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Chapter
3
E NERGY
OUTLINE
Work
3.1 The Meaning of Work
3.2 Power
Relativity
3.11 Special Relativity
3.12 Rest Energy
3.13 General Relativity
Energy
3.3 Kinetic Energy
3.4 Potential Energy
3.5 Energy Transformations
3.6 Conservation of Energy
3.7 The Nature of Heat
Energy and Civilization
3.14 The Energy Problem
3.15 The Future
Momentum
3.8 Linear Momentum
3.9 Rockets
3.10 Angular Momentum
Goals
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Explain what is meant by work.
Explain what is meant by power.
Distinguish between kinetic energy and potential energy.
Give several examples of potential energy.
State the law of conservation of energy and give several examples of energy
transformations.
Use the principle of conservation of energy to analyze events in which work and different
forms of energy are transformed into one another.
Discuss why heat is today regarded as a form of energy rather than as an actual substance.
Define linear momentum and discuss its significance.
Use the principle of conservation of linear momentum to analyze the motion of objects that
collide with each other or push each other apart, for instance, when a rocket is fired.
State what is meant by angular momentum.
Explain how conservation of angular momentum is used by skaters to spin faster and by
footballs to travel farther.
Describe several relativistic effects and indicate why they are not conspicuous in the
everyday world.
Explain what is meant by rest energy and be able to calculate the rest energy of an object of
given mass.
Describe how gravity is interpreted in Einstein’s general theory of relativity.
Discuss the various factors that are part of the energy problem of the future.
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CHAPTER SUMMARY
Chapter 3 begins by defining work and power. The difference between kinetic and potential
energy is explained, and the concept of energy transformation is introduced. Heat is shown to
be a form of energy. The law of conservation of energy is presented, and mass and energy are
stated to be equivalent. The discussion of Einstein's special theory of relativity shows that
measurements of length, time, and mass depend upon the relative velocity between the observer
and what is being observed. The discussion of Einstein's general theory of relativity explains
that gravity results from the distortion of space-time around a body of matter. The
environmental and technical problems of providing enough energy to meet the demands of the
growing global population are presented, and alternative energy sources are discussed.
CHAPTER OUTLINE
3-1.
The Meaning of Work
A. Work equals force times distance.
W = Fd
1. When a force is applied to an object, the object must move a distance or no
work is done.
2. When the force is not parallel to the distance d, the projection of the force in
the direction of d must be used to find the work.
3. No work is done when a force is perpendicular to the direction of motion of
an object.
B. The SI unit of work is the joule.
1 joule (J) = 1 newton-meter (N C m)
C. Work done against gravity is represented by:
W = mgh
where W = work, mg = mass times the acceleration of gravity (9.8 m/s2), and h = total
height.
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3-2.
Power
A. Power is the rate at which work is being done:
where P = power, W = work, and t = time.
B. The SI unit of power is the watt:
1 watt (W) = 1 joule/second (J/s)
C. The kilowatt (kW) is a convenient unit of power for many applications.
3-3.
Kinetic Energy
A. Energy is that property something has that enables it to do work.
B. The energy of a moving object is called kinetic energy (KE):
KE = ½mv2
where m = mass and v = speed.
1. Since KE is the product of mass and the square of the speed, the greater the
mass and/or speed the greater the KE.
2. KE increases very rapidly with speed because of the v2 factor.
3-4.
Potential Energy
A. Potential energy (PE) is the energy an object has by virtue of its position.
B. The amount of work an object performs as it moves toward the earth under the
influence of gravity is its gravitational potential energy:
PE = mgh
where m = mass, g = acceleration of gravity (9.8 m/s2), and h = height.
C. The gravitational PE of an object is a relative quantity because it depends on the level
from which it is reckoned.
3-5.
Energy Transformations
A. All forms of energy can be transformed or converted from one form to another; most
events in the physical world involve energy transformation.
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B. Energy exists in a variety of forms. Some forms other than kinetic and potential
include:
1. Chemical energy
2. Heat energy
3. Electric energy
4. Radiant energy
3-6.
Conservation of Energy
A. The law of conservation of energy states that energy cannot be created or destroyed
although it can be changed from one form to another.
B. Matter can be considered as a form of energy; matter can be transformed into energy
and energy into matter according to the law of conservation of energy.
3-7.
The Nature of Heat
A. Heat was once thought to be a weightless, invisible, odorless, and tasteless substance
called caloric.
B. James Prescott Joule was the first to demonstrate conclusively that heat is energy.
3-8.
