Q: A meteor of mass $$1.4 \times 10^8$ kg released 1$$ \times $$10^{16} J of $$energy upon impact. What was its approximate speed before impact?

$$v = \sqrt{\frac{2E}{m}} = \sqrt{\frac{2 \times 1 \times 10$$^{16}$$}{1.4 \times 10^8$}} \approx 12,000\ m/s$$

Q: You pull a 2 kg box with a 3 N force for 5 m horizontally. How much work do you do?

$$W = Fd = 3 \times 5 = 15\ J$$

Q: A 10 kg suitcase is pulled with a 50 N force at 37° above the horizontal for 20 m. What is the work done by the horizontal component of the force?

$$W = F_x d = (50 \cos 37^\circ) \times 20 \approx 40 \times 20 = 800\ J$$

Q: A box weighing 50 N is pulled horizontally with 60 N for 8 m. The coefficient of kinetic friction is $$\mu_k = 0.7. $$What is the work done by friction?

$$W_{f_k} = -f_k d = -\mu_k N d = -0.7 \times 50 \times 8 = -280\ J$$

Q: A 75 kg hiker climbs a 1,000 m mountain. What is the work done by gravity?

$$W_g = -mgh = -75 \times 9.8 \times 1000 = -735,000\ J$$

Q: A 100 kg box is released at the top of a 12 m incline at 37°. What is the work done by gravity?

$$W_g = mg \Delta y = 100 \times 9.8 \times (12 \sin 37^\circ) \approx 100 \times 9.8 \times 7.23 = 7,085\ J$$

Question 1

Which of the following best describes kinetic energy?

Accepted Answer

The energy an object has due to its motion, calculated as $$\frac{1}{2}mv^2$.

Question 2

A 5 kg box moves to the right at 3 m/s. What is its kinetic energy?

Accepted Answer

$$KE = \frac{1}{2}mv^2$ = \frac{1}{2}(5)(3^2$) = 22.5\ J$$

Question 3

A meteor of mass $$1.4 	imes 10^8$ kg released 1$$ 	imes $$10^{16} J of $$energy upon impact. What was its approximate speed before impact?

Accepted Answer

$$v = \sqrt{\frac{2E}{m}} = \sqrt{\frac{2 	imes 1 	imes 10$$^{16}$$}{1.4 	imes 10^8$}} \approx 12,000\ m/s$$

Question 4

Which equation correctly expresses the work done by a constant force $$\vec{F}$$ over a displacement $$\Delta \vec{x} at an $$angle $$	heta$$?

Accepted Answer

$$W = Fd\cos	heta$$

Question 5

You pull a 2 kg box with a 3 N force for 5 m horizontally. How much work do you do?

Accepted Answer

$$W = Fd = 3 	imes 5 = 15\ J$$

Question 6

A 10 kg suitcase is pulled with a 50 N force at 37° above the horizontal for 20 m. What is the work done by the horizontal component of the force?

Accepted Answer

$$W = F_x d = (50 \cos 37^\circ) 	imes 20 \approx 40 	imes 20 = 800\ J$$

Question 7

A box weighing 50 N is pulled horizontally with 60 N for 8 m. The coefficient of kinetic friction is $$\mu_k = 0.7. $$What is the work done by friction?

Accepted Answer

$$W_{f_k} = -f_k d = -\mu_k N d = -0.7 	imes 50 	imes 8 = -280\ J$$

Question 8

Which of the following statements about the work done by gravity is correct?

Accepted Answer

It depends only on the vertical displacement, not the path taken.

Question 9

A 75 kg hiker climbs a 1,000 m mountain. What is the work done by gravity?

Accepted Answer

$$W_g = -mgh = -75 	imes 9.8 	imes 1000 = -735,000\ J$$

Question 10

Calculate the dot product $$\vec{A} \cdot \vec{B}$$ for $$\vec{A} = 2\hat{i} + 3\hat{j}$$ and $$\vec{B} = \hat{i} + 2\hat{j}.$$

Accepted Answer

$$\vec{A} \cdot \vec{B} = (2)(1) + (3)(2) = 2 + 6 = 8$$

Question 11

A 100 kg box is released at the top of a 12 m incline at 37°. What is the work done by gravity?

Accepted Answer

$$W_g = mg \Delta y = 100 	imes 9.8 	imes (12 \sin 37^\circ) \approx 100 	imes 9.8 	imes 7.23 = 7,085\ J$$

Question 12

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

Accepted Answer

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

Question 13

Which of the following is the correct statement of the work-energy theorem?

Accepted Answer

$$W_{net} = \Delta K = K_f - K_i$$

Question 14

A 4 kg box speeds up from 6 m/s to 10 m/s. How much net work was done?

Accepted Answer

$$W_{net} = \Delta K = \frac{1}{2}m(v_f^2$ - v_i^2$) = \frac{1}{2} 	imes 4 	imes (100 - 36) = 2 	imes 64 = 128\ J$$

Question 15

Which of the following best describes the work done by a spring when compressed by $$x$$?

Accepted Answer

$$W_s = -\frac{1}{2}kx^2$

Question 16

A spring with $$k = 500\ N/m is $$compressed by 2 m. What is the work done by the spring?

Accepted Answer

$$W_s = -\frac{1}{2}kx^2$ = -\frac{1}{2} 	imes 500 	imes 4 = -1000\ J$$

Question 17

How is average power defined in terms of work and time?

Accepted Answer

$$P_{avg} = \frac{W}{\Delta t}$$

Question 18

An elevator motor lifts a 1000 kg elevator 100 m in 50 s at constant speed. What is the required power?

Accepted Answer

$$P = \frac{mgh}{t} = \frac{1000 	imes 9.8 	imes 100}{50} = 19,600\ W$$

Ch 09: Work and Kinetic Energy – Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards