Q: A worker pushes a box with a force of 50 N at an angle of 30° to the horizontal, moving it 10 m across a level floor. What is the work done by the worker on the box?

$$W = (50 \cos 30^\circ) \times 10 = 433 \text{ J}$$

Q: A spring with spring constant $$k = 200 \text{ N/m} is $$compressed by $$x = 0.1 \text{ m}. $$What is the work done by the spring force?

$$W = -\frac{1}{2} k x^2$ = -1 \text{ J}$$

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

$$K = \frac{1}{2} m v^2$ = 9 \text{ J}$$

Q: A car accelerates from rest to 20 m/s. If its mass is 1000 kg, what is the net work done on the car?

$$W_{net} = \frac{1}{2} m v^2$ = 200,000 \text{ J}$$

Q: A machine does 5000 J of work in 10 seconds. What is its power output?

$$P = \frac{W}{t} = 500 \text{ W}$$

Q: A 0.5 kg ball is dropped from a height of 4 m. What is its speed just before hitting the ground? (Ignore air resistance, $$g = 9.8 \text{ m/s}^2)$$

$$v = \sqrt{2 g h} = 8.85 \text{ m/s}$$

Q: Which unit is equivalent to a Joule?

$$1 \text{ J} = 1 \text{ kg} \cdot \text{m}^2 / \text{s}^2$$

Question 1

A worker pushes a box with a force of 50 N at an angle of 30° to the horizontal, moving it 10 m across a level floor. What is the work done by the worker on the box?

Accepted Answer

$$W = (50 \cos 30^\circ) 	imes 10 = 433 	ext{ J}$$

Question 2

Which of the following statements about work is correct?

Accepted Answer

Work is a scalar quantity and can be positive, negative, or zero depending on the direction of force and displacement.

Question 3

A spring with spring constant $$k = 200 	ext{ N/m} is $$compressed by $$x = 0.1 	ext{ m}. $$What is the work done by the spring force?

Accepted Answer

$$W = -\frac{1}{2} k x^2$ = -1 	ext{ J}$$

Question 4

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

Accepted Answer

$$K = \frac{1}{2} m v^2$ = 9 	ext{ J}$$

Question 5

Which of the following is NOT a form of mechanical energy?

Accepted Answer

Electromagnetic energy

Question 6

A car accelerates from rest to 20 m/s. If its mass is 1000 kg, what is the net work done on the car?

Accepted Answer

$$W_{net} = \frac{1}{2} m v^2$ = 200,000 	ext{ J}$$

Question 7

If a force is perpendicular to the displacement of an object, what is the work done by that force?

Accepted Answer

$$W = F \cos 90^\circ \Delta x = 0$$

Question 8

A person lifts a 10 kg box vertically upward by 2 m. What is the work done against gravity? (Assume $$g = 9.8 	ext{ m/s}^2)$$

Accepted Answer

$$W = m g h = 196 	ext{ J}$$

Question 9

Which of the following best describes the work-energy theorem?

Accepted Answer

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

Question 10

A machine does 5000 J of work in 10 seconds. What is its power output?

Accepted Answer

$$P = \frac{W}{t} = 500 	ext{ W}$$

Question 11

A 0.5 kg ball is dropped from a height of 4 m. What is its speed just before hitting the ground? (Ignore air resistance, $$g = 9.8 	ext{ m/s}^2)$$

Accepted Answer

$$v = \sqrt{2 g h} = 8.85 	ext{ m/s}$$

Question 12

Which unit is equivalent to a Joule?

Accepted Answer

$$1 	ext{ J} = 1 	ext{ kg} \cdot 	ext{m}^2 / 	ext{s}^2$$

Question 13

A spring is stretched by 0.2 m and the work required is 4 J. What is the spring constant $$k$$?

Accepted Answer

$$k = \frac{2W}{x^2$} = 200 	ext{ N/m}$$

Question 14

Which of the following is the correct expression for the work done by a variable force $$F(x)$$ over a displacement from $$x_1 to$$ $$x_2$$?

Accepted Answer

$$W = \int_{x_1$}^{x_2$} F(x) \, dx$$

Question 15

A 1500 kg car moving at 10 m/s comes to a stop. How much work is done by the brakes?

Accepted Answer

$$W = -\frac{1}{2} m v^2$ = -75,000 	ext{ J}$$

Question 16

Which of the following is the correct conversion for horsepower to Watts?

Accepted Answer

$$1 	ext{ hp} = 746 	ext{ W}$$

Question 17

Which of the following scenarios results in negative work being done?

Accepted Answer

A person pushes a box to the left while the box moves to the right.

Question 18

What does the unit kilowatt-hour (kWh) represent?

Accepted Answer

It is a unit of energy equal to $$3.6 	imes 10^6$ 	ext{ J}$$

Work and Kinetic Energy: Chapter 7 Study Notes

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