Q: A 10 kg box is pulled 5.0 m across a horizontal floor by a constant force of 40 N applied at an angle of 30° above the horizontal. What is the work done by the force on the box?

$$W = 40 \times 5.0 \times \cos(30^\circ) = 173\ \mathrm{J}$$

Q: A 1500 kg car is towed from rest for 200 m by a variable force, and the total work done is 500,000 J. What is the final speed of the car?

$$v = \sqrt{\frac{2 \times 500,000}{1500}} = 26\ \mathrm{m/s}$$

Q: A 2.0 kg block is attached to a spring with spring constant $$k = 50\ \mathrm{N/m}. $$The block is pulled until the spring stretches by 0.24 m, at which point it slips. If the coefficient of static friction is 0.60, what is the maximum static friction force?

$$f_{s,\mathrm{max}} = \mu_s m g = 0.60 \times 2.0 \times 9.8 = 11.76\ \mathrm{N}$$

Q: A 10 kg crate is pulled 3.0 m across a floor by a rope with 30 N of tension. The coefficient of kinetic friction is 0.20. What is the increase in thermal energy of the crate and floor?

$$\Delta E_{th} = f_k \Delta s = \mu_k m g \Delta s = 0.20 \times 10 \times 9.8 \times 3.0 = 59\ \mathrm{J}$$

Q: A 35 kg motor is lifted vertically 3.0 m in 8.0 s at constant speed. What is the average power output required?

$$P = \frac{m g h}{t} = \frac{35 \times 9.8 \times 3.0}{8.0} = 129\ \mathrm{W}$$

Question 1

A 10 kg box is pulled 5.0 m across a horizontal floor by a constant force of 40 N applied at an angle of 30° above the horizontal. What is the work done by the force on the box?

Accepted Answer

$$W = 40 	imes 5.0 	imes \cos(30^\circ) = 173\ \mathrm{J}$$

Question 2

Which of the following best describes the energy transformation that occurs when a diver jumps off a diving board and falls towards the water?

Accepted Answer

Gravitational potential energy is transformed into kinetic energy.

Question 3

A 1500 kg car is towed from rest for 200 m by a variable force, and the total work done is 500,000 J. What is the final speed of the car?

Accepted Answer

$$v = \sqrt{\frac{2 	imes 500,000}{1500}} = 26\ \mathrm{m/s}$$

Question 4

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

Accepted Answer

A satellite moving in uniform circular motion under the influence of gravity.

Question 5

A 70 kg skier starts from rest and slides down a frictionless 50 m slope inclined at 10°. What is the skier’s speed at the bottom?

Accepted Answer

$$v = \sqrt{2 g (50 \sin 10^\circ)} \approx 13.2\ \mathrm{m/s}$$

Question 6

A 2.0 kg block is attached to a spring with spring constant $$k = 50\ \mathrm{N/m}. $$The block is pulled until the spring stretches by 0.24 m, at which point it slips. If the coefficient of static friction is 0.60, what is the maximum static friction force?

Accepted Answer

$$f_{s,\mathrm{max}} = \mu_s m g = 0.60 	imes 2.0 	imes 9.8 = 11.76\ \mathrm{N}$$

Question 7

Which of the following correctly expresses the work done by a constant force $$\vec{F}$$ acting over a displacement $$\vec{\Delta s} at an $$angle $$	heta$$?

Accepted Answer

$$W = F \Delta s \cos 	heta$$

Question 8

A 10 kg crate is pulled 3.0 m across a floor by a rope with 30 N of tension. The coefficient of kinetic friction is 0.20. What is the increase in thermal energy of the crate and floor?

Accepted Answer

$$\Delta E_{th} = f_k \Delta s = \mu_k m g \Delta s = 0.20 	imes 10 	imes 9.8 	imes 3.0 = 59\ \mathrm{J}$$

Question 9

Which of the following statements about dissipative forces is correct?

Accepted Answer

Dissipative forces always increase the thermal energy of a system.

Question 10

A 35 kg motor is lifted vertically 3.0 m in 8.0 s at constant speed. What is the average power output required?

Accepted Answer

$$P = \frac{m g h}{t} = \frac{35 	imes 9.8 	imes 3.0}{8.0} = 129\ \mathrm{W}$$

Question 11

Which of the following is the correct expression for the dot product of two vectors $$\vec{A}$$ and $$\vec{B}$$ with an angle $$\alpha$$ between them?

Accepted Answer

$$\vec{A} \cdot \vec{B} = AB \cos \alpha$$

Question 12

A spring with spring constant $$k is $$compressed by a distance $$\Delta s$$ from equilibrium. What is the work done by the spring as it returns to equilibrium?

Accepted Answer

$$W = -\frac{1}{2} k (\Delta s)^2$

Question 13

Which of the following best describes the difference between the system and the environment in the context of energy transfer?

Accepted Answer

The system is the part of the universe being studied, and the environment is everything else that can exchange energy with the system.

Question 14

A 150,000 kg rocket is launched vertically with a thrust of $$4.0 	imes 10^6$ N. Ignoring air resistance, what is the net work done by gravity as the rocket rises 500 m?

Accepted Answer

$$W_{g} = -m g h = -150,000 	imes 9.8 	imes 500 = -735,000,000\ \mathrm{J}$$

Question 15

Which of the following is the correct expression for the kinetic energy of a particle of mass $$m$$ moving at speed $$v$$?

Accepted Answer

$$K = \frac{1}{2} m v^2$

Question 16

A box is pulled at constant speed across a rough floor. Which statement is true about the energy transformations involved?

Accepted Answer

The work done by the pulling force is transformed into thermal energy due to friction.

Question 17

Which of the following is the correct definition of power in terms of work and time?

Accepted Answer

$$P = \frac{dW}{dt}$$

Question 18

A force of 100 N acts at an angle of 60° to the direction of displacement of 10 m. What is the work done by the force?

Accepted Answer

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

Work and Kinetic Energy: Chapter 9 Study Notes

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