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CHA PTER
Energy
CONCEPTS
— -In A c tio n —
How do science concepts apply to your
world? Here are some questions you'll be
able to answer after you read this chapter.
m
W hy does a basketball bounce higher than
a slice of bread? (Section 15.1)
m
How can an object from space damage a
car? (Section 15.2)
m
How do gulls use energy conversion to
obtain food? (Section 15.2)
■ How do pole vaulters propel themselves
high into the air? (Section 15.2)
m
How can the wind be used to light a bulb?
(Section 15.3)
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Video Field Trip
..........
Physics of Fun
How are roller coasters designed to be
both safe and thrilling? (page 460)
PHYSICS
Chapter Preview
15.1
Energ y and Its Form s
15.2
En erg y C on version and
C o n servatio n
15.3
En erg y Resources
How Can Energy Change Form?
Procedure
Think About It
1. Examine a flashlight, a solar calculator, and
a wind-up toy. Determine how each object
operates.
1. Classifying W hat was the source of energy
2. Record the name of each object, the source of
the energy that it requires, and the kind of
energy it produces. For exam ple, does the
object require or produce electricity or light?
for each object?
2. Inferring W hat form of energy did each
object produce?
3. Drawing Conclusions How did energy
change form in each object? For exam ple, did
any of the objects convert light into another
form of energy?
Energy
445
Reading Focus
Key Concepts
©
How are energy and
work related?
©
What factors does the
kinetic energy of an
object depend on?
©
How is gravitational
potential energy
determined?
©
What are the major
forms of energy?
Reading Strategy
♦ energy
♦ kinetic energy
♦ potential energy
♦ gravitational
potential energy
♦ elastic potential
energy
♦ mechanical energy
♦ thermal energy
♦ chemical energy
♦ electrical energy
♦ electromagnetic
energy
♦ nuclear energy
Building Vocabulary Copy the partially
completed concept map below. Then, as
you read, complete it with vocabulary terms
and definitions from this section.
A he road that winds through the m ountain valley was
closed. Skiers were banned from the area. The sound of
artillery fire echoed from the mountains. It seemed out of
place in this picturesque scene of snow-covered peaks surrounding the valley. A m om ent of quiet followed the blast.
Suddenly the snow broke loose with a menacing roar.
Tumbling down the mountainside, the snow buried everything in its path. You can see in Figure 1 the enormous mass
of accumulated snow that had hung above the valley. After
the avalanche, the valley was quiet again. It is safe for skiers
and hikers to return to the area.
This is the work of researchers at the Avalanche Control
Section in Glacier National Park, Canada. These scientists
m onitor the snow as it builds up layer by layer on the
park’s upper peaks. They can predict when an avalanche is
about to happen. W ith well-timed artillery shots, they
make the avalanche happen at a time when the released
energy cannot harm anyone.
Figure 1 In an avalanche, a mass of
loose snow, soil, or rock suddenly
gives way and slides down the side
of a mountain.
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C hap ter- i 5 * *
Energy and Work
Where did the energy of the avalanche come
from? Where did it go? Energy is known by
the changes it causes. You can hear the roar
of an avalanche and see the movement of the
snow. Sound and m otion are examples of
energy in action. In order to define energy,
you need to return to the definition of a
related topic, work. Recall that work is done
when a force moves an object through a distance. Energy is the ability to do work. In
other words, energy is transferred by a force
moving an object through a distance.
Work and energy are closely related. W hen work is done on an
object, energy is transferred to that object.
Work is a transfer of
energy. Both work and energy are typically measured in joules (J).
Recall that 1 joule equals 1 newton-meter, the work done when an
object is moved 1 meter by a 1-newton force. Although energy can take
many different forms, it can always be measured in joules.
Think about the work and energy involved in doing something as
simple as carrying your backpack up a flight of stairs. You do work on
the backpack by lifting it against the force of gravity. This work requires
energy. The energy to do the work comes from your muscles. Your
muscles receive energy from the food you eat. The energy contained in
your food comes from plants that have used the energy of sunlight, or
animals that have eaten such plants. Figure 2 shows some of the many
forms of energy.
Figure 2 Energy has many
different forms. A The sun
gives off energy in the form
of heat and light. B Plants
convert sunlight into food
that we can process and
eat. C People convert food
energy into muscle
movement.
Applying Concepts How
did the skiers in the photo
obtain the energy to climb
the mountain slope?
Kinetic Energy
Many forms of energy can be classified into two general types: kinetic
energy and potential energy. The energy of motion is called kinetic energy.
