ENERGY
THE BIG
IDEA
Energy can transform from one kind
to another, and it can transfer from one
object to another, but it can never be
created or destroyed.
.& This wind farm is a collection of wind turbines.
Wind turbines catch the wind's energy and transform
it to electricity.
eople often say energy is produced at a
nuclear power plant, coal~burning plant,
wind farm, or other energy power plant.
But is energy really produced there-or is it
transformed from one form to another?
How does the energy in a peanut butter
P
sandwich differ from the energy of a roller
coaster? And in what way are these forms
of energy the same? What does it really
mean to waste energy? Our study of energy
begins with a related concept: work.
DISCOVER!
Observe and Record
1. Hold a rubber ball, or better, a superball, above
your head. Have a friend measure the distance
from the ball to the ground .
2. Drop the ball onto a hard floor. Measure how
high it bounces. Record this measurement.
3. Observe the ball as it bounces a few more times.
How high does the ball bounce each time
compared to the previous time? Record your
observations.
Analyze and Conclude
1. Making Generalizations Did the ball ever
bounce to its original height? Did the ball's
bouncing height become less with each
successive bounce?
2. Comparing Compare the ball's height before
it was dropped to its height at the first bounce .
Express your answer as a percentage . For
example, you may say the first bounce was
75% of the initial height. Was the height of the
second bounce lower than the height of the first
bounce?
3. Predicting Do you think any type of ball, when
dropped, bounces lower with each bounce? If
so, why? What does a ball "lose" each time it
bounces?
4. Inferring Before the ball was dropped, all of
its energy was stored energy-potentia/ energy.
This is energy that elevated objects have
because of their position. You noted that the
ball lost height with each bounce. That means
some of the ball's potential energy transferred
elsewhere. Specu late about whe re this energy
ended up.
91
92
PART ONE
Physics
In chapter 5 we talked
about force x time. Now we
talk about force x distance.
6.1
Work-Force X Distance
It takes effort to push something and make it move. How much effort
depends on the force we apply and on how far we push it. The quantity
force X distance is called work.
Work
=
force X distance
We do work on something when we make it move. We do work
when we lift a load against Earth's gravity. The heavier the load or the
higher we lift it, the more work we do. The amount of work done on an
object depends on (1) how much force is applied and (2) how far the
force causes the object to move.* ./ Work is done when a net force acts
on an object and the object moves in the direction of the net force.
<111111
FIGURE 6.1
When a load is lifted two stories high,
twice the work is done compared to
lifting the load one story because the
distance is twice as much.
FIGURE 6.2 _.
When two loads are lifted to the same
height, twice as much work is done because
the force needed to lift them is twice as
much.
The word work in common
usage means physical or
mental exertion . Don't
confuse the physics
definition of work with the
everyday notion of work.
"ilfcHECK
YOUR READING
When is work done on
an object?
When a weight lifter raises a heavy barbell, he does work on the barbell.
We say he gives energy to the barbell. The more energy given to the barbell,
the more ability it has to do work. So in a very real sense, energy is the
ability to do work. Interestingly, when a weight lifter simply holds a barbell
overhead, he does no work on it. He may get tired holding the barbell still,
but if the barbell is not moved by the force he exerts, he does no work on
the barbell. Work may be done on his muscles as they stretch and contract,
which is force X distance on a biological scale. But this work is not done on
the barbell. Lifting the barbell is different from holding the barbell. When
work is done on an object, the object gains energy. If it doesn't gain energy,
then no work was done on it.
The unit of work combines the unit of force (N) with the unit of distance (m), the newton-meter (N · m). We call a newton-meter the joule (J)
(rhymes with cool). One joule of work is done when a force of 1 N is exerted
over a distance of 1 m, as in lifting an apple over your head. For larger values
we speak ofkilojoules (kJ), thousands of joules, or megajoules (MJ), millions of joules. The weight lifter in Figure 6.3 does work in kilojoules. The
work done to vertically raise a heavily loaded truck can be in megajoules.
* Force and distance must be in the same direction. When force is not along the direction of
motion, then work equals the component of force in the direction of motion X distance
moved.
CHAPTER 6
ENERGY
93
CHECK YOUR THINKING
1. How much work is needed to lift an object that weighs 500 N to
a height of 4 m?
2. How much work is needed to lift it twice as high?
3. How much work is needed to lift a 1000-N load to a height of 8 m?
Answers
1. W = F X d = 500 N X 4 m = 2000 J,
2. Twice the height requires twice the work. That is, W = F X d = 500 N X 8 m = 4000
3. Lifting twice the load twice as high requires four times the work. That is, F X d =
1000 N X 8 m = 8000 J.
6.2
J.
Power-How Quickly Work
Gets Done
FIGURE 6.3 .&
Work is done in lifting the
barbel l. Lift ing it twice as high
req uires t wice as much work
and gives the barbell twice as
much energy.
Lifting a load quickly is more difficult than lifting the same load slowly.
If equal loads are lifted to the same height, the forces and distances are
equal, so the work is the same. What's different is the power. Power is the
rate at which energy is changed from one form to another. Also, power is
the rate at which work is done. ./ Power equals the amount of work
done divided by the time interval during which the work is done.
work done
Power = - - - - time interval
A high-power auto engine does work rapidly. An engine that delivers
twice the power of another, however, does not necessarily go twice as
fast. Twice the power means the engine can do twice the work in the
same amount of time-or it can do the same amount of work in half the
time. A powerful engine can speed up a car more quickly.
The unit of power is the joule per second, called the watt. This is in
honor of James Watt, the 18th-century developer of the steam engine. One
watt (W) of power is used when 1 J of work is done in 1 s. One kilowatt
(kW) equals 1000 watts. One megawatt (MW) equals 1 million watts.
CHECK YOUR THINKING
1. You do work when you do push-ups. If you do the same number
of push-ups in half the time, how does your power output
compare?