Linear Momentum
A. Linear Momentum is a measure of the tendency of a moving object to continue in
motion along a straight line:
p = mv
where p = linear momentum, m = mass, and v = velocity.
B. The greater an object's linear momentum, the harder it is to change the object's
velocity, that is, its speed and/or direction of motion.
C. The law of conservation of momentum states: In the absence of outside forces, the
total momentum of a set of objects remains the same no matter how the objects
interact with one another.
3-9.
Rockets
A. The operation of a rocket is based on conservation of momentum.
1. The momentum of the exhaust gases is balanced by the rocket's upward
momentum.
2. The total momentum of the entire system is zero.
B. Multistage rockets are more efficient than single-stage and so are widely used.
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3-10. Angular Momentum
A. Angular momentum is a measure of the tendency of a rotating object to continue
spinning about a fixed axis; conservation of angular momentum is the description
of the tendency of spinning objects to remain spinning.
1. The greater the mass of an object and the more rapidly it rotates, the greater
its angular momentum.
2. The angular momentum of a spinning object also depends upon how its mass
is distributed; the farther away from the axis of rotation its mass is distributed,
the more the angular momentum.
3-11. Special Relativity
A. Albert Einstein (1879-1955) published the special theory of relativity in 1905.
B. Special relativity is based on two postulates:
1. The laws of physics are the same in all frames of reference moving at
constant velocity.
2. The speed of light (c) in free space has the same value for all observers (c = 3
x 108 m/s)
C. According to the special theory of relativity, when there is relative motion between
an observer and what is being observed, lengths are observed to be shorter, time
intervals are observed to be longer, and masses are observed to be greater than when
at rest.
D. Nothing material can travel as fast or faster than the speed of light.
3-12. Rest Energy
A. The rest energy of a body is the energy equivalent of its mass:
EO = mOc2
where EO = rest energy, mO = rest mass, and c = speed of light.
B. Rest energy is liberated in all energy-producing reactions of chemistry and physics.
3-13. General Relativity
A. Einstein published the general theory of relativity in 1916, which related gravitation
to the structure of space and time and showed that even light was subject to gravity.
B. Einstein spent the last years of his life unsuccessfully trying to join together the
phenomena of gravitation and electromagnetism into a "unified field theory."
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3-14. The Energy Problem
A. Except for nuclear energy, heat energy from within the earth, and tidal energy, all
available energy is directly or indirectly derived from the sun.
B. Coal, oil, and natural gas are called fossil fuels because they were formed from the
remains of organisms that lived millions of years ago.
C. The use of fossil fuels presents several disadvantages.
1. Oil and natural gas reserves will not last indefinitely.
2. Although coal reserves will last several hundred more years, mining coal is
dangerous, and burning coal creates environmental problems such as acid
rain, air pollution, and enhanced global warming.
D. Nuclear energy presents both advantages and problems.
1. Nuclear fuel reserves exceed those of fossil fuels, especially with the
development of "breeder" reactors.
2. Properly built and run nuclear power plants are excellent energy sources.
3. The potential for a large-scale nuclear accident is present.
4. Discharge of radioactive wastes into the environment from badly run nuclear
power plants has occurred.
5. An unsolved disposal problem of radioactive nuclear waste exists.
3-15. The Future
A. Nuclear fusion represents a potentially safe, nonpolluting, and inexhaustible energy
source; however, the problem is how to manage until nuclear fusion arrives.
B. Alternate energy sources, such as solar energy, present various technical and
environmental problems; some are not economically feasible.
C. Wise use of alternate energy sources, conservation of energy, improved efficiency of
energy use, and a slowdown in human population growth are necessary to avoid
disaster until nuclear fusion becomes a reality.
KEY TERMS AND CONCEPTS
The questions in this section will help you review the key terms and concepts from Chapter 3.
Multiple Choice
Circle the best answer for each of the following questions.
1.
The SI unit of work is the
a. joule
b. watt
c. calorie
d. newton
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2.
The SI unit of energy is named after
a. Albert Einstein
b. James Prescott Joule
c. Count Rumford
d. James Watt
3.
The property something has that enables it to do work is
a. mass
b. energy
c. momentum
d. force
4.
A billiards player strikes the cue ball with a cue stick, thereby putting the cue ball in
motion. The cue ball will continue to move until
a. it runs out of speed
b. its inertia is balanced by its momentum
c. its linear momentum is converted into angular momentum
d. the forces of friction and air resistance bring it to a stop
5.
