Q: A person pushes a box with a constant force of 50 N over a distance of 4 m along a frictionless surface. What is the work done by the person on the box?

$W = Fd = 50 \times 4 = 200\ \mathrm{J}$

Q: A lawn mower is pushed with a force of 75 N at an angle of $35^\circ$ below the horizontal for a distance of 25 m. What is the work done by the person?

$W = Fd \cos \theta = 75 \times 25 \times \cos 35^\circ \approx 1537\ \mathrm{J}$

Q: A spring with a force constant $k = 230\ \mathrm{N/m}$ is stretched by $2.5\ \mathrm{cm}$. How much work is required to stretch the spring?

$W = \frac{1}{2} k x^2 = \frac{1}{2} \times 230 \times (0.025)^2 \approx 0.072\ \mathrm{J}$

Q: A motorcycle of mass 200 kg is cruising at 14 m/s. What is its kinetic energy?

$K = \frac{1}{2} m v^2 = \frac{1}{2} \times 200 \times 14^2 = 19,600\ \mathrm{J}$

Q: A person lifts a 10 kg box vertically upward by 2 m at constant speed. What is the work done against gravity?

$W = m g h = 10 \times 9.8 \times 2 = 196\ \mathrm{J}$

Q: A car travels 100 m down a hill inclined at $30^\circ$ to the horizontal. The force of gravity along the incline is $mg \sin 30^\circ$. What is the work done by gravity?

$W = mg \sin 30^\circ \times 100$

Q: A nurse pushes an 87-kg patient on an 18-kg gurney, producing an acceleration of $0.55\ \mathrm{m/s^2}$. What is the net force applied?

$F = (87 + 18) \times 0.55 = 57.75\ \mathrm{N}$

Question 1

A person pushes a box with a constant force of 50 N over a distance of 4 m along a frictionless surface. What is the work done by the person on the box?

Accepted Answer

$W = Fd = 50 	imes 4 = 200\ \mathrm{J}$

Question 2

A lawn mower is pushed with a force of 75 N at an angle of $35^\circ$ below the horizontal for a distance of 25 m. What is the work done by the person?

Accepted Answer

$W = Fd \cos 	heta = 75 	imes 25 	imes \cos 35^\circ \approx 1537\ \mathrm{J}$

Question 3

Which of the following statements about work is correct?

Accepted Answer

Work is zero if the force is perpendicular to the displacement.

Question 4

A car of mass 1200 kg accelerates from rest to a speed of 20 m/s. What is the change in its kinetic energy?

Accepted Answer

$\Delta K = \frac{1}{2} m v^2 - \frac{1}{2} m u^2 = \frac{1}{2} 	imes 1200 	imes 20^2 = 240,000\ \mathrm{J}$

Question 5

A spring with a force constant $k = 230\ \mathrm{N/m}$ is stretched by $2.5\ \mathrm{cm}$. How much work is required to stretch the spring?

Accepted Answer

$W = \frac{1}{2} k x^2 = \frac{1}{2} 	imes 230 	imes (0.025)^2 \approx 0.072\ \mathrm{J}$

Question 6

A motorcycle of mass 200 kg is cruising at 14 m/s. What is its kinetic energy?

Accepted Answer

$K = \frac{1}{2} m v^2 = \frac{1}{2} 	imes 200 	imes 14^2 = 19,600\ \mathrm{J}$

Question 7

If the net work done on an object is negative, what happens to its speed?

Accepted Answer

Its speed decreases.

Question 8

A person lifts a 10 kg box vertically upward by 2 m at constant speed. What is the work done against gravity?

Accepted Answer

$W = m g h = 10 	imes 9.8 	imes 2 = 196\ \mathrm{J}$

Question 9

Which equation correctly expresses the work-energy theorem?

Accepted Answer

$W_{\mathrm{total}} = \Delta K = \frac{1}{2} m v_f^2 - \frac{1}{2} m v_i^2$

Question 10

A car travels 100 m down a hill inclined at $30^\circ$ to the horizontal. The force of gravity along the incline is $mg \sin 30^\circ$. What is the work done by gravity?

Accepted Answer

$W = mg \sin 30^\circ 	imes 100$

Question 11

A nurse pushes an 87-kg patient on an 18-kg gurney, producing an acceleration of $0.55\ \mathrm{m/s^2}$. What is the net force applied?

Accepted Answer

$F = (87 + 18) 	imes 0.55 = 57.75\ \mathrm{N}$

Question 12

Which of the following best describes the unit of power?

Accepted Answer

Watt, which is equivalent to $\mathrm{J/s}$

Question 13

A person exerts a force of 100 N to move a cart at constant speed over 20 m in 10 s. What is the average power delivered?

Accepted Answer

$P = \frac{W}{t} = \frac{100 	imes 20}{10} = 200\ \mathrm{W}$

Question 14

A force acts on an object at an angle $	heta$ to the direction of displacement. Which component of the force does work?

Accepted Answer

The component parallel to the displacement, $F \cos 	heta$

Question 15

A spring is compressed by $x$ meters. What is the formula for the work done by the spring force?

Accepted Answer

$W = \frac{1}{2} k x^2$

Question 16

A runner of mass 70 kg increases her speed from 5 m/s to 8 m/s. What is the change in her kinetic energy?

Accepted Answer

$\Delta K = \frac{1}{2} m (v_f^2 - v_i^2) = \frac{1}{2} 	imes 70 	imes (64 - 25) = 1,365\ \mathrm{J}$

Question 17

A machine does 500 J of work in 2 seconds. What is its power output?

Accepted Answer

$P = \frac{W}{t} = \frac{500}{2} = 250\ \mathrm{W}$

Question 18

Which of the following scenarios results in zero work being done?

Accepted Answer

A person holds a heavy box stationary above the ground.

Question 19

A cyclist increases her speed from 10 m/s to 20 m/s. By what factor does her kinetic energy increase?

Accepted Answer

By a factor of 4

Work and Kinetic Energy – Chapter 7 Study Notes

Study Guide - Practice Questions

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