The word kinetic comes from the Greek word kinetos, meaning “moving.”
The kinetic energy of any moving object depends upon its
mass and speed. To calculate the kinetic energy of an object in joules,
multiply y by the object’s mass (m) in kilograms and the square of its
speed (v) in meters per second.
r- Kinetic E n e rg y ----------------------------------------------Kinetic energy (KE) = y m v 2
Notice that doubling the mass in the formula would double the
kinetic energy. However, doubling the speed would quadruple the
kinetic energy, since kinetic energy is proportional to the square of an
object’s speed.
Energy
447
Calculating Kinetic Energy
A 0 .1 0-kilogram bird is flying at a constant speed of 8.0 m/s. What
is the bird's kinetic energy?
P fun ilex
Read and Understand
What information are you given?
1. A 70.0-kilogram man is walking
at a speed of 2.0 m/s. W hat is
his kinetic energy?
2. A 1400-kilogram car is moving at
a speed of 25 m/s. How much
kinetic energy does the car have?
3. A 50.0-kilogram cheetah has a
kinetic energy of 18,000 J. How
fast is the cheetah running?
(Hint: Rearrange the equation to
solve for v.)
Mass, m = 0.10 kg
Speed, v = 8.0 m/s
What unknown are you trying to calculate?
Kinetic energy of the bird, KE
^
Plan and Solve
What equation contains the given quantities and
the unknown?
KE = yfflV2
Substitute the known values in the formula for KE.
KE = y(0.10 kg)(8.0 m/s)2
= 3.2 kg*m2/s2 = 3.2 J
Look Back and Check
Is your answer reasonable?
It seems reasonable because the bird has a low mass, so it
would not have much kinetic energy.
Potential Energy
Figure 3 When this musician
pulls the string of her cello to one
side, the string is stretched and
gains potential energy.
448
Chapter 15
P otential energy is energy that is stored as a result of position or
shape. The musician in Figure 3 adds energy to the cello string by
plucking it. The energy is stored in the stretched string when the
musician pulls it to one side. Then she releases the string and allows
it to vibrate. The stored energy is converted into kinetic energy. You
can also store energy just by picking up a book and holding it in the
air. Let go of the book and that stored energy will turn into the kinetic
energy of m otion as the book falls to the floor. Plucking a string and
lifting a book are two examples of stored energy— energy with the
potential to do work. Two forms of potential energy are gravitational
potential energy and elastic potential energy.
Gravitational Potential Energy When you
lift your gym bag up to the top seat of the bleachers,
you do work to increase the potential energy of your
bag. Potential energy that depends upon an object’s
height is called gravitational potential energy. This type
of potential energy increases when an object is raised to a
higher level.
The diver shown in Figure 4 is standing motionless at the
end of a diving board, so she has no kinetic energy. But she does
have energy— gravitational potential energy. She gained this
potential energy by doing work— by climbing up the steps to the
diving board. As always, the work done equals force (her weight) m ultiplied by distance (the height she climbs). You can use this work to
calculate how much potential energy is gained.
© An object’s gravitational potential energy depends on its
mass, its height, and the acceleration due to gravity. The gravitational
potential energy an object gains is equal to its weight (mg) multiplied
by its height (h).
— Gravitational Potential Energy
Potential energy (PE) = mgh
To calculate gravitational potential energy in joules, the mass of
the object is expressed in kilogram s and the height o f the object is
expressed in meters. The acceleration due to gravity, g, has a value
in SI units of 9.8 m /s2 on Earth. Note that height is m easured from
the ground or floor or some other reference level. Therefore, gravitational p o ten tial energy is m easured relative to th a t sam e
reference level.
Gravitational potential energy is directly related to the mass of
the object and its height relative to a reference level. Thus, doubling
either the mass of the object or its height doubles its gravitational
potential energy.
Suppose the diver at the top of a 10.0-meter-high diving platform
has a mass of 50.0 kilograms. You can calculate her potential energy
relative to the ground as follows.
PE = mgh
= (50.0 kg)(9.8 m /s2)(10.0 m)
= 4900 kg.m2/s2 = 4900 J
If, instead, the diver was standing on the ground, her height above the
ground would be zero. Therefore, her gravitational potential energy
relative to the ground would also be zero.
C h e ck p o in t
What is gravitational potential energy?
