value of  ?

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Question 12

Kaitlin uses a bat to hit a thrown baseball. She knocks the ball back in the direction from which it came in an inelastic collision. The bat, which is heavier than the baseball, continues to move in the same direction after the hit as Kaitlin "follows through." Is the ball moving faster before or after it was hit?

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Question 13

A 1.00-kg duck is flying overhead at 1.50 m/s when a hunter fires straight up. The 0.0100-kg bullet is moving 200 m/s when it hits the duck and stays lodged in the duck's body. What is the speed of the duck and bullet immediately after the hit?

Accepted Answer

Conservation of momentum can be applied in this situation, where the total momentum before the collision is equal to the total momentum after the collision. We can write:
(m_duck)v_duck + (m_bullet)v_bullet = (m_duck + m_bullet)v_final
Plugging in the values, we get:
(1.00 kg)(1.50 m/s) + (0.0100 kg)(200 m/s) = (1.01 kg)(v_final)
Solving for v_final, we get:
v_final = 2.48 m/s
Therefore, the best choice is C.

Question 14

Two objects, one less massive than the other, collide elastically and bounce back after the collision. If the two originally had velocities that were equal in size but opposite in direction, then which one will be moving slower after the collision?

Accepted Answer

In an elastic collision where two objects have equal and opposite velocities, the more massive object will move slower after the collision due to conservation of momentum and kinetic energy.

Question 15

A 5-kg object is moving to the right at 4 m/s and collides with another object moving to the left at 5 m/s. The objects collide and stick together. After the collision, the combined object:

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Question 16

A tennis ball is held above and in contact with a basketball, and then both are simultaneously dropped. The tennis ball bounces off the basketball at a fairly high speed. This is because:

Accepted Answer

When the basketball and tennis ball are dropped simultaneously, both experience the same gravitational acceleration due to Earth's gravitational pull. However, when they collide, the basketball being more massive transfers some of its momentum to the tennis ball causing it to bounce off at a faster speed. This is due to the conservation of momentum, which states that the total momentum of a system remains constant unless an external force acts upon it.

Question 17

A 0.10-kg object moving initially with a velocity of +0.20 m/s makes an elastic head-on collision with a 0.15-kg object initially at rest. What percentage of the original kinetic energy is gained by the 0.15-kg object?

Accepted Answer

In an elastic collision, kinetic energy is conserved. The 0.15-kg object initially at rest will gain kinetic energy equal to the kinetic energy lost by the 0.10-kg object. Since the 0.15-kg object starts with zero kinetic energy, it gains 100% of the kinetic energy transferred to it, which is 96% of the original kinetic energy of the system.

Question 18

Two identical 7-kg bowling balls roll toward each other. The one on the left is moving at +4 m/s while the one on the right is moving at -4 m/s. What is the velocity of each ball after they collide elastically?

Accepted Answer

In an elastic collision between two identical masses, they exchange velocities. Hence, the ball initially moving at +4 m/s will move at -4 m/s, and the ball initially moving at -4 m/s will move at +4 m/s after the collision.

Question 19

A baseball infielder, mass 75.0 kg, jumps up with velocity 2.00 m/s and catches a 0.150-kg baseball moving horizontally at 50.0 m/s. Of the following, which is closest to the final momentum of the system, infielder and baseball?

Accepted Answer

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Question 20

Two particles collide, one of them initially being at rest. Is it possible for both particles to be at rest after the collision?

Accepted Answer

In a collision, momentum is conserved. If one particle was moving and the other was at rest, the total system momentum was not zero. After the collision, for both particles to be at rest, the system's total momentum would have to be zero, which violates the conservation of momentum. Therefore, it's not possible for both particles to be at rest after the collision unless external forces act on the system, which is not implied in the given options.

Quiz 7: Momentum, Impulse, and Collisions