Q: A 13 kg bicycle is pushed up a 25° incline for 275 m with a constant force of 25 N parallel to the road. What is the total work done by gravity during this process?

$$W = -(13 \times 9.8)(275) \sin 25^\circ = -15,800\ \mathrm{J}$$

Q: A 0.5 kg book is lifted from a 0.7 m high table and placed on a 1.2 m high shelf. What is the work done by gravity during this process?

$$W = -0.5 \times 9.8 \times (1.2 - 0.7) = -2.45\ \mathrm{J}$$

Q: A 250 kg piano is lowered 5 m from a window to the ground using two ropes and gravity. What is the total work done by gravity?

$$W = 250 \times 9.8 \times 5 = 12,250\ \mathrm{J}$$

Q: A 60 kg person rides an escalator from ground level to a floor 5 m above. What is the work done by the escalator on the person?

$$W = 60 \times 9.8 \times 5 = 2,940\ \mathrm{J}$$

Q: A cheetah of mass 60 kg runs at its top speed of 33 m/s. What is its kinetic energy?

$$KE = \frac{1}{2} \times 60 \times 33^2$ = 32,670\ \mathrm{J}$$

Q: A 73 kg runner accelerates from rest to 7.7 m/s. What is the work required?

$$W = \frac{1}{2} \times 73 \times 7.7^2$ = 2,164\ \mathrm{J}$$

Question 1

A 13 kg bicycle is pushed up a 25° incline for 275 m with a constant force of 25 N parallel to the road. What is the total work done by gravity during this process?

Accepted Answer

$$W = -(13 	imes 9.8)(275) \sin 25^\circ = -15,800\ \mathrm{J}$$

Question 2

A skater glides on a horizontal surface. Which of the following statements is correct regarding the work done by the normal force (N) and the weight (w) on the skater?

Accepted Answer

No work is done by either N or w

Question 3

A mass swings in a horizontal circle at constant speed on a frictionless table, attached to a string. How much work does the tension in the string do on the mass during one complete revolution?

Accepted Answer

The tension does zero work

Question 4

A 0.5 kg book is lifted from a 0.7 m high table and placed on a 1.2 m high shelf. What is the work done by gravity during this process?

Accepted Answer

$$W = -0.5 	imes 9.8 	imes (1.2 - 0.7) = -2.45\ \mathrm{J}$$

Question 5

A 250 kg piano is lowered 5 m from a window to the ground using two ropes and gravity. What is the total work done by gravity?

Accepted Answer

$$W = 250 	imes 9.8 	imes 5 = 12,250\ \mathrm{J}$$

Question 6

A 60 kg person rides an escalator from ground level to a floor 5 m above. What is the work done by the escalator on the person?

Accepted Answer

$$W = 60 	imes 9.8 	imes 5 = 2,940\ \mathrm{J}$$

Question 7

According to Hooke's Law, what is the work required to stretch a spring with spring constant $$k by a $$distance $$x$$ from its equilibrium position?

Accepted Answer

$$W = \frac{1}{2}kx^2$

Question 8

A cheetah of mass 60 kg runs at its top speed of 33 m/s. What is its kinetic energy?

Accepted Answer

$$KE = \frac{1}{2} 	imes 60 	imes 33^2$ = 32,670\ \mathrm{J}$$

Question 9

A baseball player slides 3.4 m to a stop at 3.5 m/s. If the friction force is constant, what is the work done by friction?

Accepted Answer

$$W = -\frac{1}{2} m v^2$ = -\frac{1}{2} m (3.5)^2$

Question 10

A car traveling at 10 m/s needs to double its kinetic energy. What speed must it reach?

Accepted Answer

$$v = 14.1\ \mathrm{m/s}$$

Question 11

A 73 kg runner accelerates from rest to 7.7 m/s. What is the work required?

Accepted Answer

$$W = \frac{1}{2} 	imes 73 	imes 7.7^2$ = 2,164\ \mathrm{J}$$

Question 12

A microwave oven delivers 105 W of power to melt an ice cube requiring 6,300 J. How long does it take to melt the ice cube?

Accepted Answer

$$t = \frac{6,300}{105} = 60\ \mathrm{s}$$

Question 13

A person leaps off a bridge with a bungee cord. When the cord first begins to stretch, what is the sign of the work done by the cord on the person?

Accepted Answer

Negative, because the force of the cord is opposite to the direction of motion

Question 14

A 1,000 kg car and a 20,000 kg truck have the same kinetic energy. Which statement is true?

Accepted Answer

The car is moving faster than the truck

Question 15

Force $$F_1$$ does 10 J of work in 10 seconds, $$F_2$$ does 3 J in 5 seconds, $$F_3$$ does 25 J in 125 seconds. Rank the forces by the power they produce, from greatest to least.

Accepted Answer

$$F_2$$ \u003e $$F_1$$ \u003e $$F_3$$

Question 16

A 70 kg climber ascends a 90 m cliff in 15 minutes. What is the average power output?

Accepted Answer

$$P = \frac{70 	imes 9.8 	imes 90}{900} = 68.6\ \mathrm{W}$$

Question 17

A bucket of water (5 kg) is lifted from a well 10 m deep in 8 seconds. What is the minimum power required?

Accepted Answer

$$P = \frac{5 	imes 9.8 	imes 10}{8} = 61.25\ \mathrm{W}$$

Question 18

A shrimp's spring-like appendage stores 0.0103 J of energy. If the spring constant is 58 N/m, how far is the spring compressed?

Accepted Answer

$$x = \sqrt{\frac{2 	imes 0.0103}{58}} = 0.019\ \mathrm{m}$$

Question 19

A car engine outputs 34 kW to maintain a constant speed of 31 m/s. What is the total resistive force acting on the car?

Accepted Answer

$$F = \frac{34,000}{31} = 1,097\ \mathrm{N}$$

Work and Kinetic Energy: Concepts, Examples, and Applications

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