Figure 4 This diver has
gravitational potential energy as
she stands at the end of a diving
board. Predicting How would
the diver's potential energy
change i f she stood on a platform
twice as high as the one shown in
the photo?
rGo in lin e
SCllN KS
For: Links on potential and
kinetic energy
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Web Code: ccn-2151
Energy
449
Figure 5 A compressed bicycle shock
absorber and a wound-up toy robot both
have elastic potential energy.
Elastic Potential Energy The potential energy of an object that
Investigating Elastic
Potential Energy
M aterials basketball, tennis
ball, meter stick
Procedure
^
1.
Drop the basketball from a
height of 1 m. Use a meter
stick to measure how high
it bounces. Record your
result.
2.
Repeat Step 1 with the
tennis ball.
3. Place the tennis ball on top
of the basketball and drop
both together from a height
of 1 m. Record your
observations.
1. Observing How high did
the tennis ball bounce in
Steps 2 and 3?
2. Applying Concepts
From your observations of
Step 2, how can you prove
that the kinetic energy of
the tennis ball just after a
bounce is less than it was
just before the bounce?
Mechanical Energy The energy associated with the motion and
position of everyday objects is mechanical energy. Don’t be confused
by the name, however. Mechanical energy is not limited to machines.
Mechanical energy is the sum of an object’s potential energy and
kinetic energy. Speeding trains, bouncing balls, and sprinting athletes
all have mechanical energy.
3. Drawing Conclusions
Use the concepts of kinetic
and potential energy to
explain your observations
of the tennis ball in Step 3.
450
J
Chapter 15
Forms of Energy
All energy can be considered to be kinetic energy, potential energy, or
the energy in fields such as those produced by electromagnetic waves.
Some familiar examples are the chemical energy in fireworks, electrical energy in lightning bolts, and nuclear energy within the sun.
( ^ T h e major forms of energy are mechanical energy, thermal
energy, chemical energy, electrical energy, electromagnetic energy,
and nuclear energy. Each of these forms of energy can be converted
into other forms of energy.
Analyze and Conclude
v
is stretched or compressed is known as elastic potential energy.
Something is said to be elastic if it springs back to its original shape after
it is stretched or compressed. Think back to the last time you stretched
a rubber band between your fingers. By stretching the rubber band, you
did work on it. Just like the musician did with her cello string, the energy
you added was stored in the rubber band as potential energy. If you’ve
ever broken a stretched rubber band, you may have felt a painful snap
on your hand. The rubber band’s elastic potential energy was converted
into kinetic energy.
Elastic potential energy can also be stored in objects that are compressed, such as springs. Drop a slice of bread on the floor and it does
not bounce noticeably. Why doesn’t it? The bread is not very elastic.
Drop a basketball on the floor and the basketball bounces back up. The
compressed air in the ball forces the ball to spring back into shape after
hitting the ground, propelling the ball back up. Other examples of elastic potential energy are shown in Figure 5.
Mechanical energy does not include thermal energy, chemical
energy, or other forms of energy associated with the motion or the
arrangement of atoms or molecules. Most of these other forms of energy
do involve kinetic or potential energy, but on an atomic scale. However,
the mechanical energy of a speeding train and a sprinting athlete comes
from the chemical energy of the train’s fuel and the sprinter’s body cells.
Thermal Energy Almost all of the matter around you contains
atoms. These particles are always in random m otion and thus have
kinetic energy. The total potential and kinetic energy of all the microscopic particles in an object make up its th erm al energy. When an
object’s atoms move faster, its thermal energy increases and the object
becomes warmer. As Figure 6 shows, when objects are hot enough they
can emit visible light.
Chemical Energy The campers in Figure 7 are toasting m arshmallows over a campfire. The source of energy for the fire is the energy
stored in wood. When the wood is burned, energy is released and heats
the marshmallows as well as the area around the campfire. The energy
stored in wood is chemical energy. Chem ical energy is the energy
stored in chemical bonds. When bonds are broken, the released energy
can do work. All chemical compounds, including fuels such as coal
and gasoline, store energy. For example, cars can use the chemical
energy stored in gasoline to move about. The gasoline is burned in the
car’s engine and some of its chemical energy is converted into mechanical energy to move the car.
^
Checkpoint
j
W hat i$ chem ical energy?
Figure 6 Energy occurs in many
forms. This molten metal is
extremely hot. It contains a great
deal of thermal energy.
Observing What other kinds o f
energy are evident in this
photograph?
Figure 7 This family is using the
chemical energy of burning wood
to produce thermal energy for
heating marshmallows.