2. How many watts of power are needed when a force of 1 N moves
a book 2 m in a time of 1 s?
Wh at tel ls yo u wh eth er work
is done o n somethin g is
wheth er th ere is a change in
its energy. No chan ge in
energy means th at no work
was done on it.
CHECK
Answers
YOUR READING
1. Your power output is twice as much.
2. The power expended is 2 watts: P
FIGURE 6.4 .&
He may expend energy when
he pushes on the wall , but if it
doesn't move, no work is
done on the wall.
W
t
FXd
t
= - = -- =
1NX2m
1s
= 2 W.
How can you calculate
power?
94
PART ONE
Physics
Which of these does a
speeding baseball not
possess? Force, momentum,
energy. (Hint: The answer
begins with an F.)
FIGURE 6.5 •
The space shuttle can develop 33,000 MW of power when fuel is burned
at the enormous rate of 3400 kg/s. This is like emptying an average-sized
swimming pool in 20 s!
6.3 Mechanical Energy
FIGURE 6.6 •
The work done in drawing
the bow will be transferred
to the arrow as energy of
motion, kinetic energy.
"ttcHECK
YOUR READING
What are the two forms
of mechanical energy?
Work is done in lifting a heavy boulder overhead. When raised, the
boulder then has the ability to do work on a walnut beneath it when it
falls. Similarly, when work is done by an archer in drawing a bow, the
bent bow can do work on the arrow. When work is done to wind a
spring mechanism, the spring then has the ability to do work on various
gears to run a clock, ring a bell, or sound an alarm.
In each case, the ability to do work has been acquired by an object.
As mentioned earlier, this ability to do work is energy. Like work,
energy is measured in joules. Energy appears in many forms, such as
heat, light, sound, electricity, and radioactivity. Chemical energy is in the
food you eat. Energy even takes the form of mass itself, as celebrated in
Einstein's famous E = mc2 equation.
In this chapter we focus on potential energy and kinetic energy.
Potential energy is energy an object has because of its position. Kinetic
energy is energy an object has because of its motion.
Potential and
kinetic energy are two kinds of mechanical energy. So mechanical
energy may be in the form of either potential energy, kinetic energy,
or both.
6.4 Potential §nergy Is Stored Energy
An object can store energy because of its position. We call this form of
energy potential energy (PE). In the stored state, energy has the potential
to do work. For example, when an archer draws an arrow with a bow,
CHAPTER 6
ENERGY
~
Native American stories feature the coyote-a
mythical character that could shift its shape from
turtle to bird to bear and so on. In a sense, energy
is a shape-shifter too. It can appear in many
different forms, including light, heat, potential
energy, kinetic energy, and chemical energy.
All forms of energy have the ability to do work.
energy is stored in the bow. When released, energy is transferred to the
arrow.
There are various kinds of potential energy. The potential energy
that is easiest to visualize is stored in an object when work is done on
the object to elevate it against Earth's gravity. The potential energy due
to elevated position is called gravitational potential energy. A boulder
raised high in the air or water in an elevated reservoir has gravitational
potential energy.
./ The amount of gravitational potential energy possessed by
an elevated object is equal to the work done against gravity in lifting
it-the force required to move it upward multiplied by the vertical
distance moved ( W = F X d). Once upward motion begins, the upward
force to keep an object moving at constant speed equals its weight. So
the work done in lifting an object is weight X height. We say
Gravitational potential energy = weight X height
·m
An object's weight is its mass multiplied by the acceleration of gravity g.
We write weight as mg. So the work done in lifting mg through a height h
is equal to its gain in gravitational potential energy (PE):
PE = mgh
FIGURE 6.7
~
Water behind the dam has
potential energy, much
of which is transformed to
electrical energy in the
turbines below.
Note that the height h is the distance above some base level, such as the
ground or the floor of a building. The amount of potential energy is
relative to that level and depends only on weight and height h. Interestingly, it doesn't depend on the path taken to reach that height. You can
see in Figure 6.8 that the potential energy of the ball at the top of the
structure depends on height only.
CHECK YOUR THINKING
1 . The woman pushes the block of ice five times as far up the
incline as the man lifts it to the same height. How much more
force does the man exert when he lifts the ice?
CHECK
YOUR READING
How does the gravitational
potential energy of an
object compare with the
work needed to raise it?
95
96
PART ONE
Physics
2. Who does more work on the ice?
3. If both jobs are done in the same time, who produces more
power?
Answers
1. The man exerts five times as much force as the woman exerts.
2. Although the man exerts more force, both do the same amount of work on the ice.
3. They both do the same amount of work in the same time, so both produce the same
power.
_ /p
+' 11&-....
/
'
,
- .;
, ;
"' "'/;
z_
/ (;,,48'
(
(a)
'
(b)
T
l
3m
' r----'
_______, ~
·
. _ 1
(c)
FIGURE 6.8 A
The PE of the 10-N ball is the same (30 J) in all three cases. That's because
the work done in elevating it 3 m is the same whether it is (a) lifted with 10 N
of force, (b) pushed with 6 N of force up the 5-m incline, or (c) lifted with
10 N up each 1-m stair. No work is done in moving it horizontally (neglecting
friction) .
PE
=
PE
FIGURE 6.9 A
The man raises a block of ice
by·lifting it vertically. The girl
pushes an identical block of
ice up the ramp. When both
blocks are raised to the same
height, both have the same
potential energy.
CHECK YOUR THINKING
1. How much work is done in lifting
the 200-N block of ice shown in
Weight = mg, so a 20-kg
Figure 6.9 a vertical distance of
block of ice weighs 200 N.
2.5 m?
2. How much work is done in pushing the same block of ice up the
5-m-long ramp? The force needed is only
100 N (which is why inclines are used).
3. What is the increase in the block's potential
energy in each case?
Answers
1. 500 J. (We get this by either Fd or mgh.)
2. 500 J. (She pushes with half the force over twice the distance.)
