Q: A student pushes a box with a constant horizontal force of 50 N over a distance of 6.0 m in the direction of the force. What is the work done by the student on the box? Use $$W = Fd \cos \theta$$ with $$\theta = 0^\circ.$$

$$W = 50 \times 6.0 \times \cos 0^\circ = 300 J$$

Q: A rope pulls a sled with a force of 80 N at an angle of $$30^\circ$$ above the horizontal. The sled moves 5.0 m horizontally. What is the work done by the rope?

$$W = 80 \times 5.0 \times \cos 30^\circ = 346 J$$

Q: A 2.0 kg object speeds up from 3.0 m/s to 7.0 m/s. Using the work-energy theorem, what is the net work done on the object?

$$W_{net} = \frac{1}{2} \times 2.0 \times (7.0^2$ - 3.0^2$) = 56 J$$

Q: A 1200 kg car slows from 20 m/s to rest due to braking. What is the net work done on the car?

$$W_{net} = \frac{1}{2} \times 1200 \times (0^2$ - 20^2$) = -240,000 J$$

Q: A 15 kg backpack is lifted straight up 2.0 m at constant speed. What is the work done by the lifting force?

$$W = mgh = 15 \times 9.8 \times 2.0 = 294 J$$

Q: A 5.0 kg box slides 4.0 m across a rough horizontal floor. The coefficient of kinetic friction is 0.20. What is the work done by friction?

$$W_{fric} = -\mu_k mg d = -0.20 \times 5.0 \times 9.8 \times 4.0 = -39.2 J$$

Q: A 60 kg rider starts from rest at the top of a frictionless roller coaster hill and drops 12 m vertically. What is the rider's speed at the bottom?

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 12} = 15.3 m/s$$

Q: A spring with a spring constant of 200 N/m is compressed by 0.25 m. What is the elastic potential energy stored in the spring?

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} \times 200 \times (0.25)^2$ = 6.25 J$$

Q: A force-displacement graph shows force increasing linearly from 0 N at 0 m to 40 N at 4 m, then staying at 40 N from 4 m to 8 m. What is the total work done?

Work = Area under the graph = $$\frac{1}{2} \times 4 \times 40 + 40 \times 4 = 80 + 160 = 240 J$$

Q: A 0.15 kg baseball moves at 40 m/s, and a 60 kg runner moves at 2.0 m/s. Which has greater kinetic energy?

Baseball: $$KE = \frac{1}{2} \times 0.15 \times 40^2$ = 120 J$$; Runner: $$KE = \frac{1}{2} \times 60 \times 2^2$ = 120 J$$; They have equal kinetic energy.

Question 1

A student pushes a box with a constant horizontal force of 50 N over a distance of 6.0 m in the direction of the force. What is the work done by the student on the box? Use $$W = Fd \cos 	heta$$ with $$	heta = 0^\circ.$$

Accepted Answer

$$W = 50 	imes 6.0 	imes \cos 0^\circ = 300 J$$

Question 2

A rope pulls a sled with a force of 80 N at an angle of $$30^\circ$$ above the horizontal. The sled moves 5.0 m horizontally. What is the work done by the rope?

Accepted Answer

$$W = 80 	imes 5.0 	imes \cos 30^\circ = 346 J$$

Question 3

A 2.0 kg object speeds up from 3.0 m/s to 7.0 m/s. Using the work-energy theorem, what is the net work done on the object?

Accepted Answer

$$W_{net} = \frac{1}{2} 	imes 2.0 	imes (7.0^2$ - 3.0^2$) = 56 J$$

Question 4

A 1200 kg car slows from 20 m/s to rest due to braking. What is the net work done on the car?

Accepted Answer

$$W_{net} = \frac{1}{2} 	imes 1200 	imes (0^2$ - 20^2$) = -240,000 J$$

Question 5

A 15 kg backpack is lifted straight up 2.0 m at constant speed. What is the work done by the lifting force?

Accepted Answer

$$W = mgh = 15 	imes 9.8 	imes 2.0 = 294 J$$

Question 6

A 5.0 kg box slides 4.0 m across a rough horizontal floor. The coefficient of kinetic friction is 0.20. What is the work done by friction?