Energy
451
Electrical Energy Many devices you use every day use electricity, or electrical energy. Electrical energy is the energy associated
with electric charges. Electric charges can exert forces that do work.
Batteries, which convert chemical energy to electrical energy, are used
to operate portable CD players, flashlights, and calculators. Electrical
energy also occurs in nature. The powerful bolts of lightning shown
in Figure 8A are produced by electrical energy.
Electromagnetic Energy The sun radiates electromagnetic
B
Figure 8 Two major forms of
energy are electrical energy and
electromagnetic energy.
A Lightning bolts transfer electric
charge. B Galaxies are giant
structures in space that typically
contain billions of stars. The stars
give off enormous amounts of
electromagnetic energy.
energy into space and is the source, either directly or indirectly, of most
of the world’s energy supplies. Electromagnetic energy is a form of
energy that travels through space in the form of waves. Visible light
and X-rays are examples of electromagnetic energy. Because electromagnetic waves can travel long distances through air and space, they
are often used for communication. The glowing galaxy in Figure 8B is
emitting electromagnetic energy of many kinds.
Nuclear Energy The nucleus of an atom is held together by
strong and weak nuclear forces, which can store an enormous amount
of potential energy. The energy stored in atomic nuclei is known as
nuclear energy. A nuclear power plant uses nuclear fission reactions
to generate electricity. Nuclear fission is a process that releases energy
by splitting nuclei apart. A second type of nuclear reaction, nuclear
fusion, releases energy when less massive nuclei combine to form a
more massive nucleus. The heat and light of the sun are produced by
the fusion of hydrogen nuclei into helium nuclei.
Section 15.1 Assessment
Reviewing Concepts
1. ® Describe the relationship between work
and energy.
7. Applying Concepts Can an object have
both kinetic energy and potential energy at
the same time? Explain.
2. O How is the kinetic energy of an
object determined?
3. ® W hat factors determine the gravitational
potential energy of an object?
4. ® Give an example of each of the major
forms of energy.
5. When you heat a pot of water over a flame,
what form of energy is added to the water?
Critical Thinking
6. Applying Concepts W hat kind of
energy is represented by an archer
stretching a bow string?
452
Chapter 15
8. A 60.0-kg person walks from the
ground to the roof of a 74.8-m-tall
building. How much gravitational
potential energy does she have at the
top of the building?
9. A pitcher throws a 0.145-kg baseball at
a velocity of 30.0 m/s. How much
kinetic energy does the ball have?
15.2 Energy Conversion
and Conservation
Key Concepts
Vocabulary
Reading Strategy
©
Can energy be converted
from one form into
another?
♦ energy conversion
©
What is the law of
conservation of energy?
Relating Cause and Effect Copy the flow­
chart below. As you read, complete the chart
to explain an energy conversion. Make two
similar charts for pendulums and pole vaults.
©
What energy conversion
takes place as an object
falls toward Earth?
©
How are energy and
mass related?
O n October 9,1992, people from Kentucky to New York reported
seeing a bright streak of white light shooting across the night sky.
Most observers, having seen “shooting stars” before, expected this
one to quickly b urn out and disappear. However, that did not
happen. The shooting star, or meteor, continued streaking across the
sky. After a few seconds, pieces of the meteor broke off, creating a
series of smaller streaks of light. Eventually, the streaks disappeared
from view. Although the event was interesting, most witnesses probably soon forgot about it.
However, the meteor was not soon forgotten by the owners of a
red automobile in Peekskill, New York. Unfortunately for them, a large
chunk of the meteor made it through Earth’s atmosphere and struck
their parked car. The car was badly damaged, as shown in Figure 9.
Luckily, no one was in the car at the time, and so
no one was hurt.
As the Peekskill meteor traveled through
the atmosphere, some of its kinetic energy
was converted into light and heat. The light
made the meteor visible in the sky. The heat
caused a large portion of the meteor to
vaporize in the atmosphere. Upon impact,
much of the m eteor’s remaining kinetic energy
went into smashing the metal body of the car.
Figure 9 A meteor crashed into
the rear of this car, causing
considerable damage.
Energy
453
Energy Conversion
Figure 10 Energy is converted
from one form to another as
this match is lit.
A p p lyin g Concepts What
energy conversions take place
when you turn on a batterypow ered portable radio?
The Peekskill m eteor clearly shows that energy can change forms.
Energy can be converted from one form to another. The process
of changing energy from one form to another is energy conversion.
Not all energy conversions are as dramatic as the Peekskill meteor.