3. Either way increases the block's potential energy by 500 J. The ramp simply makes this
work easier to perform.
CHAPTER 6
t
ENERGY
97
6.5 Kinetic Energy Is Energy
of Motion
When you push on an object, you can make it move. Then a moving
object becomes capable of doing work. It has energy of motion, or
kinetic energy (KE). The kinetic energy of an object depends on its
mass and speed. Specifically, kinetic energy is equal to the mass multiplied by the square of the speed, multiplied by the constant ! :
Kinetic energy = ! mass X speed2
KE = 12 mv 2
Because kinetic energy depends on mass, heavy objects have more
kinetic energy than light ones moving at the same speed. For example,
a car moving along the road has a certain amount of kinetic energy.
A twice-as-massive car moving at the same speed has twice as much
kinetic energy.
Kinetic energy also depends on speed. In fact, kinetic energy
depends on speed more than it depends on mass. Why? Look at the
equation. Kinetic energy depends on mass multiplied by speed squared.
.I So if a car moving along the road has a certain amount of kinetic
energy, when it moves twice as fast it has 2 2 or four times as much
kinetic energy! The same car moving with three times the speed has 32
or nine times as much kinetic energy. So we see that small changes in
speed produce large changes in kinetic energy.
FIGURE 6.10 ....
The downhill"fall" of the
roller coaster results in its
roaring speed in the dip, and
this kinetic energy sends it up
the steep track to the next
summit.
CHECK YOUR THINKING
1. A car travels at 30 km/h and has kinetic energy of 1 MJ. If it
travels twice as fast, 60 km/h, how much kinetic energy will it
have?
2. If it travels three times as fast, at 90 km/h, what will be its kinetic
energy?
3. If it travels four times as fast, at 120 km/h, what will be its kinetic
energy?
4. Does a cockroach hitching a ride under the floor mat of the
moving car have kinetic energy?
Answers
l. Twice as fast means (2 2 ) four times the kinetic energy, or 4 MJ.
2. Three times as fast means (3 2 ) nine times the kinetic energy, or 9 MJ.
3. Four times as fast means (42 ) sixteen times the kinetic energy, or 16 MJ.
4. The cockroach has kinetic energy relative to the road outside, but no kinetic energy
relative to the car itself. Kinetic energy, like velocity, is relative to a reference frame,
usually taken to be the surface of Earth. (Recall this discussion back on page 24.)
.!cHECK
YOUR READING
If a car moves twice as fast,
how much more kinetic
energy does it have?
98
PART ONE
Physics
&.& The Work-Energy Theorem
To increase the kinetic energy of an object, work must be done on it. Or,
if an object is moving, work is required to bring it to rest. In either case,
the change in kinetic energy is equal to the work done. This important
relationship is called the work-energy theorem. We abbreviate "change
in" with the delta symbol, ~' and say
Work= LlKE
Energy is nature's way of
keeping score!
,..,._
"'-1
UNIFYING
CONCEPT
Friction
SECTION
3.6
FIGURE 6.11 ...
When the car goes twice as
fast, it has four times the
kinetic energy (and will need
four times the stopping
distance when braking).
Work equals change in kinetic energy. The work in this equation is the
net work-that is, the work based on the net force.
.I The work-energy theorem states that whenever work is done,
energy changes. If there is no change in an object's energy, then no
work was done on it. This theorem applies to changes in potential
energy also. Recall our previous example of the weight lifter raising the
barbell. When work was being done on the barbell, its potential energy
was being changed. But when it was held stationary, no further work
was being done on the barbell-as evidenced by no further change in
its energy.
Similarly, push against a box on a floor. If it doesn't slide, then you
are not doing work on the box. Put the box on a very slippery floor and
push again. If it slides, then you're doing work on it. When the amount
of work done to overcome friction is small, the amount of work done
on the box is practically matched by its gain in kinetic energy.
The work-energy theorem applies to decreasing speed as well. The
more kinetic energy something has, the more work is required to stop it.
Twice as much kinetic energy means twice as much work. When we
apply the brakes to slow a car, we do work on it. This work is the friction
force supplied by the brakes, multiplied by the distance over which the
friction force acts.
Interestingly, the friction supplied by the brakes is the same whether
the car moves slowly or quickly. Friction doesn't depend on speed. The
variable is the distance of braking. This means that a car moving at twice
the speed of another takes four times (2 2 = 4) as much work to stop.
Therefore it takes four times as much distance to stop. Accident investigators are well aware that an automobile going 100 km/h has four times the
kinetic energy that it would have at 50 km/h. So a car going 100 km/h will
skid four times as far when its brakes are applied as it would going
50 km/h. Kinetic energy depends on speed squared.
CHECK YOUR THINKING
1. When the brakes of a car are locked, the car skids to a stop.
How much farther will the car skid if it's moving three times
as fast?
2. Can an object have energy?
3. Can an object have work?
CHAPTER 6
ENERGY
99
~CHECK
Answers
1. Nine times as far. The car has nine times as much energy when it travels three times as
=I
fast:! m(3v) 2
m9v2 = 9(! mv2). The friction force will ordinarily be the same in
either case. Therefore, to do nine times the work requires nine times as much sliding
distance.
2. Yes, but only in a relative sense. For example, an elevated object may possess PE relative
to the ground, but none relative to a point at the same elevation. Similarly, the kinetic
energy of an object is relative to a frame of reference, usually taken to be Earth's
surface.
3. No, unlike energy, work is not something an object has. Work is something an object
does to some other object. An object can do work only if it has energy.
Kinetic energy often appears hidden in different forms of energy,
such as heat, sound, light, and electricity. Random molecular motion is
sensed as heat: when fast-moving molecules bump into others in the surface of your skin, they transfer kinetic energy to your molecules similar to
the way colliding billiard balls transfer energy. Sound consists of molecules vibrating in rhythmic patterns. When a vibrating object pushes
nearby molecules, those molecules are pushed into action. In turn, they
disturb neighboring molecules that disturb others, preserving the rhythm
of the vibration throughout the region. When the moving molecules hit
your ears, you hear sound. Even light energy comes from the motion of
electrons within atoms. Electrons in motion make electric currents. We
see that kinetic energy has many far-reaching applications in our lives.
