Q: A 0.40 kg ball hits a wall moving horizontally to the left at 30 m/s and rebounds horizontally to the right at 20 m/s. What is the impulse delivered to the ball by the wall?

$$\text{Impulse} = m(v_{f,x} - v_{i,x}) = 0.40 \times (20 - (-30)) = 0.40 \times 50 = 20\ \text{kg} \cdot \text{m/s}$$

Q: A soccer ball of mass 0.40 kg is initially moving horizontally to the left at 20 m/s. After being kicked, it moves at 30 m/s at 45° upward and to the right. What is the impulse in the x-direction?

$$J_x = m(v_{f,x} - v_{i,x}) = 0.40 \times (30 \cos 45^\circ - (-20)) = 0.40 \times (21.21 - (-20)) = 0.40 \times 41.21 = 16.48\ \text{kg} \cdot \text{m/s}$$

Q: A rocket in space ejects $$\frac{1}{60} of $$its mass in 1 second with an exhaust velocity of 2400 m/s. What is its acceleration?

$$a = \frac{\Delta m}{M} v_{ex} = \frac{1}{60} \times 2400 = 40\ \text{m/s}^2$$

Q: A force acts on a ball for 8 ms, reaching a maximum of 300 N. If the force-time graph is triangular, what is the impulse delivered to the ball?

$$\text{Impulse} = \frac{1}{2} \times 300 \times 0.008 = 1.2\ \text{N} \cdot \text{s}$$

Question 1

A 0.40 kg ball hits a wall moving horizontally to the left at 30 m/s and rebounds horizontally to the right at 20 m/s. What is the impulse delivered to the ball by the wall?

Accepted Answer

$$	ext{Impulse} = m(v_{f,x} - v_{i,x}) = 0.40 	imes (20 - (-30)) = 0.40 	imes 50 = 20\ 	ext{kg} \cdot 	ext{m/s}$$

Question 2

Which of the following best describes the principle of momentum conservation in a collision between two cars, assuming no external forces?

Accepted Answer

The total momentum before the collision equals the total momentum after the collision.

Question 3

A soccer ball of mass 0.40 kg is initially moving horizontally to the left at 20 m/s. After being kicked, it moves at 30 m/s at 45° upward and to the right. What is the impulse in the x-direction?

Accepted Answer

$$J_x = m(v_{f,x} - v_{i,x}) = 0.40 	imes (30 \cos 45^\circ - (-20)) = 0.40 	imes (21.21 - (-20)) = 0.40 	imes 41.21 = 16.48\ 	ext{kg} \cdot 	ext{m/s}$$

Question 4

In a completely inelastic collision, which of the following statements is true?

Accepted Answer

The colliding objects stick together and move with a common velocity after the collision.

Question 5

A rocket in space ejects $$\frac{1}{60} of $$its mass in 1 second with an exhaust velocity of 2400 m/s. What is its acceleration?

Accepted Answer

$$a = \frac{\Delta m}{M} v_{ex} = \frac{1}{60} 	imes 2400 = 40\ 	ext{m/s}^2$$

Question 6

Which of the following is the correct formula for the center of mass position $$x_{cm} of a $$system of particles?

Accepted Answer

$$x_{cm} = \frac{m_A x_A + m_B x_B + m_C x_C + \cdots}{m_A + m_B + m_C + \cdots}$$

Question 7

A force acts on a ball for 8 ms, reaching a maximum of 300 N. If the force-time graph is triangular, what is the impulse delivered to the ball?

Accepted Answer

$$	ext{Impulse} = \frac{1}{2} 	imes 300 	imes 0.008 = 1.2\ 	ext{N} \cdot 	ext{s}$$

Question 8

Which statement best describes the motion of the center of mass after a shell explodes in mid-air?

Accepted Answer

The center of mass continues to follow the original trajectory of the shell.

Question 9

Two 1.0 kg stationary cue balls are struck by cue sticks. Ball 1 receives a force of 100 N for 2 ms, Ball 2 receives a force of 10 N for 20 ms. Which ball has the greater final speed?

Accepted Answer

Both balls have the same final speed.

Question 10

Which formula correctly relates impulse to change in momentum?

Accepted Answer

$$\Delta p = J = F \Delta t$$

Question 11

A tennis ball bounces off a racket. Which type of collision is most likely occurring?

Accepted Answer

Elastic collision, where both momentum and kinetic energy are conserved.

Question 12

In rocket propulsion, why does the rocket accelerate when it ejects exhaust gases?

Accepted Answer

The rocket gains momentum equal and opposite to the momentum of the ejected gases, due to conservation of momentum.

Question 13

Which equation gives the velocity of the center of mass for a system of particles?

Accepted Answer

$$\vec{v}_{cm} = \frac{m_A \vec{v}_A + m_B \vec{v}_B + m_C \vec{v}_C + \cdots}{m_A + m_B + m_C + \cdots}$$

Question 14

A force varies with time as shown in a force-time graph. How can you approximate the impulse delivered?

Accepted Answer

By calculating the area under the force-time curve.

Question 15

In a collision between two astronauts in space, which law ensures their total momentum remains unchanged?

Accepted Answer

Conservation of momentum, since there are no external forces.

Question 16

A golf ball is struck by a club, causing it to accelerate rapidly. Which concept best explains the change in the ball's momentum?

Accepted Answer

Impulse, which is the product of force and the time interval during which it acts.

Question 17

During a car crash, why is the impulse important for understanding the forces experienced by passengers?

Accepted Answer

Impulse determines the change in momentum, which relates to the force experienced over the collision time.

Question 18

If a shell explodes in mid-air, what happens to the total momentum of the fragments?

Accepted Answer

The total momentum of the fragments equals the momentum of the shell just before the explosion.

Chapter 8: Momentum, Impulse, and Center of Mass

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