Question 1

Which of the following best explains why conservation laws, such as conservation of momentum, are so useful in physics?

Accepted Answer

They allow us to ignore the details of what happens between the initial and final states.

Question 2

A Winchester rifle (mass $$M = 4.3\ \mathrm{kg}) $$fires a bullet (mass $$m = 0.013\ \mathrm{kg}) at $$velocity $$v_b. If $$the rifle is initially at rest, what is the recoil velocity $$v_r of $$the rifle after firing?

Accepted Answer

$$v_r = -\frac{m}{M} v_b$$

Question 3

In the rifle and bullet example, why does the bullet carry away almost all the kinetic energy after firing?

Accepted Answer

Because the bullet has much less mass than the rifle.

Question 4

A person on a cart throws a ball to the left, and the ball bounces off a screen mounted on the cart. Which way does the cart eventually move?

Accepted Answer

Left

Question 5

Which of the following is true for an elastic collision between two objects of equal mass, where one is initially at rest?

Accepted Answer

The moving object comes to rest and the stationary object moves with the initial velocity of the first.

Question 6

In Newton’s cradle, if two balls are lifted and released, what happens on the other side?

Accepted Answer

Two balls are launched with the same velocity as the initial two.

Question 7

A ball of mass $$m_1$$ moving at velocity $$v$$ collides head-on and sticks to a stationary ball of mass $$m_2. $$What is their final velocity $$v'$$?

Accepted Answer

$$v' = \frac{m_1$}{m_1$ + m_2$} v$$

Question 8

In a perfectly inelastic collision where two objects stick together, what fraction of the initial kinetic energy is lost if $$m_1$$ collides with stationary $$m_2$$?

Accepted Answer

$$1 - \frac{m_1$}{m_1$ + m_2$}$$

Question 9

Which of the following statements about momentum in more than one dimension is correct?

Accepted Answer

All components of the momentum vector are conserved independently.

Question 10

A ball of mass $$m_1$$ moving at velocity $$v_1$$ collides elastically with a stationary wall (mass $$m_2$$ \gg $$m_1). $$What is the velocity of the ball after the collision?

Accepted Answer

$$-v_1$

Question 11

Which of the following is NOT a requirement for momentum to be conserved in a system?

Accepted Answer

The net external force on the system must be nonzero.

Question 12

In a movie, a gunslinger fires a gun and the target flies backward while the shooter is unaffected. Why is this scenario unrealistic?

Accepted Answer

Momentum conservation requires both shooter and target to experience equal and opposite changes in momentum.

Question 13

Which of the following best describes an elastic collision?

Accepted Answer

Both momentum and kinetic energy are conserved.

Question 14

A glancing collision occurs in two dimensions. If the initial transverse component of momentum is zero, what must be true after the collision?

Accepted Answer

The total transverse component of momentum remains zero.

Question 15

Which of the following is a real-world example of an inelastic collision?

Accepted Answer

A car crash where the vehicles crumple and stick together.

Question 16

If a system is isolated and the net external force is zero, which of the following must be true?

Accepted Answer

The total momentum of the system is conserved.

Question 17

In a two-body breakup (such as a rifle firing a bullet), what is the relationship between the momenta of the two objects after the event?

Accepted Answer

They are equal in magnitude and opposite in direction.

Question 18

Which of the following is a correct statement about the kinetic energy distribution in the rifle-bullet system after firing?

Accepted Answer

The bullet carries almost all the kinetic energy due to its much smaller mass.

Question 19

Which equation correctly expresses Newton’s second law in terms of momentum?

Accepted Answer

$$\vec{F}_{net} = \frac{d\vec{p}}{dt}$$

Momentum and Collisions: Conservation Laws in Physics

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