Question 1

A tennis ball is struck by a racket, causing it to momentarily flatten and then rebound. Which physical quantity best describes the effect of the force exerted by the racket over the short time interval of contact?

Accepted Answer

Impulse, $$J_x = \int_{t_i}^{t_f} F_x(t) dt$$

Question 2

During a collision, the force exerted on an object is not constant. How can the impulse delivered to the object be calculated from a force vs. time graph?

Accepted Answer

By finding the area under the $$F_x vs$$. $$t$$ curve, $$J_x = \int_{t_i}^{t_f} F_x(t) dt$$

Question 3

A 0.5 kg ball moving at 2 m/s collides elastically with a stationary 0.5 kg ball. What are the final velocities of both balls after the collision?

Accepted Answer

Ball 1: $$0 m/s$$, Ball 2: $$2 m/s$$

Question 4

Which statement best describes the law of conservation of momentum for an isolated system?

Accepted Answer

The total momentum of the system remains constant, $$P_f = P_i$$

Question 5

A rocket burns fuel and expels exhaust gases downward. Which principle explains why the rocket accelerates upward?

Accepted Answer

Conservation of momentum: the momentum lost by the exhaust is gained by the rocket

Question 6

In a perfectly inelastic collision, two objects stick together after colliding. Which of the following is true?

Accepted Answer

Momentum is conserved, but mechanical energy is not

Question 7

A 10 g projectile traveling east at 2 m/s explodes into three fragments. One 3 g fragment moves west at 10 m/s, another 3 g fragment moves 40° north of east at 12 m/s. What is the speed and direction of the third fragment?

Accepted Answer

The third fragment moves southeast with a speed calculated using vector conservation of momentum

Question 8

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

Accepted Answer

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

Question 9

A force acts on an object for a short time interval, changing its velocity from $$v_i to$$ $$v_f. $$Which equation relates impulse to the change in momentum?

Accepted Answer

$$\Delta p_x = J_x$$

Question 10

In a perfectly elastic collision between two balls where $$m_1$$ \gg $$m_2$$, what are the approximate final velocities?

Accepted Answer

$$v_{f1} \approx v_{i1}$$, $$v_{f2} \approx 2v_{i1}$$

Question 11

Which of the following best describes the difference between impulse and momentum?

Accepted Answer

Impulse is the effect of a force over time, while momentum is the product of mass and velocity

Question 12

A system consists of a ball and the Earth. If the ball is dropped, why is momentum conserved when both are included in the system?

Accepted Answer

The gravitational interaction is internal, so the system is isolated

Question 13

Which equation gives the final velocity of two objects after a perfectly inelastic collision?

Accepted Answer

$$v_f = \frac{m_1$ v_{i1} + m_2$ v_{i2}}{m_1$ + m_2$}$$

Question 14

In a two-dimensional explosion, how is the velocity of the third fragment determined?

Accepted Answer

By using vector conservation of momentum for both $$x$$ and $$y$$ components

Question 15

Which of the following is true for a perfectly elastic collision?

Accepted Answer

Both momentum and kinetic energy are conserved

Question 16

A force acts on an object for a duration $$\Delta t. If $$the average force is $$F_{avg}$$, what is the impulse delivered?

Accepted Answer

$$J_x = F_{avg} \Delta t$$

Question 17

Which scenario best illustrates the conservation of momentum in real life?

Accepted Answer

A billiard ball striking another and both moving after the collision

Question 18

In a collision, why is it possible to analyze the interaction using momentum even if the force is unknown?

Accepted Answer

Because the law of conservation of momentum does not depend on the force details

Impulse, Momentum, and Collisions: A Comprehensive Study Guide

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