Q: A 5 kg box is pushed across a horizontal surface with a constant force of 20 N for 4 m. The force is applied at an angle of $$30^\circ$$ above the horizontal. What is the work done by the applied force?

$$W = Fd\cos\theta = 20 \times 4 \times \cos 30^\circ = 69.3\ \text{J}$$

Q: A 2 kg object is dropped from a height of 10 m. What is the work done by gravity during the fall?

$$W_g = -mg\Delta y = -2 \times 9.8 \times (-10) = 196\ \text{J}$$

Q: A 10 kg box slides down a 5 m long ramp inclined at $$30^\circ to $$the horizontal. What is the work done by gravity?

$$W_g = mg\Delta y = 10 \times 9.8 \times (5 \sin 30^\circ) = 245\ \text{J}$$

Q: A 3 kg box is pulled horizontally with a force of 15 N across a rough surface for 6 m. The coefficient of kinetic friction is 0.2. What is the net work done on the box?

$$W_{NET} = (F - f_k)d = (15 - 0.2 \times 3 \times 9.8) \times 6 = 15.8\ \text{J}$$

Q: A spring with a spring constant $$k = 200\ \text{N/m} is $$compressed by 0.1 m. What is the work done BY the spring as it returns to its equilibrium position?

$$W_s = -\frac{1}{2}kx^2$ = -\frac{1}{2} \times 200 \times (0.1)^2$ = -1\ \text{J}$$

Q: A force vs. displacement graph for a box shows a constant force of 10 N applied over 5 m. What is the total work done?

$$W = Fd = 10 \times 5 = 50\ \text{J}$$

Q: A 4 kg box is initially at rest. A variable force is applied, and the area under the force vs. displacement graph from $$x=0 to$$ $$x=4 m is 20 J. $$What is the speed of the box at $$x=4 m$$?

$$K = \frac{1}{2}mv^2$ = 20 \implies v = \sqrt{\frac{2 \times 20}{4}} = \sqrt{10} = 3.16\ \text{m/s}$$

Q: A 7 kg crate slides 2.5 m down a ramp inclined at $$26^\circ. $$The coefficient of friction is 0.36. What is the work done by friction?

$$W_f = -\mu_k mg \cos \theta \times d = -0.36 \times 7 \times 9.8 \times \cos 26^\circ \times 2.5 = -55.6\ \text{J}$$

Question 1

Which of the following statements best describes the Work-Energy Theorem?

Accepted Answer

The net work done on an object is equal to its change in kinetic energy: $$W_{NET} = \Delta K = K_f - K_i$$

Question 2

A 5 kg box is pushed across a horizontal surface with a constant force of 20 N for 4 m. The force is applied at an angle of $$30^\circ$$ above the horizontal. What is the work done by the applied force?

Accepted Answer

$$W = Fd\cos	heta = 20 	imes 4 	imes \cos 30^\circ = 69.3\ 	ext{J}$$

Question 3

A 2 kg object is dropped from a height of 10 m. What is the work done by gravity during the fall?

Accepted Answer

$$W_g = -mg\Delta y = -2 	imes 9.8 	imes (-10) = 196\ 	ext{J}$$

Question 4

A 10 kg box slides down a 5 m long ramp inclined at $$30^\circ to $$the horizontal. What is the work done by gravity?

Accepted Answer

$$W_g = mg\Delta y = 10 	imes 9.8 	imes (5 \sin 30^\circ) = 245\ 	ext{J}$$

Question 5

A 3 kg box is pulled horizontally with a force of 15 N across a rough surface for 6 m. The coefficient of kinetic friction is 0.2. What is the net work done on the box?

Accepted Answer

$$W_{NET} = (F - f_k)d = (15 - 0.2 	imes 3 	imes 9.8) 	imes 6 = 15.8\ 	ext{J}$$

Question 6

A spring with a spring constant $$k = 200\ 	ext{N/m} is $$compressed by 0.1 m. What is the work done BY the spring as it returns to its equilibrium position?

Accepted Answer

$$W_s = -\frac{1}{2}kx^2$ = -\frac{1}{2} 	imes 200 	imes (0.1)^2$ = -1\ 	ext{J}$$

Question 7

A 1000 kg elevator is lifted at a constant speed to a height of 50 m in 25 seconds. What is the average power supplied by the motor?

Accepted Answer

$$P_{avg} = \frac{W}{\Delta t} = \frac{mgh}{t} = \frac{1000 	imes 9.8 	imes 50}{25} = 19,600\ 	ext{W}$$

Question 8

A force vs. displacement graph for a box shows a constant force of 10 N applied over 5 m. What is the total work done?

Accepted Answer

$$W = Fd = 10 	imes 5 = 50\ 	ext{J}$$

Question 9

A 4 kg box is initially at rest. A variable force is applied, and the area under the force vs. displacement graph from $$x=0 to$$ $$x=4 m is 20 J. $$What is the speed of the box at $$x=4 m$$?

Accepted Answer

$$K = \frac{1}{2}mv^2$ = 20 \implies v = \sqrt{\frac{2 	imes 20}{4}} = \sqrt{10} = 3.16\ 	ext{m/s}$$

Question 10

A 7 kg crate slides 2.5 m down a ramp inclined at $$26^\circ. $$The coefficient of friction is 0.36. What is the work done by friction?

Accepted Answer

$$W_f = -\mu_k mg \cos 	heta 	imes d = -0.36 	imes 7 	imes 9.8 	imes \cos 26^\circ 	imes 2.5 = -55.6\ 	ext{J}$$

Question 11

Which of the following is true about kinetic energy?

Accepted Answer

Kinetic energy is always positive and has no direction: $$K = \frac{1}{2}mv^2$

Question 12

A 15 kg block is accelerated from 10 m/s to 30 m/s in 5 seconds. What is the average power delivered to the block?

Accepted Answer

$$\Delta K = \frac{1}{2} 	imes 15 	imes (30^2$ - 10^2$) = 6000\ 	ext{J}$$, $$P_{avg} = \frac{6000}{5} = 1200\ 	ext{W}$$

Question 13

A 1.0 m-long spring requires 200 J to compress to 70 cm. How much additional work is needed to compress it from 70 cm to 50 cm?

Accepted Answer

$$W = \frac{1}{2}k(x_2$^2 - x_1$^2)$$,\ where\ $$x_1 = 0.3$$\ 	ext{m},\ $$x_2 = 0.5$$\ 	ext{m}$

Question 14

Which of the following best describes the work done by friction on a moving object?

Accepted Answer

Friction always does negative work because it opposes the direction of motion.

Question 15

A 19 kg crate is pulled up a 15 m ramp inclined at $$36^\circ$$ with a constant 130 N force parallel to the ramp. What is the work done by gravity?

Accepted Answer

$$W_g = -mg\Delta y = -19 	imes 9.8 	imes (15 \sin 36^\circ) = -1,734\ 	ext{J}$$

Question 16

Which of the following is true about the work done by gravity on an object moving along any path between two points?

Accepted Answer

The work done by gravity depends only on the vertical displacement, not the path taken.

Work & Energy: Physics Study Guide

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