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

$$K = \frac{1}{2} \times 5 \times 3^2$ = 22.5\ \text{J}$$

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

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

Q: You pull a 10 kg suitcase with a 50 N force at 37° above the floor for 20 m. What is the work done by your pull?

$$W = 50 \times 20 \times \cos 37^\circ = 798\ \text{J}$$

Q: A 5.1 kg book falls from a 2 m shelf. What is the work done by gravity?

$$W_g = mg\Delta y = 5.1 \times 9.8 \times 2 = 99.96\ \text{J}$$

Q: 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?

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

Q: A spring with $$k = 500\ \text{N/m} is $$compressed by 2 m. What is the work done BY the spring?

$$W_s = -\frac{1}{2}kx^2$ = -\frac{1}{2} \times 500 \times 2^2$ = -1000\ \text{J}$$

Q: A 15 kg block accelerates from 10 m/s to 30 m/s. What is the change in its kinetic energy?

$$\Delta K = \frac{1}{2}m(v_f^2$ - v_i^2$) = \frac{1}{2} \times 15 \times (30^2$ - 10^2$) = 3000\ \text{J}$$

Question 1

Which of the following best describes kinetic energy?

Accepted Answer

The energy an object has due to its motion, calculated by $$K = \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

$$K = \frac{1}{2} 	imes 5 	imes 3^2$ = 22.5\ 	ext{J}$$

Question 3

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

Accepted Answer

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

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 10 kg suitcase with a 50 N force at 37° above the floor for 20 m. What is the work done by your pull?

Accepted Answer

$$W = 50 	imes 20 	imes \cos 37^\circ = 798\ 	ext{J}$$

Question 6

A 5.1 kg book falls from a 2 m shelf. What is the work done by gravity?

Accepted Answer

$$W_g = mg\Delta y = 5.1 	imes 9.8 	imes 2 = 99.96\ 	ext{J}$$

Question 7

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

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

Question 8

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

Accepted Answer

It depends only on the change in vertical position, not the path taken.

Question 9

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

Accepted Answer

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

Question 10

A force vs. displacement graph is shown for a box. The work done by the force is:

Accepted Answer

The area under the $$F vs$$. $$x$$ graph.

Question 11

A 15 kg block accelerates from 10 m/s to 30 m/s. What is the change in its kinetic energy?

Accepted Answer

$$\Delta K = \frac{1}{2}m(v_f^2$ - v_i^2$) = \frac{1}{2} 	imes 15 	imes (30^2$ - 10^2$) = 3000\ 	ext{J}$$

Question 12

Which of the following is the correct expression for average power?

Accepted Answer

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

Question 13

A 1000 kg elevator is lifted 100 m in 50 s at constant speed. What is the required power?

Accepted Answer

$$P = \frac{mg\Delta y}{\Delta t} = \frac{1000 	imes 9.8 	imes 100}{50} = 19,600\ 	ext{W}$$

Question 14

A 3 kg box is pulled horizontally with a force of 40 N at 53° for 2 m. What is the work done by the horizontal component of the force?

Accepted Answer

$$W = 40 	imes \cos 53^\circ 	imes 2 = 48.1\ 	ext{J}$$

Question 15

A 51 kg crate is pulled 3 m with a 100 N force at 37° above the horizontal. The coefficient of friction is 0.16. What is the total work done on the crate?

Accepted Answer

$$W_{net} = 29\ 	ext{J}$$

Question 16

A box slides across the floor with an initial speed of 3.5 m/s. The coefficient of kinetic friction is 0.15. How far will the box slide before stopping?

Accepted Answer

$$d = \frac{v_0$^2}{2\mu_k g} = \frac{3.5^2$}{2 	imes 0.15 	imes 9.8} = 4.17\ 	ext{m}$$

Question 17

Which of the following is true about the net work done on an object?

Accepted Answer

It equals the change in kinetic energy: $$W_{net} = \Delta K$$

Question 18

A spring is compressed from 1.0 m to 0.7 m with 200 J of work. How much additional work is needed to compress it from 0.7 m to 0.5 m?

Accepted Answer

$$W = \frac{1}{2}k(x_1$^2 - x_2$^2)$$, where $$k = \frac{2 	imes 200}{(1.0^2$ - 0.7^2$)} = 588.2\ 	ext{N/m}$$, so $$W = \frac{1}{2} 	imes 588.2 	imes (0.7^2$ - 0.5^2$) = 117.6\ 	ext{J}$$

Work & Kinetic Energy: Structured Study Notes (Young & Freedman, Ch 06)

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