The same billiards player "breaks" by striking the cue ball with the cue stick and sending it
into a stationary formation of billiard balls, thereby putting the balls in motion. The law of
conservation of momentum tells us
a. the total momentum of the cue ball and the billiard balls has been reduced
b. it is impossible for the momentum of the billiard balls to be changed
c. the total combined momentum of the cue ball and the billiard balls remains unchanged
after the break
d. the momentum of the cue ball is reduced by a factor equal to the number of billiard
balls put into motion
6.
A spinning top eventually falls over and comes to rest because
a. it has lost all of its angular momentum
b. it has lost all of its linear momentum
c. the force of gravity has brought it to a stop
d. it has lost all of its original inertia
7.
In the cylinder of an automobile engine, the chemical energy of gasoline is initially
transformed into
a. mechanical energy
b. heat energy
c. electrical energy
d. potential energy
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8.
The wound spring of a watch possesses _______________ energy.
a. potential
b. kinetic
c. chemical
d. zero
9.
A 75-kg window air conditioner falls a distance of 6 m to the street below (no one is
injured). What was the PE of the air conditioner while it sat at rest within the window
frame?
a. 735 J
b. 2205 J
c. 3601.5 J
d. 4410 J
10.
A 1000-kg car is traveling at a speed of 10 m/s. If the speed of the car is increased to 20
m/s, the car's kinetic energy is
a. doubled
b. halved
c. quadrupled
d. unchanged
11. The law of conservation of energy states
a. mass is a form of energy
b. it is illegal to waste energy
c. the end product of all energy transformation is heat
d. energy transformations occur without a net gain or loss of energy
12.
Einstein's general theory of relativity
a. relates the movement of small particles in a fluid to their bombardment by molecules
b. describes light as having both wave and particle properties
c. interprets gravity as a distortion in the structure of space and time
d. proposed that heat was a form of energy
13.
A spaceship and its crew travel at near the speed of light to reach the star Proxima
Centauri. Observers on earth note that it takes 4.3 years for the crew to reach Proxima
Centauri. To the spaceship crew the trip takes
a. more than 4.3 years
b. less than 4.3 years
c. exactly 4.3 years
d. zero time
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14.
The distance from Earth to Proxima Centauri is approximately 40.7 trillion kilometers as
measured by earthbound observers. From the frame of reference of the spaceship crew, the
distance to Proxima Centauri is _______________, and the clock on board the spaceship is
running _______________ than clocks on earth.
a. shorter; faster
b. shorter; slower
c. longer; faster
d. longer; slower
15.
All are advantages of solar cells except
a. little or no maintenance expense
b. no moving parts
c. can be installed close to where electricity is needed
d. generate electricity more cheaply than fossil fuel plants for a given power output
True or False
Decide whether each statement is true or false. If false, either briefly state why it is false or
correct the statement to make it true. See previous chapters for an example.
__________ 1.
Farmer Ben attempts to remove an 80-kg rock from his field. If he applies a
force of 789 N for 10 seconds yet fails to move the rock, he has done no work.
__________ 2.
Upon eating food, the chemical energy contained within the food is destroyed
by the process of digestion.
__________ 3.
In a nuclear weapon, a small amount of matter is converted into energy.
__________ 4.
Energy can be defined as the rate at which work is being done.
__________ 5.
Kinetic energy may be thought of as the energy of motion.
__________ 6.
Your car runs out of gas along a level highway. If the car's mass is 1000 kg
and you push the car 20 m to the nearest gas station, the work you have done
is the product of the car's mass (1000 kg) and distance the car was pushed (20
m).
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__________ 7.
According to Einstein’s special theory of relativity, the speed of light in free
space has the same value for all observers.
__________ 8.
Einstein’s general theory of relativity predicts that light is subject to gravity.
__________ 9.
Coal reserves are expected to be depleted within the next few decades.
__________ 10.
Nuclear energy accounts for about 45 percent of the energy generated in the
United States.
Fill in the Blank
In the above drawing, the car coasts from point A to point C (assume friction is not acting on the
car). Refer to this drawing to answer questions 1 through 4.
1.
As the car coasts from point A to point B, its initial potential energy is converted into
____________________ energy.
2.
The kinetic energy of the car is greatest at point ____________________.
3.
The kinetic energy of the car is totally converted into potential energy at
point ____________________.
4.
As the car coasts from point A to point C, the total amount of energy (KE + PE) is
____________________.
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In the above drawing, the pendulum ball is moving to the right. Refer to this drawing to answer
questions 5 and 6.
