Q: A weightlifter lifts a 100 kg barbell from the ground to a height of 2 m at constant speed. What is the work done by the weightlifter on the barbell? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

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

Q: A box is pulled 5 m across a floor by a constant horizontal force of 20 N. How much work is done by the force?

$$W = 20 \times 5 = 100\ \mathrm{J}$$

Q: A spring with force constant $$k = 200\ \mathrm{N/m} is $$stretched 0.1 m from equilibrium. What is the work done on the spring?

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

Q: A tractor pulls a sled with a force of 5000 N at an angle of $$36.9^\circ$$ above the horizontal for 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 3 kg object is moving at 4 m/s. What is its kinetic energy?

$$K = \frac{1}{2} \times 3 \times 4^2$ = 24\ \mathrm{J}$$

Q: A 1500 kg car accelerates from rest to 20 m/s. How much work is done on the car?

$$W = \frac{1}{2} \times 1500 \times 20^2$ = 300,000\ \mathrm{J}$$

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

$$P = \frac{70 \times 9.8 \times 443}{15 \times 60} = 33.7\ \mathrm{W}$$

Question 1

A weightlifter lifts a 100 kg barbell from the ground to a height of 2 m at constant speed. What is the work done by the weightlifter on the barbell? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

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

Question 2

A force $$\vec{F}$$ acts at an angle $$	heta to $$the direction of displacement $$\vec{s}. $$Which equation correctly gives the work done by the force?

Accepted Answer

$$W = F s \cos 	heta$$

Question 3

A box is pulled 5 m across a floor by a constant horizontal force of 20 N. How much work is done by the force?

Accepted Answer

$$W = 20 	imes 5 = 100\ \mathrm{J}$$

Question 4

A spring with force constant $$k = 200\ \mathrm{N/m} is $$stretched 0.1 m from equilibrium. What is the work done on the spring?

Accepted Answer

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

Question 5

A tractor pulls a sled with a force of 5000 N at an angle of $$36.9^\circ$$ above the horizontal for 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 6

A 3 kg object is moving at 4 m/s. What is its kinetic energy?

Accepted Answer

$$K = \frac{1}{2} 	imes 3 	imes 4^2$ = 24\ \mathrm{J}$$

Question 7

A force acts on a particle, causing its velocity to change from $$v_1 to$$ $$v_2$$ over a displacement $$s. $$Which equation expresses the work-kinetic energy theorem?

Accepted Answer

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

Question 8

A 1500 kg car accelerates from rest to 20 m/s. How much work is done on the car?

Accepted Answer

$$W = \frac{1}{2} 	imes 1500 	imes 20^2$ = 300,000\ \mathrm{J}$$

Question 9

A force $$F_x$$ varies with position as shown in a graph. How do you calculate the work done by the force as the object moves from $$x_1 to$$ $$x_2$$?

Accepted Answer

$$W = \int_{x_1$}^{x_2$} F_x\ dx$$

Question 10

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

Accepted Answer

$$P = \frac{70 	imes 9.8 	imes 443}{15 	imes 60} = 33.7\ \mathrm{W}$$

Question 11

A weightlifter lowers a barbell to the floor. What is the sign of the work done by the weightlifter's hands on the barbell?

Accepted Answer

Negative, because the force exerted by the hands is opposite to the displacement.

Question 12

A block is pushed along a curved path by a force $$\vec{F}. $$How is the total work done calculated?

Accepted Answer

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

Question 13

A spring is compressed from $$x = 0 to$$ $$x = -0.2 m. If$$ $$k = 50\ \mathrm{N/m}$$, what is the work done by the spring?

Accepted Answer

$$W = -\frac{1}{2} 	imes 50 	imes (0.2)^2$ = -1\ \mathrm{J}$$

Question 14

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

Accepted Answer

$$W_{g} = -3000 	imes 9.8 	imes 2 = -58,800\ \mathrm{J}$$

Question 15

Which of the following statements about power is correct?

Accepted Answer

Power is the rate at which work is done: $$P = \frac{dW}{dt}$$

Question 16

A force of 10 N acts perpendicular to the displacement of an object. What is the work done by this force?

Accepted Answer

$$W = 0$$

Question 17

A block slides down a frictionless incline. Which of the following is true about the work done by gravity?

Accepted Answer

It equals the change in kinetic energy of the block.

Work and Kinetic Energy: Mechanics Chapter 6 Study Notes

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