&. 'I Conservation of Energy
By studying how energy changes from one form to another, scientists
have developed one of the greatest generalizations in science-the law of
conservation of energy:
Energy cannot be created or destroyed; it may be transformed
from one form into another or transferred from one object to
another, but the total amount of energy never changes.
For any system, whether as simple as a swinging pendulum or as
complex as an exploding star, energy remains the same. .I Energy may
change form or be transferred from one place to another, but the
total energy score stays the same.
This energy score takes into account the fact that atoms that make up
matter are themselves concentrated bundles of energy. When the nuclei
of atoms rearrange themselves, enormous amounts of energy can be
released. We will learn in Chapter 38 that enormous gravitational forces
in the deep, hot interior of the Sun push hydrogen nuclei together to
form helium. This welding together of atomic cores is called
FIGURE 6.12 ~
The potentia l energy of the elevated ram is converted to kinetic energy w hen
it is released .
YOU
READING
How does the work-energy
theorem relate to changes
in energy?
PhysicsPiace.com
Videos
Bowling Ball and Conservation
of Energy; Conservation of
Energy; Conservation of Energy:
Numerical Example
100
PART ONE
Physics
.....
Potential energy
to Potential + kinetic to
Kinetic energy
to
And so o~
FIGURE 6.13 _.
Energy transitions in a pendulum. PE is relative to the lowest point of the
pendulum when it is vertical.
PE = 10000
KE = o
PE = 7500
KE = 2500
PE = 5000
KE = 5000
PE = 2500
KE = 7500
PE = 0
KE = 10000
FIGURE 6.15 _.
A circus diver at the top of a
pole has a potential energy
of 10,000 J. As he dives, his
potential energy converts to
kinetic energy. Note that at
successive positions onefourth, one-half, three-fourths,
and all the way down, the
total energy is constant.
Peg
Potential energy
~
~
o
......... ,
....... -~---- -'J ----
... ... -
-.,
;
FIGURE 6.14 _.
The pendulum bob will swing
to its original height whether
or not the peg is present.
thermonuclear fusion. This process releases radiant energy, some of which
reaches Earth as sunshine.
Part of the energy of sunshine falls on plants, and part of this in turn
later becomes coal. So the energy in coal began in the Sun. Animal life is
sustained by plant life, and eventually becomes oil. So the energy in oil
began in the Sun. Part of the Sun's energy goes into evaporating water
from the ocean, and part of this returns to Earth as rain, some of which
may become trapped behind a dam. The potential energy of the
dammed water may be used to power a generating plant below, where it
will be transformed to electric energy. So the energy generated at dams
began in the Sun. And this energy travels through wires to homes, where
it is used for lighting, heating, cooking, and operating electric gadgets.
How wonderful that energy changes from one form to another!
Note that energy conservation in the physics sense is altogether
different from energy conservation in an environmental sense. In
physics, energy can never be lost from the universe-it can be only
transferred or transformed. In the sense of everyday life and environmental awareness, however, energy can be wasted. Energy should be
conserved, or used wisely, so there will be enough of it to power helpful
technologies in the future.
CHECK YOUR THINKING
1. Does an automobile consume more fuel when its air conditioner
is turned on? When its lights are on? When its radio is on while
the auto is sitting in the parking lot?
2. Wind farms such as the one shown on page 91 feature rows of
wind-powered generators that generate electric power. Does the
power generated affect the speed of the wind? Would locations
behind the "windmills" be windier if they weren't there?
Answers
1. The answer to all three questions is yes, because the energy consumed ultimately
comes from the fuel. Even energy from the battery must be given back to the battery by
the alternator, which is turned by the engine, which runs from the energy of the fuel.
All energy that is used has to come from some source. There's no free lunch!
2. Windmills generate power by taking kinetic energy from the wind, so the wind is
slowed by interaction with the windmill blades. So yes, it would be windier behind the
windmills if they weren't there.
CHAPTER 6
ENERGY
101
MATH CONNECTION
The values of kinetic energy and potential energy for
the block freely sliding down a ramp are shown only at
the bottom of the ramp. Fill in the missing values.
PE
=
0
~------------------------~ KE=75J
6.8 Machines-Devices
CHECK
YOUR READING
to Multiply Forces
A machine is a device for multiplying forces or simply changing the
direction of forces. All machines employ the conservation of energy.
Consider one of the simplest machines, the lever. A lever is shown in
Figure 6.16. When you do work by pushing one end of the lever down,
work is done at the other end. The work done on the output side of the
lever raises a load. If heat from friction forces is small enough to neglect,
the work input is equal to the work output:
What remains the same as
systems change form or
transfer energy from one
place to another?
Work input = work output
Because work equals force multiplied by distance, we can say that input
force X input distance= output force X output distance. ./ A machine
transfers energy from one place to another or transforms it from one
form to another.
(Force X distance)input = (force X distance)output
The support or point of support on which a lever rotates is called
a fulcrum. When the fulcrum is close to the load, a large output force
is produced by a small input force. This is because the input force is
exerted through a large distance and the load is moved over a short
distance. In this way, a lever can multiply force. But no lever or machine
has been found that can multiply work or energy. Our understanding of
energy suggests that none ever will be found. We are so confident of this
that we say energy is never created or destroyed.
FIGURE 6.17 .6.
Work done on one end equals the work done on
a load at the other end.
FIGURE 6.16 .6.
A simple lever.
PhysicsPiace.com
Video
Machines: Pulleys
FIGURE 6.18 .6.
Force is multiplied. Note that a small input force X
large distance = large output force X small distance.
102
PART ONE
Physics
In what two ways can a
machine use energy?