Energy conversions are constantly talcing place all around you, often without you noticing. W ind-up toys store elastic potential energy in a
compressed spring. When the spring unwinds, potential energy is converted into the kinetic energy of the toy’s moving parts. Light bulbs
convert electrical energy into thermal energy and electromagnetic energy.
In some cases, energy is converted from one form into
another in a series of steps. The striking of the match shown
in Figure 10 is a good example. In lighting a match, your
muscles use chemical energy moving your hand to strike
the match against a rough area on the matchbox. Friction
between the match and the matchbox converts some of the
match’s kinetic energy into thermal energy. The thermal
energy triggers a chemical reaction on the match tip, releasing some of the match’s stored chemical energy. The stored
chemical energy is then converted into thermal energy and
electromagnetic energy in the flame.
Reading
Checkpoint J
What energy conversions occur in
lighting a match?
Exploring Energy Conversion
M aterials
5.
small steel ball of known mass, box lined with soft
modeling clay, meter stick, graph paper
Procedure r a
Analyze and Conclude
1.
Construct a data table with 3 blank rows and
5 columns labeled Mass, Height, Diameter,
Potential Energy, and Kinetic Energy.
1. Using Graphs According to your graph,
2.
Drop the ball into the box of clay from a
height of 30 cm . Record this height.
3.
Measure and record the diameter of the crater
that the ball formed.
4.
Repeat Steps 2 and 3, dropping the ball from
60 cm and 90 cm .
V
454
Graph your data. Plot the crater diameter
on the vertical axis and height on the
horizontal axis.
how are crater diam eter and the height of
the ball related?
2.
Calculating For each height, calculate and
record the initial potential energy of the ball.
3.
Drawing Conclusions How are kinetic
energy and crater diameter related? (Hint: The
ball's kinetic energy when it hits the clay equals
the potential energy it started with, mgh.)
_________________________________
Chapter 15
Figure 11 Although speed
skaters slide quickly over smooth
ice, they are still slowed down
by friction with the air and the
surface of the ice.
Inferring What are tw o ways
that skaters can reduce friction?
Conservation of Energy
When energy changes from one form to another, the total energy
remains unchanged even though many energy conversions may occur.
This is one of the most im portant concepts in science, the law of conservation of energy. (^ The law of conservation of energy states that
energy cannot be created or destroyed. According to the law of conservation of energy, energy can be converted from one form to
another. However, in a closed system, the am ount of energy present at
the beginning of a process is the same as the am ount of energy at the
end. (In a closed system, nothing can enter or leave.)
You know that if you stop pedaling when you’re riding a bike on a flat
path, the bike will eventually come to a stop. The moving bike had kinetic
energy. Where did the bike’s kinetic energy go? The bike slowed down
and stopped because of frictional forces acting over a distance. The work
done by friction changes kinetic energy into thermal energy.
As a bicycle moves, it encounters friction with the ground and the
air. Such friction causes a continual conversion of kinetic energy into
thermal energy. Thus, as the bicycle slows, it gains thermal energy. So
do the ground and the air. W hen the energy lost to frictional forces is
accounted for, energy is conserved overall.
Recall that friction within machinery reduces efficiency. Friction is
a major cause of energy consumption in cars and factories. All moving
parts are subject to friction.
You can reduce friction but you can’t avoid it. Friction is everywhere. Even the skaters in Figure 11 are subject to friction. Recall that
objects moving through the air are slowed by air resistance. In many
cases, most of a falling object’s potential energy is converted into thermal energy because of air resistance.
You can ignore the effects of friction in many everyday situations.
A marble dropped from one meter above the ground, for example,
encounters so little air resistance that it can be ignored.
c
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• « » > ,/
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Energy
455
Figure 12 Some gulls use energy
conversion to obtain food by
dropping oysters onto rocks.
A p p lyin g Concepts Where is
the oyster's potential energy
greatest? Where is its kinetic
energy greatest?
Energy Conversions
One of the m ost com m on energy conversions is between potential
energy and kinetic energy.
The gravitational potential energy of
an object is converted to the kinetic energy of motion as the object
falls. That’s what happens when an avalanche brings tons of snow from
the top of a m ountain to the valley floor. Similarly, when you
release a compressed spring, the elastic potential energy of
the spring is converted into kinetic energy as the spring
expands. Conversions between kinetic and potential energy can
happen in both directions, that is, from kinetic to potential energy, or
from potential to kinetic energy.