5.
The pendulum ball has minimum potential energy and maximum kinetic energy at point
____________________.
6.
As the pendulum ball moves from point A to point B, the ____________________ energy
of the ball is transformed to ____________________ energy.
7.
In the above drawing, the stretched spring has ____________________ energy.
8.
The potential energy of a raised object is equal to the ____________________ used to lift
it.
9.
According to general relativity, gravity is a warping of the structure of space and time due
to the presence of ____________________.
10.
The kinetic energy of a moving object is proportional to the square of its
____________________.
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Matching
Match the term on the left with its definition on the right.
1._____
fossil fuels
2._____
sun
3._____
power
4._____
work
5._____
rest energy
6._____
joule
7._____
angular momentum
8._____
potential energy
9._____
kinetic energy
10.____
linear momentum
a. rate of doing work
b. the energy an object has by virtue of its
mass
c. the energy an object has by virtue of its
motion
d. one newton-meter
e. measure of the tendency of a rotating
object to continue spinning about a fixed
axis
f. force times distance
g. the energy an object has by virtue of its
position
h. coal, oil, and natural gas
i. measure of the tendency of a moving
object to continue motion along a
straight line
j. original source of most energy on earth
SOLVED PROBLEMS
Study the following solved example problems as they will provide insight into solving the
problems listed at the end of Chapter 3 in The Physical Universe. Review the mathematics
refresher in the text if you are unfamiliar with the basic mathematical operations presented in
these examples.
Example 3-1
A total of 784 J of work is needed to lift a metal chair a height of 10 m. What is the mass of the
chair?
Solution
The work W needed to raise an object of mass m to a height h above its original position is
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To determine the mass of the body, we must solve for m by dividing both sides of the equation
by gh:
Substituting the quantities given in the problem and the acceleration of gravity for g, we have:
The answer must be expressed in kg. To do this, we must use the definitions of joule, newtonmeter, and newton.
The mass of the chair is 8 kg.
Example 3-2
An 80-kg person hikes to the top of Diamond Head near Honolulu, Hawaii. If the vertical gain
in elevation is 171 m and it took 60 minutes to reach the top, how much power did the person
develop?
Solution
The formula for power is:
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We must first find the value for W, the work done by the person in climbing 171 m. In Chapter
3, we learned that the work needed to raise an object of mass m to a height h above its original
position is
W = mgh
where g is the acceleration of gravity (9.8 m/s2). Substituting the quantities for m and h into the
formula for W, we get
W = (80 kg)(9.8 m/s2)(171 m)
W = 134,064 kg C m/s2 C m
W = 134,064 N C m
W = 134,064 J
We can now determine P by substituting the quantities for W and t into the formula for power.
Note that the SI unit of power is the watt (W), where
1 watt (W) = 1 joule/second (J/s)
We must convert time in minutes as given in the problem into time in seconds.
The power the person developed is:
WEB LINKS
Participate in an interactive demonstration of linear momentum at:
http://library.thinkquest.org/3042/java/linear_demo.html
Investigate the theory of relativity and time dilation at:
http://www.walter-fendt.de/ph14e/timedilation.htm
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Investigate special relativity at:
http://www.phy.ntnu.edu.tw/ntnujava/viewtopic.php?t=70
Learn about renewable and alternate energy sources at:
http://www.repp.org/
ANSWER KEY
Multiple Choice
1. a 2. b
15. d
3. b
4. d
5. c
6. a
7. b
8. a
9. d
10. c
11. d
12. c
13. b
14. b
True or False
1.
2.
True
False. According to the law of conservation of energy, energy cannot be created or
destroyed.
3.
True
4. False. Power is the rate at which work is being done.
5.
True
6. False. Work would be calculated by the formula W = Fd. Since the amount of force
needed to move the car is not given, the amount of work cannot be determined. The car's
weight (w = mg) does not matter since the downward pull of gravity is a force acting
perpendicular to the direction of motion and can do no work on the car.
7.
True
8.
True
9. False. Coal reserves are expected to last for several centuries.
10. False. Nuclear energy accounts for about one-fifth (20 percent) of the energy generated in
the United States.
Fill in the Blanks
1.
2.
3.
4.
5.
kinetic
B
C
unchanged
B
6.
7.
8.
9.
10.
potential, kinetic
potential
work
matter
speed
Matching
1. h 2. j 3. a 4. f 5. b 6. d 7. e 8. g 9. c 10. i
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