The principle of the lever was understood by the Greek scientist
Archimedes in the third century BC. He said that he could move the
whole world if he had a long enough lever and a place to put the
fulcrum. Some good science has been around for a long time!
CHECK YOUR THINKING
If a lever is arranged so that input distance is twice output distance,
can we predict that energy output will be doubled?
Answer
No, no, a thousand times no! We can predict that output force will be doubled, but never
energy. Work and energy stay the same, which means force X distance stays the same.
Shorter distance means greater force, and vice versa. Be careful to distinguish between the
concepts of force and energy!
FIGURE 6.19 _..
FIGURE 6.20 _..
INTERACTIVE FIGURE,
INTERACTIVE FIGURE,
This pulley acts like a lever. It changes only the direction of
the input force.
In this arrangement, a load
can be lifted with half the
input force.
Another simple machine is a pulley. Can you see that it is a lever "in
disguise"? When it is used as in Figure 6.19, it changes only the direction
of the force. But when it is used as in Figure 6.20, the output force is
doubled. Force is increased and distance moved is decreased.
Forces can be nicely multiplied with a system of pulleys. Such pulley
arrangements are common wherever heavy loads are lifted, such as automobile service centers or machine shops. An ideal pulley system is
shown in Figure 6.21. The man pulls 7 m of rope with a force of 50 N
.... FIGURE 6.21
Input force X input distance= output force X output distance. Note that the
load is supported by seven strands of rope. Each strand supports oneseventh of the load. The tension in the rope pulled by the man is likewise
one-seventh of the load.
CHAPTER 6
ENERGY
103
DISCOVER!
Rub your hands briskly together. The friction
between them multiplied by the distance of
rubbing produces work that beco mes heat.
Note how quickly your palms
are warmed.
and lifts 500 N through a vertical distance of 0. 7 m. The work the man
does when pulling the rope is numerically equal to the increased potential energy of the 500-N block.
Any machine that multiplies force does so at the expense of distance.
Likewise, any machine that multiplies distance does so at the expense of
force. No machine or device can put out more energy than is put into it.
No machine can create energy; it can only transfer it or transform it
from one form to another.
6.9 Efficiency-A Measure of Work
Done for Energy Spent
Given the same energy input, some machines can do more work than
others. ./ The machines that can do more work are said to be more
efficient.
Efficiency can be expressed by the ratio
Efficiency =
work done
d
energy use
Even a lever converts a small fraction of input energy into heat when
it rotates about its fulcrum. We may put in 100 J of work but get out
98 J. The lever is then 98% efficient, and we waste 2 J of work input on
heat. In a pulley system, a larger fraction of input energy goes into heat.
If we do 100 J of work, the forces of friction acting through the distances
through which the pulleys turn and rub about their axles may dissipate
60 J of energy as heat. So the work output is only 40 J, and the pulley
system has an efficiency of 40 percent. The lower the efficiency of a
machine, the greater the amount of energy wasted as heat.
CHECK YOUR THINKING
Consider an imaginary miracle car that has a 100% efficient engine
and burns fuel that has an energy content of 40 megajoules per liter
(MJ/L). If the air drag plus frictional forces on the car traveling at
highway speed is 500 N, what is the maximum distance the car can
travel on 1 L of fuel?
A machine can multiply force,
but never energy. No way!
104
PART ONE
Physics
Answer
From the definition work= force X distance, simple rearrangement gives distance=
work/force. If the entire 40 million J of energy in 1 L is used to do the work of overcoming
the air drag and frictional forces, the distance covered is
work
40,000,000 J
Distance = - - =
= 80,000 m = 80 km
force
500 N
What can more-efficient
machines do compared with
less-efficient machines?
The important point here is that even with a perfect engine, there is
an upper limit of fuel economy dictated by the conservation of energy.
An automobile engine is a machine that transforms chemical energy
stored in gasoline into mechanical energy. But only a fraction of the
energy in the gas is used by the car to move forward. Some of the fuel
energy in the gas goes out in the hot exhaust gases and is wasted. Also,
nearly half of the energy stored in the gas is wasted in the friction of the
moving engine parts. In addition to these inefficiencies, some of the gas
doesn't even burn completely. So the energy in the unburned gasoline
also goes unused. We await cars that burn no gasoline!
Pate~
,.,
"'"!
_... .-:..
:
~
energy
+more heat
of molecular
motion
Still more
heat (faster
molecular motion)
----------
" .,. .. ... Less ki netic energy- -- - ...
, , ... " ~to + more potential energy ....... . . . ,
1">'1..41
"to Kinetic+ potential energy
Cf?d ~
,
jlJ~cal en_?JSY
_
,
lJto
-:;;z:;:: _
',,
Heat (kinetic energy' ,
-::==of""m<1eculesl . ~ii)
FIGURE 6.22 .A
Energy transitions. The graveyard of kinetic energy is thermal energy.
,...,_ INTEGRATED SCIENCE
----------.,., CHEMISTRY, BIOLOGY, EARTH SCIENCE,
ASTRONOMY
Alternative Sources of Energy
The law of conservation of energy tells us that energy cannot be created
or destroyed. So why do newspapers feature so many stories about
energy shortages now and in the future? Is the world really running out
of energy?
The total amount of energy in the universe is constant, and the
world cannot run out of it. However, the useful energy delivered to
CHAPTER 6
humans from convenient sources is indeed limited. Most comes from
the burning of fossil fuels-coal and petroleum. You know that petroleum powers conventional cars and other vehicles. But did you know
that most electricity is generated by burning fossil fuels? But fossil fuels
are a finite resource-they will one day be depleted. (Fossil fuels are
discussed again in Chapter 37.) What alternative energy sources can
replace fossil fuels?
One promising alternative energy source is solar energy. Solar
energy is energy captured directly from the Sun. Solar energy is clean,
safe, and renewable. A renewable resource is a resource that is present
in great abundance and is continually produced. Solar energy is now
harnessed in three ways: as passive solar heating, active solar heating,
and solar cells. Passive solar heating is a method of heating buildings
that requires no pumps or fans. Buildings are constructed so they face
the Sun. They are made of heat-absorbing materials so that a maximum
amount of solar radiation is captured. The only requirement is a good
supply of sunlight. Structures heated by active solar heating have a series
of solar collectors that absorb solar energy and convert it to heat. The
heat warms a tank of water. Pumps or fans circulate the heated water
throughout the building. Solar cells are devices that convert the Sun's
energy directly to electricity. Solar cells are sometimes called
photovoltaics. Until recently, solar cells did not have many applications
beyond watches and calculators because they were expensive to produce
and not very efficient. However, strides are being made and there is
promise that solar power may provide substantial amounts of energy to
sunny locations.
t
ENERGY
105
Fossil fuels are running out.
What alternative sources
of energy can replace fossil
fuels?
FIGURE 6.23 £
The Sun is the ultimate source
of the energy trapped in fossil
fuels. The Sun's heat underlies
the wind and wind energy.
Biomass energy is solar energy
plants have trapped. Solar
energy technology is the
direct usage of sunlight. No
doubt about it, the Sun is the
source of a great deal of the
energy we use to run our
technology.
<!Ill
FIGURE 6.24
These buildings, which use
passive solar technology,
are student dormitories at
the University of Glasgow in
Scotland. Both the coverings
of the solar panels and the
windows incorporate transparent insulation (TI). Tl allows
the Sun's rays to enter the
building but slows the loss of
heat from inside to outside.
106
PART ONE
Physics
FIGURE 6.25 £.
A biodiesel filling station in
Germany. Biodiesel is less
polluting and contributes
much less to global warming
than fossil fuels. Also of major
importance-biodiesel is
renewable.
,.,._
"'-'
UNIFYING
CONCEPT
The Greenhouse Effect
CHAPTER
35
Integrated Science-Physics:
Heating the Atmosphere
CHECK
YOUR READING
What fuel may be a leading
form of biomass energy in
the future?
Moving air-wind-is another alternative energy source for the
future. Wind power captures some of the kinetic energy in wind and
converts it to electricity. As a strong wind blows, it pushes the blades of a
turbine. A turbine is a machine with large spinning blades that resembles
a fan. The turbine is connected to a generator, a machine that converts
mechanical energy to electrical energy through a clever application of
magnets and coiled wire. (You will learn more about generators in
Chapter 10.) Wind power, like solar power, is safe, clean, and renewable.
However, like solar power, wind power is restricted to locations with the
proper climate.
Geothermal energy is a third source of clean and safe energy. But like
wind and solar, geothermal energy is restricted to areas with the right
local conditions. Geo means "Earth" and thermal means "heat";
geothermal energy is energy that comes from Earth's hot interior. Earth's
heat is used to warm water enough to make steam. The steam then
pushes turbines connected to a generator. Heat energy is converted to
electricity.
Hydroelectricity converts the energy of falling water to electricity.
Dams hold water in elevated reservoirs. When the water falls, it gives up
a great deal of potential energy that is used to turn blades of a heavy
turbine. As in wind power and geothermal energy, a generator converts
the turbine's motion to electricity. Hydroelectric power is clean and
renewable and leaves no waste. However, dams can have many environmental impacts, and building them is expensive.
Biomass is the organic matter in plants. Biomass is a worldwide energy
source that is rising in importance. It is currently as cheap to use as coal.
Much biomass exists in the form of waste material. Some industries are
now using this huge resource. The U.S. pulp and paper industry, for
instance, generates more than half the energy it uses from its own waste
products. if~, Biodiesel may be a leading biomass energy source for the
future. Biodiesel is a fuel made from pure oils of plants such as soybeans,
corn, and peanuts. It is also produced from filtered vegetable oils, principally restaurant grease. The exhaust from biodiesel cars is less polluting
than gasoline exhaust, and it contributes less (and sometimes not at all) to
the greenhouse effect and global warming. Biodiesel may make you hungry, however, because it does have the slight aroma of French fries! Watch
for biodiesel as an alternative to gasoline in powering automobiles.
The most concentrated form of usable energy is stored in uranium
and plutonium, which are nuclear fuels. Nuclear power is discussed in
much greater detail in Chapter 15.
CHECK YOUR THINKING
1. Which alternative energy source is not tied to a particular climate
or location?
2. What is the reason for the current widespread use of fossil fuels?
Why is there concern about fossil fuels?
CHAPTER 6
Answers
1. Biomass.
2. Fossil fuels are a concentrated source of energy and up until now have been fairly easy
to produce and use. The present concern has arisen because fossil fuels are a finite
resource.
ENERGY
107
In biology, you'll learn how
the body takes energy from
the food you eat to build
molecules of adenosine
triphosphate, or ATP, and
how this supply of ATP is
used to run all the chemical
reactions that sustain life.
,.... INTEGRATED SCIENCE
"J BIOLOGY AND CHEMISTRY
Energy for Life
Your body is in many ways a machine-a fantastically complex machine.
It is made up of smaller machines, the living cells (Figure 6.26). Like any
machine, a living cell needs a source of energy.
The source of energy for plants is the Sun. Energy is taken in by
plants during photosynthesis. Photosynthesis is the process by which
plants, algae, and certain kinds of bacteria convert light energy from the
Sun to chemical energy in sugar molecules. Some plants, of course, don't
have the opportunity to consume the energy they take in. Instead they
donate it to the animals that consume them. Thus, almost all life on
Earth is either directly or indirectly dependent on photosynthesis.
Each of us has a fundamental
responsibility to treat our
planet with respect and a
sense of stewardship.
FIGURE 6.26 .A.
Plants capture solar energy and transform it into chemical energy, which is
stored in large molecules. When animals consume the plants, they obtain the
energy they need for life.
