Q: A 2 kg object is moving at 3 m/s. What is its kinetic energy?

$$K = \frac{1}{2}mv^2$ = \frac{1}{2} \times 2 \times 3^2$ = 9\ \mathrm{J}$$

Q: A 0.5 kg ball is dropped from a height of 10 m. What is its speed just before hitting the ground? (Ignore air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 10} = 14\ \mathrm{m/s}$$

Q: A 0.25 kg block compresses a spring ($$k = 5000\ \mathrm{N/m}) by 0.1 m $$and is then released. What is the maximum height it reaches above the release point? ($$g = 9.8\ \mathrm{m/s^2$})$$

$$h = \frac{1}{2}kx^2$ / mg = \frac{1}{2} \times 5000 \times 0.1^2$ / (0.25 \times 9.8) = 10.2\ \mathrm{m}$$

Q: A 1 kg object is thrown vertically upward with an initial speed of 10 m/s. What is the maximum height it reaches? ($$g = 9.8\ \mathrm{m/s^2$})$$

$$h = \frac{v^2$}{2g} = \frac{10^2$}{2 \times 9.8} = 5.1\ \mathrm{m}$$

Question 1

A 2 kg object is moving at 3 m/s. What is its kinetic energy?

Accepted Answer

$$K = \frac{1}{2}mv^2$ = \frac{1}{2} 	imes 2 	imes 3^2$ = 9\ \mathrm{J}$$

Question 2

A car increases its speed from 10 m/s to 20 m/s. By what factor does its kinetic energy increase?

Accepted Answer

The kinetic energy increases by a factor of 4.

Question 3

Which of the following best describes gravitational potential energy?

Accepted Answer

It depends only on the vertical height from a reference point: $$U = mgh$$

Question 4

A 0.5 kg ball is dropped from a height of 10 m. What is its speed just before hitting the ground? (Ignore air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 10} = 14\ \mathrm{m/s}$$

Question 5

A block of mass $$m$$ slides down a frictionless incline of height $$h. $$What is its speed at the bottom?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 6

A 0.25 kg block compresses a spring ($$k = 5000\ \mathrm{N/m}) by 0.1 m $$and is then released. What is the maximum height it reaches above the release point? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$h = \frac{1}{2}kx^2$ / mg = \frac{1}{2} 	imes 5000 	imes 0.1^2$ / (0.25 	imes 9.8) = 10.2\ \mathrm{m}$$

Question 7

Which of the following is true about conservative forces?

Accepted Answer

The work done by a conservative force is independent of the path taken.

Question 8

A sled of mass $$m is $$given an initial speed $$v_0 on $$ice with kinetic friction coefficient $$\mu_k. $$What is the distance $$d it $$travels before stopping?

Accepted Answer

$$d = \frac{v_0$^2}{2\mu_k g}$$

Question 9

A simple pendulum of length $$L = 2\ \mathrm{m} is $$released from $$30^\circ$$ with the vertical. What is the speed at the lowest point? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2gL(1-\cos 30^\circ)} = 2.29\ \mathrm{m/s}$$

Question 10

Which equation correctly expresses the conservation of mechanical energy for a falling object (ignoring air resistance)?

Accepted Answer

$$mgh_A + \frac{1}{2}mv_A^2$ = mgh_B + \frac{1}{2}mv_B^2$

Question 11

A spring with spring constant $$k is $$compressed by $$x. $$What is the potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2}kx^2$

Question 12

A 1 kg object is thrown vertically upward with an initial speed of 10 m/s. What is the maximum height it reaches? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$h = \frac{v^2$}{2g} = \frac{10^2$}{2 	imes 9.8} = 5.1\ \mathrm{m}$$

Question 13

Which of the following statements about friction is correct?

Accepted Answer

Friction is a nonconservative force and causes a loss of mechanical energy.

Question 14

A 3 kg object is moving at 4 m/s. How much work is required to bring it to rest?

Accepted Answer

$$W = -\frac{1}{2}mv^2$ = -\frac{1}{2} 	imes 3 	imes 4^2$ = -24\ \mathrm{J}$$

Question 15

A ball is thrown straight up with an initial velocity $$v_0. At $$its highest point, what is its kinetic and potential energy (relative to the launch point)?

Accepted Answer

Kinetic energy is zero; potential energy is $$U = \frac{1}{2}mv_0$^2$$

Question 16

A block slides down two different frictionless paths from the same height. Which statement is true about its speed at the bottom?

Accepted Answer

The speed is the same for both paths.

Question 17

If a nonconservative force does work $$W_{on} on a $$system, how is the total mechanical energy affected?

Accepted Answer

$$E_B = E_A + W_{on}$$

Question 18

A 5 kg box is lifted vertically 2 m at constant speed. What is the work done by gravity?

Accepted Answer

$$W = -mgh = -5 	imes 9.8 	imes 2 = -98\ \mathrm{J}$$

Work, Kinetic Energy, Potential Energy, and Conservation of Energy

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