Q: A 0.15 kg baseball is pitched at 40 m/s and is hit straight back at 60 m/s by a bat. What is the change in momentum of the baseball?

$$\Delta p = 0.15 \times (60 - (-40)) = 15\ \mathrm{kg \cdot m/s}$$

Q: A 22-kg shopping cart is pushed with a force of 6.5 N for 1.9 s. What is the magnitude of the impulse delivered to the cart?

$$I = F \Delta t = 6.5 \times 1.9 = 12.35\ \mathrm{kg \cdot m/s}$$

Q: A cyclist and bicycle (total mass 80 kg) are moving at 5 m/s. If the cyclist stops pedaling and no external horizontal forces act, what happens to the system's momentum?

The momentum remains constant at $$p = 80 \times 5 = 400\ \mathrm{kg \cdot m/s}$$

Question 1

A 0.15 kg baseball is pitched at 40 m/s and is hit straight back at 60 m/s by a bat. What is the change in momentum of the baseball?

Accepted Answer

$$\Delta p = 0.15 	imes (60 - (-40)) = 15\ \mathrm{kg \cdot m/s}$$

Question 2

Which of the following best describes the impulse delivered to an object?

Accepted Answer

Impulse is the product of the average force and the time interval over which it acts: $$I = F_{avg} \Delta t$$

Question 3

A 22-kg shopping cart is pushed with a force of 6.5 N for 1.9 s. What is the magnitude of the impulse delivered to the cart?

Accepted Answer

$$I = F \Delta t = 6.5 	imes 1.9 = 12.35\ \mathrm{kg \cdot m/s}$$

Question 4

A hailstorm and a rainstorm deliver the same mass of water per second to an umbrella. Why does the hailstorm require a greater force to hold the umbrella upright?

Accepted Answer

Because hail bounces back, resulting in a greater change in momentum and thus a greater impulse and force.

Question 5

Which of the following statements about the conservation of momentum is correct?

Accepted Answer

The total momentum of a system is conserved if the net external force acting on the system is zero.

Question 6

A 1-kg rubber ball falls at 4 m/s and bounces straight up at 4 m/s. What is the change in momentum of the ball?

Accepted Answer

$$\Delta p = p_f - p_i = (4) - (-4) = 8\ \mathrm{kg \cdot m/s}$$

Question 7

A cyclist and bicycle (total mass 80 kg) are moving at 5 m/s. If the cyclist stops pedaling and no external horizontal forces act, what happens to the system's momentum?

Accepted Answer

The momentum remains constant at $$p = 80 	imes 5 = 400\ \mathrm{kg \cdot m/s}$$

Question 8

Which of the following is true about internal and external forces in a system?

Accepted Answer

Internal forces always cancel out in pairs and do not affect the total momentum of the system.

Question 9

A 2,000 kg car moving at 10 m/s collides with a stationary 1,000 kg car. If the cars stick together after the collision, what is their final velocity?

Accepted Answer

$$v_f = \frac{m_1$ v_1$ + m_2$ v_2$}{m_1$ + m_2$} = \frac{2000 	imes 10 + 1000 	imes 0}{2000 + 1000} = \frac{20000}{3000} = 6.67\ \mathrm{m/s}$$

Question 10

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

Accepted Answer

The colliding objects stick together after the collision.

Question 11

A 0.5 kg ball moving at 2 m/s collides elastically with a 0.5 kg ball at rest. What is the velocity of the first ball after the collision?

Accepted Answer

$$v_{1f} = 0\ \mathrm{m/s}$$

Question 12

Which of the following best describes an elastic collision?

Accepted Answer

Both momentum and kinetic energy are conserved.

Question 13

A 1.5 kg cart moving at 3 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

$$v_{1f} = \frac{m_1$ - m_2$}{m_1$ + m_2$} v_{1i} = \frac{1.5 - 2.5}{1.5 + 2.5} 	imes 3 = \frac{-1}{4} 	imes 3 = -0.75\ \mathrm{m/s}$$

Question 14

A gun of mass 2 kg fires a 0.05 kg bullet at 400 m/s. What is the recoil velocity of the gun?

Accepted Answer

$$v_{gun} = -\frac{m_{bullet} v_{bullet}}{m_{gun}} = -\frac{0.05 	imes 400}{2} = -10\ \mathrm{m/s}$$

Question 15

Which of the following is a real-world example of momentum conservation?

Accepted Answer

A person jumping off a boat causes the boat to move in the opposite direction.

Question 16

A 1 kg beanbag is dropped from a height and comes to rest upon hitting the ground. If its speed just before impact is 4 m/s, what is the magnitude of the impulse delivered by the ground?

Accepted Answer

$$I = \Delta p = m (0 - (-4)) = 4\ \mathrm{kg \cdot m/s}$$

Question 17

Which of the following statements about impulse is correct?

Accepted Answer

Impulse has the same units as momentum: $$\mathrm{kg \cdot m/s}$$

Question 18

Why do bicycle helmets reduce the risk of head injury in a crash?

Accepted Answer

They increase the time over which the head comes to rest, reducing the average force experienced.

Question 19

In a two-object system, which of the following is always true if no external forces act?

Accepted Answer

The total momentum of the system remains constant.

Linear Momentum and Collisions: Study Notes

Study Guide - Practice Questions

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