Q: A 0.3-kg hockey puck moves on frictionless ice at 8 m/s toward a wall. It bounces back away from the wall at 5 m/s. The puck is in contact with the wall for 0.2 s. What is the average force exerted by the wall on the puck during the bounce?

$$F_{avg} = \frac{0.3\,\mathrm{kg} \times (5\,\mathrm{m/s} - (-8\,\mathrm{m/s}))}{0.2\,\mathrm{s}} = 19.5\,\mathrm{N}$$

Q: A 1800 kg car traveling at 27.8 m/s comes to a stop in $$1 \times 10$$^{-3}$$ s after hitting a stone embankment. What is the magnitude of the average force exerted on the car?

$$F = \frac{1800\,\mathrm{kg} \times 27.8\,\mathrm{m/s}}{1 \times 10$$^{-3}$$\,\mathrm{s}} = 5.0 \times 10^7$\,\mathrm{N}$$

Q: A 1000 kg car (Car A) moving at 5 m/s collides with a 5000 kg car (Car B) moving at 3 m/s in the same direction. If the cars stick together after the collision, what is their final velocity?

$$v_f = \frac{1000 \times 5 + 5000 \times 3}{1000 + 5000} = 3.33\,\mathrm{m/s}$$

Q: A system consists of two masses, $$m_1 = 3$$\,\mathrm{kg}$$ at x_1$ = 2\,\mathrm{m}$$ and $$m_2 = 5$$\,\mathrm{kg}$$ at x_2$ = 6\,\mathrm{m}. $$What is the $$x-$$coordinate of the center of mass?

$$x_{CM} = \frac{3 \times 2 + 5 \times 6}{3 + 5} = 4.5\,\mathrm{m}$$

Question 1

A 0.3-kg hockey puck moves on frictionless ice at 8 m/s toward a wall. It bounces back away from the wall at 5 m/s. The puck is in contact with the wall for 0.2 s. What is the average force exerted by the wall on the puck during the bounce?

Accepted Answer

$$F_{avg} = \frac{0.3\,\mathrm{kg} 	imes (5\,\mathrm{m/s} - (-8\,\mathrm{m/s}))}{0.2\,\mathrm{s}} = 19.5\,\mathrm{N}$$

Question 2

Which of the following statements about momentum is correct?

Accepted Answer

Momentum is a vector quantity defined as $$\vec{p} = m\vec{v}.$$

Question 3

A 1800 kg car traveling at 27.8 m/s comes to a stop in $$1 	imes 10$$^{-3}$$ s after hitting a stone embankment. What is the magnitude of the average force exerted on the car?

Accepted Answer

$$F = \frac{1800\,\mathrm{kg} 	imes 27.8\,\mathrm{m/s}}{1 	imes 10$$^{-3}$$\,\mathrm{s}} = 5.0 	imes 10^7$\,\mathrm{N}$$

Question 4

Which of the following best describes the impulse-momentum theorem?

Accepted Answer

The impulse on an object is equal to the change in its momentum: $$\vec{J} = \Delta \vec{p}.$$

Question 5

Two ice skaters, Skater A (50 kg) and Skater B (80 kg), stand on frictionless ice. Skater A pushes Skater B, causing Skater B to move away at 10 m/s. What is the velocity of Skater A after the push?

Accepted Answer

$$v_A = -16\,\mathrm{m/s}$$

Question 6

A 1000 kg car (Car A) moving at 5 m/s collides with a 5000 kg car (Car B) moving at 3 m/s in the same direction. If the cars stick together after the collision, what is their final velocity?

Accepted Answer

$$v_f = \frac{1000 	imes 5 + 5000 	imes 3}{1000 + 5000} = 3.33\,\mathrm{m/s}$$

Question 7

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

Accepted Answer

Both momentum and kinetic energy are conserved.

Question 8

A 2 kg object moving at 4 m/s collides elastically with a stationary 2 kg object. What are their velocities after the collision?

Accepted Answer

The first object stops, and the second moves at 4 m/s.

Question 9

Which of the following best describes the center of mass (CM) of a system?

Accepted Answer

The CM is the point where all the mass of the system is concentrated for the purpose of analyzing translational motion.

Question 10

A system consists of two masses, $$m_1 = 3$$\,\mathrm{kg}$$ at x_1$ = 2\,\mathrm{m}$$ and $$m_2 = 5$$\,\mathrm{kg}$$ at x_2$ = 6\,\mathrm{m}. $$What is the $$x-$$coordinate of the center of mass?

Accepted Answer

$$x_{CM} = \frac{3 	imes 2 + 5 	imes 6}{3 + 5} = 4.5\,\mathrm{m}$$

Question 11

Which of the following is NOT a requirement for the conservation of momentum in a system?

Accepted Answer

The total kinetic energy of the system must remain constant.

Question 12

A 1 kg ball moving at 2 m/s collides inelastically with a 3 kg ball at rest. What is their final velocity after sticking together?

Accepted Answer

$$v_f = \frac{1 	imes 2 + 3 	imes 0}{1 + 3} = 0.5\,\mathrm{m/s}$$

Question 13

Which of the following statements about impulse is correct?

Accepted Answer

Impulse is the area under the force vs. time curve.

Question 14

A 0.5 kg ball moving at 6 m/s collides elastically with a stationary 1.5 kg ball. What is the velocity of the 0.5 kg ball after the collision?

Accepted Answer

$$v_1$$' = \frac{0.5 - 1.5}{0.5 + 1.5} 	imes 6 = -3\,\mathrm{m/s}$$

Question 15

Which of the following best explains why the total kinetic energy is not conserved in a perfectly inelastic collision?

Accepted Answer

Some kinetic energy is converted into internal energy such as heat or deformation.

Question 16

A rocket expels fuel at a constant rate in space. Which form of Newton's second law is most appropriate for analyzing its motion?

Accepted Answer

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

Question 17

Which of the following is true about the center of mass of a system of particles?

Accepted Answer

The center of mass moves as if all external forces act at that point.

Question 18

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

Accepted Answer

$$v_1$$' = \frac{2 - 1}{2 + 1} 	imes 3 + \frac{2 	imes 1}{2 + 1} 	imes (-2) = 1 + (-1.33) = -0.33\,\mathrm{m/s}$$

Momentum, Impulse, and Collisions: Structured Study Notes

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