Some gulls use energy conversion to obtain food. Oysters are a food
source for gulls. However, it is difficult for a gull to break open an
oyster’s hard shell with its beak. Unfortunately for the oyster, gulls have
learned a clever way to use gravitational potential energy, as shown in
Figure 12. A hungry gull picks up an oyster and flies high into the air
directly over some rocks. The gull does work on the oyster by raising
it against the force of gravity, thereby increasing the oyster’s potential
energy. While over the rocks, the gull lets the oyster fall. As the oyster
falls, its gravitational potential energy is converted into kinetic energy.
The oyster picks up speed until it hits the rocks. The impact breaks
open the shell. The gull then swoops down to enjoy its meal.
Energy Conversion in Pendulums At the lake, you grab a
Figure 13 Pendulum clocks
use pendulums to maintain
accurate time.
456
Chapter 15
rope hanging from a tree branch. With a yell, you swing down toward
the lake, and pick up speed until you land with a giant splash. A rope
swing is an example of a pendulum. A pendulum consists of a weight
swinging back and forth from a rope or string.
Pendulums were used in the first truly accurate clocks. The Dutch
scientist Christiaan Huygens (1629-1695) made the first pendulum
clock in 1656. Pendulum clocks such as the one shown in Figure 13
make use of the fact that the time it takes for a pendulum to swing
back and forth once is precisely related to its length.
Kinetic energy and potential energy undergo constant conversion
as a pendulum swings. At the highest point in its swing, the pendulum
is momentarily motionless as it changes direction. At this point, the
weight at the end of the pendulum has zero kinetic energy and maxim um potential energy.
As the pendulum swings downward, potential energy is converted
to kinetic energy. At the bottom of the swing, the pendulum has maximum kinetic energy and zero potential energy. The pendulum then
moves upward again, repeating the process. Eventually, frictional forces
slow down the pendulum. In a clock, a spring mechanism or hanging
weights provide energy to keep the pendulum swinging despite the
effects of friction.
Energy Conversion in the Pole Vault The pole vault is a
difficult track and field event that requires a combination of speed,
strength, timing, and energy conversion. In the pole vault, an athlete
uses a flexible pole to propel himself over a high bar. Look at the polevaulter’s jum p in Figure 14 and think about how energy changes
during the jump.
In order to start the jum p with as much kinetic energy as possible,
the pole-vaulter sprints down the runway as fast as he can. At the end
of his sprint, he plants the end of a long pole at the base of the high bar
and propels himself into the air. The pole-vaulter’s kinetic energy is
partially converted into elastic potential energy as the pole bends.
The pole springs back into shape, propelling the pole-vaulter
upward, hopefully high enough to clear the bar.
As the pole-vaulter soars, his kinetic
energy decreases while he gains gravitational
potential energy. Once the highest point has
been reached, his gravitational potential
energy begins to convert back to kinetic
energy. The pole-vaulter picks up speed as he
falls back to the ground.
/ Reading
| | / Checkpoint
What energy changes
occur in a pole vault?
Energy Conversion Calculations W hen friction is small
enough to be ignored, and no mechanical energy is added to a system,
then the system’s mechanical energy does not change. Recall that
mechanical energy is the total kinetic and potential energy of an object.
Figure 14 A pole-vaulter
converts kinetic energy into
potential energy in order to
propel himself high into the air.
Applying Concepts A t which
point does a pole-vaulter have
the m ost gravitational
potential energy?
Mechanical energy = KE + PE
You can apply the law of conservation of energy to any mechanical
process. A mechanical process can be any action, such as the m otion of
a pendulum, water falling in a waterfall, or a diver propelled by a diving
board. In all of these processes, if friction can be neglected, the
mechanical energy at the beginning equals the mechanical energy at
the end. That is, total mechanical energy remains constant. This equality can be stated as follows.
Conservation of Mechanical Energy
(KE + PEjbeghming
(KE + PE)en(j
The Math Skills box on the following page shows how the conservation
of mechanical energy equation can be used.
Energy
457
Conservation of Mechanical Energy
At a construction site, a 1.50-kg brick is dropped from rest and hits
the ground at a speed of 26.0 m/s. Assuming air resistance can be
ignored, calculate the gravitational potential energy of the brick
before it was dropped.
Read and Understand
1. A 10-kg rock is dropped and hits
the ground below at a speed of
60 m/s. Calculate the gravi­
tational potential energy of the
rock before it was dropped. You
can ignore the effects of friction.
2. A diver with a mass of 70.0 kg
stands motionless at the top of a
3.0-m-high diving platform.
Calculate his potential energy
relative to the water surface while
standing on the platform, and his
speed when he enters the pool.
(Hint: Assume the diver's initial
vertical speed after diving is zero.)
3. A pendulum with a 1.0-kg
weight is set in motion from a
position 0.04 m above the lowest
point on the path of the weight.
What is the kinetic energy of the
pendulum at the lowest point?
(Hint: Assume there is no friction.)
What information are you given?
Mass, m — 1.50 kg
Final speed, v = 26.0 m/s
What unknown are you trying to calculate?
Gravitational potential energy of the brick
before it was dropped, PE
Plan and Solve
What equations or formulas contain the given quantities and
the unknow n?
Because the brick falls without air resistance, the
conservation of mechanical energy equation can be used.
(KE + PE) beginning — (KE + PE)en(J
You will also need to use the formula for kinetic energy (KE).
KE = y my2
N ote that the KE at the beginning is zero because the brick
has not yet begun to fall. Also, when the brick hits the
ground, its potential energy is zero. Substitute these values
into the conservation of energy formula.
(PE)beginning ~~ (KE)end
Substitute the formula for KE.
PE = KE = y m v 2
Substitute the known values and calculate the PE.
PE = y (1.50 kg) (26.0 m/s)2 = 507 kg*m2/s2 = 507 J
Look Back and Check
Is your answ er reasonable?
Check the answer by finding the initial height of the brick,
using PE = 507 J = mgh. Substituting in m and g gives
h = 34.5 m. This is a reasonable height for an object in
free fall to reach a speed of 26.0 m/s.
458
Chapter 15
Energy and Mass
Physicist Albert Einstein (1879-1955), shown in Figure 15,
developed his special theory of relativity in 1905. This theory
included the now-famous equation E = me2. In Einstein’s
equation, E is energy, m is mass, and c is the speed of light.
This seemingly ordinary equation has surprising consequences. ® Einstein’s equation, E = me2, says that energy
and mass are equivalent and can be converted into each
other. In other words, energy is released as m atter is
destroyed, and matter can be created from energy.
Notice that the speed of light is squared in Einstein’s
equation. The speed of light is an extremely large number,
3.0 X 108 meters per second. Thus, a tiny am ount of matter
can produce an enorm ous am ount of energy. Suppose
1 gram of matter were entirely converted into energy.
Figure 15 Albert Einstein made
important contributions to many
areas of physics. His theory of
special relativity showed that
energy and mass are equivalent.
E = me2 = (10“3 kg) X (3 X 108 m/s) X (3 X 108 m/s)
= 9 X 1013 kg*mr/s2 = 9 X 1013 J
In comparison, 1 gram of TNT produces only 2931 joules of energy. In
nuclear fission and fusion reactions, however, large amounts of energy
are released by the destruction of very small am ounts of matter.
Therefore, the law of conservation of energy has been modified to say
that mass and energy together are always conserved.
Section 15.2 Assessment
Reviewing Concepts
1. ® Describe how energy can be converted
from one form to another in a wind-up toy.
2. ® W hat does the law of conservation of
energy state?
8. Applying Concepts To begin a dive, a diver
jumps into the air and then lands on the
diving board, causing it to bend. W hat type of
energy conversions occur as the board springs
back and propels the diver up into the air?
3. ® As an object falls in free fall, w hat energy
change is taking place?
4 . ® W hat did Einstein conclude about the
relationship between energy and mass?
5. W hat type of energy change results when
friction slows down an object?
6. Describe the energy of a playground swing at
its highest position.
Critical Thinking
7. Inferring W hy does a bouncing ball rise to a
lower height with each bounce? W hat energy
conversion is taking place?
9. A 0.15-kg ball is thrown into the air
and rises to a height of 20.0 m. How
much kinetic energy did the ball
initially have?
10. A 125-g steel ball with a kinetic energy
of 0.25 J rolls along a horizontal track.
How high up an inclined track will the
ball roll if friction can be ignored?
Energy
459
Roller
Coasters
A roller coaster is a train powered by
gravity. An initial store of potential energy
is released dramatically during the ride.
A roller coaster’s first hill, called the lift hill, is the
highest point of the ride. As the coaster plunges
down the first drop, its potential energy is
converted into kinetic energy, the energy of
motion. Later, some of this kinetic energy is converted back into potential energy as the coaster’s
speed decreases during a climb. Over the course of
the ride, the coaster’s total mechanical energy
(potential plus kinetic energy) gradually decreases.