REVIEW
WORDS TO KNOW AND USE
2. Which requires more work-lifting a 50-kg sack a
vertical distance of 2 m or lifting a 25-kg sack a
vertical distance of 4 m?
Biodiesel Fuel made from pure oils of plants or by
filtering used vegetable oils, principally cooking grease.
Conservation of energy Energy cannot be created or
destroyed; it may be transformed from one form into
another or transferred from one object to another, but
the total amount of energy never changes. In an ideal
machine, where no energy is transformed into heat,
6.2 Power-How Quickly Work Gets Done
3. If both sacks in Question 2 are lifted their respec-
tive distances in the same time, how does the
power required for each compare? How about for
the case in which the lighter sack is moved its
distance in half the time?
workinput = workoutput and (Fd\nput = (Fd)outpue
Efficiency The percentage of the work put into a
machine that is converted into useful work output.
6.3 Mechanical Energy
4. Exactly what is it that a body having energy is
capable of doing?
Energy The property of a system that enables it to
do work.
5. What are the two main forms of mechanical
Kinetic energy Energy of motion, described by the
relationship kinetic energy=~ mv2•
6.4 Potential Energy Is Stored Energy
Machine A device such as a lever or pulley that
increases (or decreases) a force or simply changes the
direction of a force.
Potential energy The stored energy that a body
possesses because of its position.
Power The time rate of doing work:
power= work/time.
Renewable resource A resource that is present in great
abundance and is continually produced.
Watt The unit of power, the joule per second.
Work The product of the force and the distance
through which the force moves: W = Pd.
Work-energy theorem The work done on an object is
equal to the energy gained by the object: Work= ~E.
REVIEW QUESTIONS
6.1 Work-Force X Distance
1. Cite an example in which a force is exerted on an
object without doing work on the object.
108
energy?
6. A car is lifted a certain distance in a service station
and therefore has potential energy relative to the
floor. If it were lifted twice as high, how much
potential energy would it have?
7. Two cars are lifted to the same elevation in a
service station. If one car is twice as massive as the
other, how do their potential energies compare?
8. How many joules of potential energy does a 1-N
book gain when it is elevated 4 m? When it is
elevated 8 m?
6.5 Kinetic Energy Is Energy of Motion
9. A moving car has kinetic energy. If it speeds up
until it is going four times as fast, how much
kinetic energy does it have in comparison?
6.6 The Work-Energy Theorem
1 0.
Compared to some original speed, how much work
must the brakes of a car supply to stop a car
moving three times as fast? How will the stopping
distance compare?
6.7 Conservation of Energy
11.
What will be the increase in kinetic energy of a pile
driver ram when it undergoes a 10-kJ decrease in
potential energy? (Assume no energy goes to heat.)
CHAPTER 6
6.8 Machines-Devices to Multiply Forces
12. Can a machine multiply input force? Input
distance? Input energy? (If your three answers are
the same, seek help, because the last question is
especially important.)
13. If a machine multiplies force by a factor of four,
what other quantity is diminished, and how much?
6.9 Efficiency-A Measure of Work Done
for Energy Spent
14. What is the efficiency of a machine that miracu-
lously converts all the input energy to useful
output energy?
15. Is a machine physically possible that has an
efficiency greater than 100%? Discuss.
ENERGY
109
Compare the temperatures of the water in the two
bowls. Explain your observations.
2. Pour some dry sand into a tin can with a cover.
Compare the temperature of the sand before and
after vigorously shaking the can for a couple of
minutes.
3. ~ Investigate which materials are best for conU verting sunlight to heat. Collect materials
such as aluminum, glass, black plastic from
garbage bags, wood, rock, and soil. Put same-size
samples of each material in the same sunny location. Tape a thermometer to each sample. Measure
the temperature of each material. After an hour,
measure the temperature of each material again.
Record your results. Which material would be best
for building a passive solar heating system?
THINK AND EXPLAIN
1. When the velocity of an object is doubled, how is
,..._ INTEGRATED SCIENCE
.._, THINK AND LINK
Chemistry, Biology, Earth Science,
Astronomy-Alternative Sources of Energy
1. Explain why fossil fuels, biomass, and windmills
are all really sources of stored solar energy.
2. What is the source of geothermal energy?
3. Describe the three forms of solar energy. Which
one of these can be used on the widest scale? Why
do you think so?
its kinetic energy changed?
2. Consider a ball thrown straight up in the air. At
what position is its potential energy at maximum?
Where is its kinetic energy a maximum?
3. A science teacher demonstrates energy conservation by releasing a heavy
pendulum bob, as shown
in the sketch, allowing it
to swing to and fro. What
would happen if, in his
exuberance, he gave the
bob a slight shove as it
left his nose? Explain.
4. Discuss the design of the roller coaster shown in
the sketch in terms of the conservation of energy.
Biology and Chemistry-Energy for Life
1. Why do cells need energy?
2. What is the ultimate source of energy that powers
most life on Earth?
3. Name the process that changes light energy into
the chemical energy in sugar molecules?
THINK AND DO
1. Fill two mixing bowls with water from the cold tap
and take their temperatures. Then run an electric
or hand beater in the first bowl for a few minutes.
5. Suppose that you and two classmates are
discussing the design of a roller coaster. One
classmate says that each summit must be lower
than the previous one. Your other classmate says
110
6.
7.
8.
9.
PART ONE
Physics
this is nonsense, for as long as the first one is the
highest, it doesn't matter what height the others
are. What do you say?
Consider molecules of hydrogen (tiny ones) and
oxygen (bigger ones) in a gas mixture. If they have
the same average kinetic energy (they will at the
same temperature), which molecules have the
greatest average speed?
On a slide, a child has potential energy that
decreases by 1000 J while her kinetic energy
increases by 900 J. What other form of energy is
involved, and how much?
According to the work-energy theorem, in the
absence offriction, if you do 100 J of work on
a cart, how much will you increase its kinetic
energy?
The photo shows author Paul Hewitt delivering a
blow to a cement block that rests on a bed of nails.
Sandwiched bravely between them is San Mateo
High School physics teacher Pablo Robinson.
Because the blow is shared by many nails on
Robinson's body, the force per nail won't puncture
his skin. Discuss what Robinson's fate might be if
the block were less massive and unbreakable, and
the beds contained fewer nails.
lower part of track B, which ball has the greatest
average speed on the ramps?)
~---- A
~. .--------..J~
8
11. You tell your friend that no machine can possibly
12.
13.
14.
15.
put out more energy than is put into it, and your
friend states that a nuclear reactor puts out more
energy than is put into it. What do you say?
Scissors for cutting paper have long blades and
short handles, whereas metal-cutting shears
have long handles and short blades. Bolt cutters
have very long handles and very short blades. Why
is this so?
Does a high-efficiency machine convert a relatively
high or relatively low percentage of energy to
thermal energy?
If an automobile had a 100% efficient engine,
transferring all of the fuel's energy to work, would
the engine be warm to your touch? Would its
exhaust heat the surrounding air? Would it make
any noise? Would it vibrate? Would any of its fuel
go unused?
A friend says the energy of oil and coal is actually
a form of solar energy. Is your friend correct, or
mistaken?
THINK AND COMPARE
1. The mass and speed of three vehicles is shown in
the figure.
2.0 m/s
A 1.o_m/s
•
800 kg
Tracks A and B as shown. When they reach the
right ends of the tracks, which will have the greater
speed? (Hint: Will their KEs be the same at the
end?) Which will get to the end in the shortest
time? (Hint: Considering the extra speed in the
1000 kg
-
£
90 kg
Rank the vehicles by momentum, from most to
least.
(b) Rank the vehicles by kinetic energy, from most
to least.
2. Consider the following four situations. Assume
zero gravitational potential energy (PE) at ground
level. Some have kinetic energy (KE) and some
(a)
10. Consider the identical balls released from rest on
8
8.0 m/s
CHAPTER 6
don't. (As always, tie scores can be part of your
ranking.)
A. A 3-kg ball at rest atop a S-m-tall hill
B. A 4-kg ball at rest atop a S-m-tall hill
C. A 3-kg ball moving at 2 m/s atop a S-m-tall hill
D. A 4-kg ball moving at 2 m/s at ground level.
(a) Rank the situations by PE, from most to least.
(b) Rank the situations by KE, from most to least.
(c) Rank the situations by total mechanical energy,
from most to least.
3. The roller coaster ride shown in the figure begins
at point A, assume at rest, then proceeds down the
incline. Assume that PE at ground level is zero.
Rank the following values for points A-E from
most to least.
(a) Speed
(b) KE
(c) PE
+
ENERGY
111
4. Consider an ideal pulley system. If you pull one
end of the rope downward with 50 N a distance of
1 m, show that you will lift a 200-N load 0.2S m.
5. Show that 4 W of power are expended when a
force of 2 N moves a book 4 m in a time interval
of2 s.
MULTIPLE CHOICE PRACTICE
Choose the best answer to the following. Check
your answers with your teacher.
1. How much work is done on a 100-kg crate that is
hoisted 2 m in a time of 4 s?
(a) 200 J
(b)
soo J
800 J
2000 J
2. How much power is required to raise a
100-kg crate a vertical distance of 2 min a
time of 4 s?
(a) 200W
(c)
(d)
4. Consider the efficiency of the following four
machines.
(a) Energy in, 100 J; energy out, 60 J
(b) Energy in, 100 J; energy out, SO J
(c) Energy in, 200 J; energy out, 80 ].
(d) Energy in, 200 J; energy out, 120 J.
Rank the machines by efficiency, from highest to
lowest.
THINK AND SOLVE
1. Show that 2 Jof work are done when a force of 1 N
moves a book 2 m.
2. This question is typical on some driver's license
exams: A car moving at SO km/h skids 1S m with
locked brakes. How far will the car skid with
locked brakes at 1SO km/h?
3. A force of SO N is applied to the end of a lever,
which is moved a certain distance. If the other end
of the lever moves one-third as far, show that it can
exert a force of 1SO N.
(b)
soow
800 W
(d) 2000W
3. Raising an auto in a service station increases its
potential energy. Raising it twice as high increases
its potential energy by
(a) half.
(b) the same amount.
(c) twice.
(d) four times.
4. A model airplane moves three times as fast as
another identical model airplane. Compared to the
kinetic energy of the slower airplane, the kinetic
energy of the faster airplane is
(a) the same for level flight.
(b) twice as much.
(c) four times as much.
(d) more than four times as much.
(c)
112
PART ONE
Physics
5. Which of the following equations is most useful
for solving a problem that asks for the distance a
fast-moving box slides across a post office floor
and comes to a stop?
(a)
F =ma
(b) Ft=~mv
=t
KE
mv2
(d) Fd =~t mv2
6. A shiny sports car at the top of a vertical cliff has a
potential energy of 100 MJ relative to the ground
below. Unfortunately, a mishap occurs and it falls
over the edge. When it is half way to the ground its
kinetic energy is
(a) the same as its potential energy at that point.
(b) negligible.
(c) about 60 MJ.
(d) more than 60 MJ.
7. When a huge truck brakes to a stop, much of its
kinetic energy is transformed to
(a) heat.
(b) work.
(c) electric potential energy.
(d) gravitational potential energy.
(c)
8. In an ideal pulley system, a woman lifts a 100-N
crate by pulling a rope downward with a force of
25 N. For every one-meter length of rope she pulls
downward, the crate rises
(a) 50 em.
(b) 45 em.
(c) 25 em.
(d) None of the above
9. When 100 J are put into a device that puts out 40 J,
the efficiency of the device is
(a) 40%.
(b) 50%.
(c) 60%.
(d) 140%.
10. A machine cannot multiply
(a) forces.
(b) distances.
(c) energy.
(d) All of the above