Q: A weightlifter lifts a 100 kg barbell vertically upward a distance of 2 m. What is the work done by the weightlifter on the barbell? (Assume $$g = 9.8 \ \mathrm{m/s^2$}$$ and ignore air resistance.)

$$W = 100 \times 9.8 \times 2 = 1960 \ \mathrm{J}$$

Q: A box is pulled 5 m along a horizontal surface by a constant force of 20 N that makes an angle of $$30^\circ$$ with the horizontal. What is the work done by the force?

$$W = 20 \times 5 \times \cos 30^\circ = 86.6 \ \mathrm{J}$$

Q: A spring with a force constant $$k = 200 \ \mathrm{N/m} is $$compressed by 0.1 m. What is the work required to compress the spring?

$$W = \frac{1}{2} \times 200 \times (0.1)^2$ = 1 \ \mathrm{J}$$

Q: A 1500 kg car accelerates from rest to 20 m/s over a distance of 200 m. What is the net work done on the car?

$$W = \Delta K = \frac{1}{2} \times 1500 \times (20^2$ - 0^2$) = 300,000 \ \mathrm{J}$$

Q: A tractor pulls a sled with a force of 5000 N at an angle of $$36.9^\circ$$ above the horizontal for a distance of 20 m. What is the work done by the tractor?

$$W = 5000 \times 20 \times \cos 36.9^\circ = 80,000 \ \mathrm{J}$$

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

$$K = \frac{1}{2} \times 2 \times 3^2$ = 9 \ \mathrm{J}$$

Q: A 70 kg marathon runner climbs the stairs of a 443 m tall building in 15 minutes. What is the average power output in watts? (Assume $$g = 9.8 \ \mathrm{m/s^2$}.)$$

$$P = \frac{70 \times 9.8 \times 443}{15 \times 60} \approx 336 \ \mathrm{W}$$

Q: A person pulls a sled with a force of 100 N at an angle of $$60^\circ$$ above the horizontal for 10 m. What is the work done by the person?

$$W = 100 \times 10 \times \cos 60^\circ = 500 \ \mathrm{J}$$

Question 1

A weightlifter lifts a 100 kg barbell vertically upward a distance of 2 m. What is the work done by the weightlifter on the barbell? (Assume $$g = 9.8 \ \mathrm{m/s^2$}$$ and ignore air resistance.)

Accepted Answer

$$W = 100 	imes 9.8 	imes 2 = 1960 \ \mathrm{J}$$

Question 2

A box is pulled 5 m along a horizontal surface by a constant force of 20 N that makes an angle of $$30^\circ$$ with the horizontal. What is the work done by the force?

Accepted Answer

$$W = 20 	imes 5 	imes \cos 30^\circ = 86.6 \ \mathrm{J}$$

Question 3

A spring with a force constant $$k = 200 \ \mathrm{N/m} is $$compressed by 0.1 m. What is the work required to compress the spring?

Accepted Answer

$$W = \frac{1}{2} 	imes 200 	imes (0.1)^2$ = 1 \ \mathrm{J}$$

Question 4

A 1500 kg car accelerates from rest to 20 m/s over a distance of 200 m. What is the net work done on the car?

Accepted Answer

$$W = \Delta K = \frac{1}{2} 	imes 1500 	imes (20^2$ - 0^2$) = 300,000 \ \mathrm{J}$$

Question 5

A force of 10 N acts on a box as it moves 3 m in a direction perpendicular to the force. What is the work done by the force?

Accepted Answer

$$W = 0 \ \mathrm{J}$$

Question 6

A tractor pulls a sled with a force of 5000 N at an angle of $$36.9^\circ$$ above the horizontal for a distance of 20 m. What is the work done by the tractor?

Accepted Answer

$$W = 5000 	imes 20 	imes \cos 36.9^\circ = 80,000 \ \mathrm{J}$$

Question 7

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

Accepted Answer

$$K = \frac{1}{2} 	imes 2 	imes 3^2$ = 9 \ \mathrm{J}$$

Question 8

A block is pushed along a frictionless surface by a constant force $$F$$ over a distance $$s. If $$the block starts at velocity $$v_1$$ and ends at $$v_2$$, which equation correctly relates the work done to the change in kinetic energy?

Accepted Answer

$$W = \frac{1}{2} m v_2$^2 - \frac{1}{2} m v_1$^2$$

Question 9

A force $$F(x)$$ varies with position as shown in the graph, increasing linearly from $$F_1 at$$ $$x_1 to$$ $$F_2 at$$ $$x_2. $$What is the work done by the force as the object moves from $$x_1 to$$ $$x_2$$?

Accepted Answer

$$W = \frac{1}{2} (F_1$ + F_2$) (x_2$ - x_1$)$$

Question 10

A 70 kg marathon runner climbs the stairs of a 443 m tall building in 15 minutes. What is the average power output in watts? (Assume $$g = 9.8 \ \mathrm{m/s^2$}.)$$

Accepted Answer

$$P = \frac{70 	imes 9.8 	imes 443}{15 	imes 60} \approx 336 \ \mathrm{W}$$

Question 11

A person pulls a sled with a force of 100 N at an angle of $$60^\circ$$ above the horizontal for 10 m. What is the work done by the person?

Accepted Answer

$$W = 100 	imes 10 	imes \cos 60^\circ = 500 \ \mathrm{J}$$

Question 12

A 3 kg block slides down a frictionless incline of height 5 m. What is its speed at the bottom?

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 5} \approx 9.9 \ \mathrm{m/s}$$

Question 13

A force of 50 N stretches a spring by 0.25 m. What is the spring constant $$k$$?

Accepted Answer

$$k = \frac{F}{x} = \frac{50}{0.25} = 200 \ \mathrm{N/m}$$

Question 14

A 3000 kg truck is lifted by a crane with an upward force of 31,000 N over a distance of 2 m. What is the work done by the crane?

Accepted Answer

$$W = 31,000 	imes 2 = 62,000 \ \mathrm{J}$$

Question 15

A block is pulled along a rough surface by a force $$F at an $$angle $$	heta$$ above the horizontal. The friction force is $$f. $$What is the net work done on the block after moving a distance $$d$$?

Accepted Answer

$$W_{net} = F \cos 	heta \cdot d - f d$$

Question 16

A force $$F$$ acts on a particle moving along a curved path. How is the work done by the force calculated?

Accepted Answer

$$W = \int_{C} \vec{F} \cdot d\vec{s}$$

Question 17

A 5 kg object is moving at 10 m/s. If a constant force acts on it and increases its speed to 20 m/s, what is the change in kinetic energy?

Accepted Answer

$$\Delta K = \frac{1}{2} 	imes 5 	imes (20^2$ - 10^2$) = 750 \ \mathrm{J}$$

Question 18

A person lowers a 50 kg box down a ramp 4 m long at constant speed. What is the work done by gravity if the ramp is inclined at $$30^\circ$$?

Accepted Answer

$$W = 50 	imes 9.8 	imes 4 	imes \sin 30^\circ = 980 \ \mathrm{J}$$

Work and Kinetic Energy: Physics with Calculus Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards