Q: A 70 kg boater steps out of a stationary 50 kg boat onto a dock with a velocity of 2.5 m/s to the right. What is the velocity of the boat immediately after the boater steps out? (Assume no external forces and both start at rest.)

$$v_{\text{boat}} = -3.5\ \text{m/s}$$

Q: A 0.1 kg rubber ball moving at 5 m/s collides with a wall and bounces back at 4 m/s. What is the change in momentum of the ball?

$$-0.1\ \text{kg} \cdot \text{m/s}$$

Question 1

Which of the following best describes the law of conservation of momentum in a closed system?

Accepted Answer

The total momentum before a collision is equal to the total momentum after the collision.

Question 2

A 70 kg boater steps out of a stationary 50 kg boat onto a dock with a velocity of 2.5 m/s to the right. What is the velocity of the boat immediately after the boater steps out? (Assume no external forces and both start at rest.)

Accepted Answer

$$v_{	ext{boat}} = -3.5\ 	ext{m/s}$$

Question 3

Which of the following is true for an elastic collision?

Accepted Answer

Both momentum and kinetic energy are conserved.

Question 4

Two marbles collide head-on elastically on a frictionless surface. Marble A (0.02 kg) moves right at 0.200 m/s, and Marble B (0.03 kg) moves left at 0.180 m/s. After the collision, Marble A moves left at 0.315 m/s. What is the velocity of Marble B after the collision?

Accepted Answer

$$v_B = 0.085\ 	ext{m/s}$$

Question 5

Which of the following best describes a perfectly inelastic collision?

Accepted Answer

Two objects collide and stick together, moving as one mass after the collision.

Question 6

A 2000 kg sedan is stopped at a traffic light and is hit from behind by a 975 kg convertible moving at 22.0 m/s. The two cars become entangled and move together after the collision. What is their velocity immediately after the collision?

Accepted Answer

$$v = 6.8\ 	ext{m/s}$$

Question 7

Which equation correctly represents the conservation of momentum for a two-object system before and after a collision?

Accepted Answer

$$m_1 v$$_{1B} + $$m_2 v$$_{2B} = $$m_1 v$$_{1A} + $$m_2 v$$_{2A}$$

Question 8

In a real-world car accident, why is the collision between two cars typically considered inelastic rather than elastic?

Accepted Answer

Because kinetic energy is not conserved due to deformation and heat.

Question 9

A 0.5 kg ball moving at 4 m/s collides elastically with a stationary 0.5 kg ball. What is the velocity of the first ball after the collision?

Accepted Answer

$$-4\ 	ext{m/s}$$

Question 10

Which of the following statements is true about momentum in all types of collisions (elastic, inelastic, perfectly inelastic) in a closed system?

Accepted Answer

Momentum is always conserved.

Question 11

A hockey puck of mass 0.2 kg slides on ice at 3 m/s and collides with a stationary puck of mass 0.3 kg. If the collision is perfectly inelastic, what is their velocity after the collision?

Accepted Answer

$$1.0\ 	ext{m/s}$$

Question 12

Which of the following is NOT a characteristic of an elastic collision?

Accepted Answer

Objects stick together after the collision.

Question 13

A 1.5 kg cart moving at 2 m/s collides elastically with a 2.5 kg cart at rest. What is the velocity of the 1.5 kg cart after the collision?

Accepted Answer

$$-0.5\ 	ext{m/s}$$

Question 14

In a perfectly inelastic collision, which of the following is always true?

Accepted Answer

The two objects move together with the same velocity after the collision.

Question 15

A 0.1 kg rubber ball moving at 5 m/s collides with a wall and bounces back at 4 m/s. What is the change in momentum of the ball?

Accepted Answer

$$-0.1\ 	ext{kg} \cdot 	ext{m/s}$$

Question 16

Which of the following real-life scenarios is best modeled as a perfectly inelastic collision?

Accepted Answer

A lump of clay thrown at a wall and sticking to it.

Question 17

If two ice skaters push off from each other on frictionless ice, what can be said about their momenta after they separate?

Accepted Answer

Their momenta are equal in magnitude and opposite in direction.

Question 18

A 0.4 kg ball moving at 3 m/s collides inelastically with a 0.6 kg ball at rest. What is their velocity after the collision?

Accepted Answer

$$1.2\ 	ext{m/s}$$

Collisions: Conservation of Momentum and Types of Collisions

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