Q: A bowling ball of mass 7 kg rolls down the lane at 4 m/s and strikes a group of stationary pins with a total mass of 2 kg. If the ball and pins move together after the collision, what is their common velocity immediately after the collision? (Assume a completely inelastic collision and ignore friction.)

$$v = \frac{7 \times 4}{7 + 2} = \frac{28}{9} \approx 3.1\ \mathrm{m/s}$$

Q: A bullet of mass 0.01 kg is fired horizontally at 400 m/s into a carrot of mass 0.2 kg at rest on a frictionless surface. The bullet embeds in the carrot. What is the speed of the carrot-bullet system immediately after the collision?

$$v = \frac{0.01 \times 400}{0.01 + 0.2} = \frac{4}{0.21} \approx 19.0\ \mathrm{m/s}$$

Q: A 0.06 kg tennis ball is hit by a racket, changing its velocity from 0 m/s to 55 m/s in 0.004 s. What is the average force exerted on the ball by the racket?

$$F_{avg} = \frac{0.06 \times 55}{0.004} = 825\ \mathrm{N}$$

Q: A soccer player kicks a stationary ball of mass 0.5 kg, giving it a velocity of 20 m/s. If the player's foot was in contact with the ball for 0.05 s, what was the average force exerted on the ball?

$$F_{avg} = \frac{0.5 \times 20}{0.05} = 200\ \mathrm{N}$$

Q: A 0.4 kg ball is thrown at a wall at 30 m/s to the left and rebounds at 20 m/s to the right. What is the impulse delivered to the ball by the wall?

$$J = m(v_{f} - v_{i}) = 0.4 \times (20 - (-30)) = 0.4 \times 50 = 20\ \mathrm{kg \cdot m/s}$$

Q: A system of two particles, one of mass 2 kg at (2,0) and one of mass 3 kg at (0,4), has its center of mass at which coordinates?

$$(x_{cm}, y_{cm}) = \left( \frac{2 \times 2 + 3 \times 0}{2 + 3}, \frac{2 \times 0 + 3 \times 4}{2 + 3} \right ) = (0.8, 2.4)$$

Question 1

A bowling ball of mass 7 kg rolls down the lane at 4 m/s and strikes a group of stationary pins with a total mass of 2 kg. If the ball and pins move together after the collision, what is their common velocity immediately after the collision? (Assume a completely inelastic collision and ignore friction.)

Accepted Answer

$$v = \frac{7 	imes 4}{7 + 2} = \frac{28}{9} \approx 3.1\ \mathrm{m/s}$$

Question 2

A bullet of mass 0.01 kg is fired horizontally at 400 m/s into a carrot of mass 0.2 kg at rest on a frictionless surface. The bullet embeds in the carrot. What is the speed of the carrot-bullet system immediately after the collision?

Accepted Answer

$$v = \frac{0.01 	imes 400}{0.01 + 0.2} = \frac{4}{0.21} \approx 19.0\ \mathrm{m/s}$$

Question 3

Two rams of equal mass run directly toward each other and collide head-on. If both have the same speed but in opposite directions, what is the total momentum of the system after the collision (assuming they stick together)?

Accepted Answer

$$0$$

Question 4

A railroad car loaded with rocks coasts on a level track without friction. A worker at the back of the car starts throwing the rocks horizontally backward from the car. What happens to the speed of the car?

Accepted Answer

The car speeds up.

Question 5

A 0.06 kg tennis ball is hit by a racket, changing its velocity from 0 m/s to 55 m/s in 0.004 s. What is the average force exerted on the ball by the racket?

Accepted Answer

$$F_{avg} = \frac{0.06 	imes 55}{0.004} = 825\ \mathrm{N}$$

Question 6

Which of the following statements about impulse is correct?

Accepted Answer

Impulse is equal to the change in momentum of a particle.

Question 7

A soccer player kicks a stationary ball of mass 0.5 kg, giving it a velocity of 20 m/s. If the player's foot was in contact with the ball for 0.05 s, what was the average force exerted on the ball?

Accepted Answer

$$F_{avg} = \frac{0.5 	imes 20}{0.05} = 200\ \mathrm{N}$$

Question 8

A 0.4 kg ball is thrown at a wall at 30 m/s to the left and rebounds at 20 m/s to the right. What is the impulse delivered to the ball by the wall?

Accepted Answer

$$J = m(v_{f} - v_{i}) = 0.4 	imes (20 - (-30)) = 0.4 	imes 50 = 20\ \mathrm{kg \cdot m/s}$$

Question 9

A tennis ball of mass $$m is $$dropped from height $$h$$ and rebounds to height $$h'. $$What is the magnitude of the impulse delivered to the ball by the floor?

Accepted Answer

$$J = m(\sqrt{2gh} + \sqrt{2gh'})$$

Question 10

Which of the following best describes the difference between momentum and kinetic energy?

Accepted Answer

Momentum depends on the time over which a net force acts, while kinetic energy depends on the distance over which the net force acts.

Question 11

A 2 kg object moving at 3 m/s collides elastically with a stationary 1 kg object. What is the velocity of the 2 kg object after the collision?

Accepted Answer

$$v_{1f} = \frac{m_1$ - m_2$}{m_1$ + m_2$} v_{1i} = \frac{2 - 1}{2 + 1} 	imes 3 = \frac{1}{3} 	imes 3 = 1\ \mathrm{m/s}$$

Question 12

A system of two particles, one of mass 2 kg at (2,0) and one of mass 3 kg at (0,4), has its center of mass at which coordinates?

Accepted Answer

$$(x_{cm}, y_{cm}) = \left( \frac{2 	imes 2 + 3 	imes 0}{2 + 3}, \frac{2 	imes 0 + 3 	imes 4}{2 + 3} ight ) = (0.8, 2.4)$$

Question 13

A wrench is thrown across a smooth tabletop with a spinning motion. What path does the center of mass of the wrench follow?

Accepted Answer

A straight line, as if all the mass were concentrated at that point.

Question 14

A 3 kg object moving at 2 m/s collides inelastically with a 2 kg object at rest. What is the final velocity of the combined mass?

Accepted Answer

$$v = \frac{3 	imes 2}{3 + 2} = \frac{6}{5} = 1.2\ \mathrm{m/s}$$

Question 15

Which of the following is true about the conservation of momentum in a system?

Accepted Answer

Momentum is conserved if the vector sum of external forces on the system is zero.

Question 16

A 0.5 kg ball moving at 10 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 17

A 1 kg object moving at 3 m/s collides with a 2 kg object moving at -2 m/s. What is the total momentum of the system before the collision?

Accepted Answer

$$p_{total} = 1 	imes 3 + 2 	imes (-2) = 3 - 4 = -1\ \mathrm{kg \cdot m/s}$$

Momentum, Impulse, and Collisions: Structured Study Notes

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