Q: A 30.0-kg package is pushed with a constant force of 120 N through a distance of 0.800 m against a friction force of 5.00 N. What is the net work done on the package?

$$W_{net} = (120\,\text{N} - 5.00\,\text{N}) \times 0.800\,\text{m} = 92.0\,\text{J}$$

Q: A child pulls a wagon with a force of 16.0 N for 10.0 m at an angle of 25.0° above the horizontal. How much work does the child do?

$$W = 16.0\,\text{N} \times 10.0\,\text{m} \times \cos(25.0^\circ) = 145\,\text{J}$$

Q: A force of 50.0 N is applied at an angle of 30.0° to the horizontal to move a vacuum cleaner 3.00 m. What is the work done by the applied force?

$$W = 50.0\,\text{N} \times 3.00\,\text{m} \times \cos(30.0^\circ) = 130\,\text{J}$$

Q: A 2.0 kg object is dropped from a height of 10 m. What is the work done by gravity?

$$W = mgh = 2.0\,\text{kg} \times 9.8\,\text{m/s}^2 \times 10\,\text{m} = 196\,\text{J}$$

Q: A 50-kg crate is pulled 40 m along a horizontal floor by a force of 100 N at a 37° angle. The friction force is 50 N. What is the net work done on the crate?

$$W_{net} = (100\,\text{N} \times \cos(37^\circ) - 50\,\text{N}) \times 40\,\text{m} = 1195\,\text{J}$$

Q: A force $$\vec{F} = (5.0\hat{i} + 2.0\hat{j}) N $$acts on a particle that undergoes a displacement $$\vec{r} = (2.0\hat{i} + 3.0\hat{j}) m. $$What is the work done by the force?

$$W = \vec{F} \cdot \vec{r} = 5.0 \times 2.0 + 2.0 \times 3.0 = 10 + 6 = 16\,\text{J}$$

Question 1

A 30.0-kg package is pushed with a constant force of 120 N through a distance of 0.800 m against a friction force of 5.00 N. What is the net work done on the package?

Accepted Answer

$$W_{net} = (120\,	ext{N} - 5.00\,	ext{N}) 	imes 0.800\,	ext{m} = 92.0\,	ext{J}$$

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 angle between force and displacement.

Question 3

A child pulls a wagon with a force of 16.0 N for 10.0 m at an angle of 25.0° above the horizontal. How much work does the child do?

Accepted Answer

$$W = 16.0\,	ext{N} 	imes 10.0\,	ext{m} 	imes \cos(25.0^\circ) = 145\,	ext{J}$$

Question 4

A force of 50.0 N is applied at an angle of 30.0° to the horizontal to move a vacuum cleaner 3.00 m. What is the work done by the applied force?

Accepted Answer

$$W = 50.0\,	ext{N} 	imes 3.00\,	ext{m} 	imes \cos(30.0^\circ) = 130\,	ext{J}$$

Question 5

A 2.0 kg object is dropped from a height of 10 m. What is the work done by gravity?

Accepted Answer

$$W = mgh = 2.0\,	ext{kg} 	imes 9.8\,	ext{m/s}^2 	imes 10\,	ext{m} = 196\,	ext{J}$$

Question 6

Which of the following situations results in zero work being done?

Accepted Answer

A force is applied perpendicular to the direction of displacement.

Question 7

A 50-kg crate is pulled 40 m along a horizontal floor by a force of 100 N at a 37° angle. The friction force is 50 N. What is the net work done on the crate?

Accepted Answer

$$W_{net} = (100\,	ext{N} 	imes \cos(37^\circ) - 50\,	ext{N}) 	imes 40\,	ext{m} = 1195\,	ext{J}$$

Question 8

A force $$\vec{F} = (5.0\hat{i} + 2.0\hat{j}) N $$acts on a particle that undergoes a displacement $$\vec{r} = (2.0\hat{i} + 3.0\hat{j}) m. $$What is the work done by the force?

Accepted Answer

$$W = \vec{F} \cdot \vec{r} = 5.0 	imes 2.0 + 2.0 	imes 3.0 = 10 + 6 = 16\,	ext{J}$$

Question 9

In a baseball game, the catcher stops a fast-moving ball. What is the sign of the work done by the catcher on the ball?

Accepted Answer

Negative, because the force exerted by the catcher is opposite to the ball's displacement.

Question 10

A box is being pulled up a rough incline by a rope connected to a pulley. How many forces are doing work on the box?

Accepted Answer

Three forces: tension, friction, and gravity.

Question 11

Which equation correctly expresses the work done by a constant force $$\vec{F}$$ acting at an angle $$	heta to $$the displacement $$\vec{d}$$?

Accepted Answer

$$W = Fd \cos 	heta$$

Question 12

A weightlifter holds a barbell stationary above his head. What is the work done by the weightlifter on the barbell?

Accepted Answer

Zero, because the displacement is zero.

Question 13

A force of 20.0 N acts at 30° to the direction of displacement of 0.600 m up a frictionless incline. What is the work done by this force?

Accepted Answer

$$W = 20.0\,	ext{N} 	imes 0.600\,	ext{m} 	imes \cos(30^\circ) = 10.4\,	ext{J}$$

Question 14

Which of the following is the SI unit of work?

Accepted Answer

Joule ($$1\,	ext{J} = 1\,	ext{N} \cdot 	ext{m})$$

Question 15

A force of 60 N is applied at a 35° angle to the horizontal to pull a box 45 m on a level floor. What is the work done by the force?

Accepted Answer

$$W = 60\,	ext{N} 	imes 45\,	ext{m} 	imes \cos(35^\circ) = 2200\,	ext{J}$$

Question 16

If a force is applied in the opposite direction to the displacement, what is the sign of the work done?

Accepted Answer

Negative

Question 17

Which of the following best describes the relationship between work and energy?

Accepted Answer

Whenever work is done, energy is transferred.

Question 18

A force of 10 N is applied perpendicular to a displacement of 5 m. What is the work done by the force?

Accepted Answer

$$W = 10\,	ext{N} 	imes 5\,	ext{m} 	imes \cos(90^\circ) = 0\,	ext{J}$$

Work and Kinetic Energy: Concepts, Calculations, and Applications

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