Q: A 0.15 kg baseball is thrown at 20 m/s toward a bat and is hit straight back at 40 m/s. If the contact time between the bat and the ball is 0.0030 s, what is the average force exerted by the bat on the ball?

$$F_{\text{avg}} = \frac{9.0\,\text{kg m/s}}{0.0030\,\text{s}} = 3000\,\text{N}$$

Q: A 10 kg cart moving at 2 m/s to the left bounces off a wall and moves at 1 m/s to the right. What is the change in momentum of the cart?

$$\Delta p = 10\,\text{kg} \times (1\,\text{m/s}) - 10\,\text{kg} \times (-2\,\text{m/s}) = 10 - (-20) = 30\,\text{kg m/s}$$

Q: A 1 kg box slides at 3 m/s on a frictionless surface and collides with a stationary 2 kg box. If they stick together after the collision, what is their final speed?

$$v_{\text{final}} = \frac{1\,\text{kg} \times 3\,\text{m/s}}{1\,\text{kg} + 2\,\text{kg}} = 1\,\text{m/s}$$

Q: A 2.0 kg object moving to the right with speed 0.50 m/s experiences a force that delivers an impulse of -1.0 kg m/s. What is its final velocity?

$$v_{f} = \frac{0.0\,\text{kg m/s}}{2.0\,\text{kg}} = 0\,\text{m/s}$$

Q: A 55 kg athlete on a 2 kg skateboard throws a 0.6 kg javelin at 25 m/s. What is her recoil speed after the throw?

$$v_{\text{recoil}} = -\frac{0.6\,\text{kg} \times 25\,\text{m/s}}{55\,\text{kg} + 2\,\text{kg}} = -0.26\,\text{m/s}$$

Question 1

A 0.15 kg baseball is thrown at 20 m/s toward a bat and is hit straight back at 40 m/s. If the contact time between the bat and the ball is 0.0030 s, what is the average force exerted by the bat on the ball?

Accepted Answer

$$F_{	ext{avg}} = \frac{9.0\,	ext{kg m/s}}{0.0030\,	ext{s}} = 3000\,	ext{N}$$

Question 2

Which of the following best describes impulse in physics?

Accepted Answer

Impulse is the area under the force-versus-time graph.

Question 3

A 10 kg cart moving at 2 m/s to the left bounces off a wall and moves at 1 m/s to the right. What is the change in momentum of the cart?

Accepted Answer

$$\Delta p = 10\,	ext{kg} 	imes (1\,	ext{m/s}) - 10\,	ext{kg} 	imes (-2\,	ext{m/s}) = 10 - (-20) = 30\,	ext{kg m/s}$$

Question 4

A light plastic cart and a heavy steel cart are both pushed with the same force for 1.0 s, starting from rest. After the force is removed, how do their momenta compare?

Accepted Answer

Their momenta are equal.

Question 5

A 1 kg box slides at 3 m/s on a frictionless surface and collides with a stationary 2 kg box. If they stick together after the collision, what is their final speed?

Accepted Answer

$$v_{	ext{final}} = \frac{1\,	ext{kg} 	imes 3\,	ext{m/s}}{1\,	ext{kg} + 2\,	ext{kg}} = 1\,	ext{m/s}$$

Question 6

In a perfectly elastic collision between two balls, ball 1 (mass $$m_1) $$moves at $$v_{i1}$$ and ball 2 (mass $$m_2) is at $$rest. What is the final velocity of ball 2?

Accepted Answer

$$v_{f2} = \frac{2 m_1$}{m_1$ + m_2$} v_{i1}$$

Question 7

A 2.0 kg object moving to the right with speed 0.50 m/s experiences a force that delivers an impulse of -1.0 kg m/s. What is its final velocity?

Accepted Answer

$$v_{f} = \frac{0.0\,	ext{kg m/s}}{2.0\,	ext{kg}} = 0\,	ext{m/s}$$

Question 8

A rocket expels exhaust gases backward at a speed $$v_{	ext{ex}}$$ and burns fuel at a rate $$\dot{m}. $$What is the thrust produced by the rocket?

Accepted Answer

$$F = v_{	ext{ex}} \dot{m}$$

Question 9

A 55 kg athlete on a 2 kg skateboard throws a 0.6 kg javelin at 25 m/s. What is her recoil speed after the throw?

Accepted Answer

$$v_{	ext{recoil}} = -\frac{0.6\,	ext{kg} 	imes 25\,	ext{m/s}}{55\,	ext{kg} + 2\,	ext{kg}} = -0.26\,	ext{m/s}$$

Question 10

Which scenario results in the largest impulse delivered to a door: throwing a sticky ball of clay or a super-bouncy Superball of equal mass and speed?

Accepted Answer

Throwing the Superball delivers the largest impulse.

Question 11

In a head-on collision between a mosquito and a truck, which has the greater change in momentum magnitude?

Accepted Answer

Both have the same change in momentum magnitude.

Question 12

A force pushes a cart for 1 s, starting from rest. To achieve the same speed with a force half as big, how long must the force be applied?

Accepted Answer

2 s

Question 13

A 200 g glider moves at 3.0 m/s toward a 400 g glider at rest. After a perfectly inelastic collision, the combined gliders move at -0.40 m/s. What was the initial velocity of the 400 g glider?

Accepted Answer

$$v_{i2} = -2.1\,	ext{m/s}$$

Question 14

Which of the following is true for a perfectly elastic collision between two identical balls, one at rest and one moving?

Accepted Answer

The moving ball stops and the stationary ball moves with the initial velocity of the first ball.

Question 15

A 1 kg ball moving at 4 m/s collides elastically with a 2 kg ball at rest. What is the final velocity of the 1 kg ball?

Accepted Answer

$$v_{f1} = \frac{1 - 2}{1 + 2} 	imes 4 = -\frac{1}{3} 	imes 4 = -1.33\,	ext{m/s}$$

Question 16

Which principle allows you to solve for the final velocities in a collision when no external forces act on the system?

Accepted Answer

Conservation of momentum

Question 17

In a two-dimensional collision, which quantities must be conserved?

Accepted Answer

Both the x- and y-components of momentum

Question 18

A system of two boxes (1 kg and 2 kg) is at rest. An explosion pushes them apart. If the 1 kg box moves at 2 m/s to the left, what is the speed of the 2 kg box?

Accepted Answer

1 m/s to the right

11 - Impulse and Momentum: Principles, Applications, and Problem-Solving

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