Accepted Answer

$$W_{fric} = -\mu_k mg d = -0.20 	imes 5.0 	imes 9.8 	imes 4.0 = -39.2 J$$

Question 7

A 60 kg rider starts from rest at the top of a frictionless roller coaster hill and drops 12 m vertically. What is the rider's speed at the bottom?

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 12} = 15.3 m/s$$

Question 8

A spring with a spring constant of 200 N/m is compressed by 0.25 m. What is the elastic potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} 	imes 200 	imes (0.25)^2$ = 6.25 J$$

Question 9

A force-displacement graph shows force increasing linearly from 0 N at 0 m to 40 N at 4 m, then staying at 40 N from 4 m to 8 m. What is the total work done?

Accepted Answer

Work = Area under the graph = $$\frac{1}{2} 	imes 4 	imes 40 + 40 	imes 4 = 80 + 160 = 240 J$$

Question 10

A 0.15 kg baseball moves at 40 m/s, and a 60 kg runner moves at 2.0 m/s. Which has greater kinetic energy?

Accepted Answer

Baseball: $$KE = \frac{1}{2} 	imes 0.15 	imes 40^2$ = 120 J$$; Runner: $$KE = \frac{1}{2} 	imes 60 	imes 2^2$ = 120 J$$; They have equal kinetic energy.

Question 11

A person pushes a lawn mower with a force of 120 N at an angle of $$40^\circ$$ below the horizontal. The mower moves 10 m horizontally. What is the work done by the applied force?

Accepted Answer

$$W = 120 	imes 10 	imes \cos 40^\circ = 919 J$$

Question 12

A 20 kg sled starts from rest. It is pulled horizontally with a 100 N force for 15 m while friction exerts a 25 N force opposite the motion. What is the sled's final speed?

Accepted Answer

Net work: $$W_{net} = (100 - 25) 	imes 15 = 1125 J$$; $$\frac{1}{2} m v^2$ = 1125$$; $$v = \sqrt{2 	imes 1125 / 20} = 10.6 m/s$$

Question 13

A 0.50 kg ball is thrown straight upward at 18 m/s. Ignore air resistance. What is the work done by gravity from the release point to the highest point?

Accepted Answer

$$W_{gravity} = -\Delta KE = -\frac{1}{2} 	imes 0.50 	imes 18^2$ = -81 J$$

Question 14

A 500 kg elevator moves upward 3.0 m while speeding up from rest to 2.0 m/s. What is the work done by the cable on the elevator?

Accepted Answer

$$W_{cable} = \Delta KE + \Delta PE = \frac{1}{2} 	imes 500 	imes 2^2$ + 500 	imes 9.8 	imes 3.0 = 1000 + 14,700 = 15,700 J$$

Question 15

Which of the following best explains how the sign of work affects an object's kinetic energy? Give an example.

Accepted Answer

Positive net work increases kinetic energy (e.g., pushing a car to speed it up); negative net work decreases kinetic energy (e.g., friction slowing a sliding box).

Question 16

A hiker lifts a 10 kg pack vertically upward 1.5 m and then carries it horizontally for 20 m. What is the total work done by gravity during both parts of the trip?

Accepted Answer

$$W_{gravity} = -mgh = -10 	imes 9.8 	imes 1.5 = -147 J$; 0$ J$$ during horizontal motion; total $$-147 J$$

Question 17

A 3.0 kg object is dropped from a height of 5.0 m. What is its kinetic energy just before hitting the ground? (Ignore air resistance.)

Accepted Answer

$$KE = mgh = 3.0 	imes 9.8 	imes 5.0 = 147 J$$

Question 18

A 10 kg crate is pulled up a 5.0 m long ramp inclined at $$30^\circ to $$the horizontal with a constant force parallel to the ramp. What is the minimum work required to move the crate up the ramp (ignore friction)?

Accepted Answer

$$W = mgh = 10 	imes 9.8 	imes (5.0 	imes \sin 30^\circ) = 10 	imes 9.8 	imes 2.5 = 245 J$$

Physics with Algebra: Work, Energy, and the Work-Energy Theorem Study Guide

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드