This change occurs due to friction from the rails
and the air, which causes the coaster’s mechanical
energy to be converted into heat. By the end of the
ride, all the potential energy created on the lift hill
has been lost as heat.
460
Chapter 15
As it falls,
the coaster
converts
potential
energy into
kinetic
energy.
Releasing energy
A roller coaster goes through a
series of exchanges between
potential and kinetic energy.
A cable pulls cars
Potential
energy rapidly
turns into kinetic
energy during
the first plunge.
Kinetic energy reaches a
maximum as the coaster reaches
the bottom o f the first hill.
The second loop has a lower
peak than the first because the
coaster's energy is reduced
friction.
to the top o f the
lift hill. During
the climb, the
coaster builds up
potential energy.
Design and safety
The job of a roller coaster designer is to
make sure that a ride is terrifying but safe.
Some people are concerned that designers
are providing riders with greater thrills at
the expense of their safety. Safety experts
say that the risk of injury is small, but it is
important to pay attention to restrictions
regarding height and medical conditions.
Coaster forces
During a ride, you are kept in your seat by the
safety bar and by the force of the seat pushing on
you. The coaster also exerts large forces on the
track, which must be inspected daily for structural
damage.
Going Further
Acceleration
An early loop ride at Coney Island subjected riders
to about 12 g's (12 times the acceleration due to
gravity). For safety reasons, most modern rides
do not exceed 5 g's.
Select an am usem ent p ark ride th at
you enjoy. Use lib rary or In tern et
resources to discover th e
principles o f physics th a t
a llo w th is ride to w o rk .
W rite a p aragraph or d raw
a diagram exp lain in g w h a t
you have learned.
Take a Discovery Channel Video
Field Trip by w atch in g "Physics
o f Fu n ."
f t
D
ouerv
0 0 1
:
Video Field Trip
15.3 Energy Resources
Reading Focus
Key Concepts
Vocabulary
Reading Strategy
©
♦ n on ren ewable
en ergy resources
♦ fossil fuels
♦ ren ewable en ergy
resources
♦ hydroelectric
en ergy
♦ solar en ergy
♦ geothermal en ergy
♦ biomass en ergy
♦ hydrogen fuel cell
♦ en ergy con servation
Identifying Main Ideas Copy the table
©
What are the major
nonrenewable and
renewable sources
of energy?
How can energy resources
be conserved?
Figure 16 Crude oil is pumped
out of the groun d or ocean floor.
It is then refin ed an d turn ed in to
gasolin e, fuel oil, an d other
oil products.
below. As you read, write the main idea for
each headin g.
Headin g
Main Idea
Non ren ewable en ergy
resources
a.
?
Ren ew able en ergy
resources
b.
?
Con servin g en ergy
resources
c.
?
rom the alarm clock that wakes you up each morning to the light
that you turn off before you sleep, you depend on energy resources to
operate many different devices to get you through each day. Energy
resources can be classified as either renewable or nonrenewable.
Nonrenewable Energy Resources
Nonrenewable energy resources exist in limited quantities
and, once used, cannot be replaced except over the course of
millions of years. ® Nonrenewable energy resources
include oil, natural gas, coal, and uranium. Such resources
are currently being used much faster than they can be
replaced, creating concern about how long they will last.
Oil, natural gas, and coal are known as fossil fuels
because they were formed underground from the remains
of once-living organisms. Currently, fossil fuels account for
the great majority of the world’s energy use. These fuels are
not distributed evenly throughout the world. For example,
about 60 percent of known oil supplies are located in a small
area in the Middle East. The United States has just 2 percent
of the world’s oil supplies but about 25 percent of the world’s
coal supplies. Fossil fuels are relatively inexpensive and are
usually readily available, but their use creates pollution.
462
Chapter 15
Renewable Energy Resources
Renewable energy resources are resources that can be replaced in a relatively short period of time. Most renewable energy resources originate
either directly or indirectly from the sun. The sun and Earth are constantly releasing large am ounts of energy. This energy could be used
for generating electric power, heating buildings or other purposes.
Renewable energy resources include hydroelectric, solar, geothermal, wind, biomass, and, possibly in the future, nuclear fusion. The
challenge for engineers and scientists is to find efficient ways to make
these energy resources inexpensive and convenient.
Hydroelectric Energy Energy obtained from flowing water is
known as hydroelectric energy. As water flows downhill, its gravitational
potential energy is converted into kinetic energy. This kinetic energy can
be used to turn turbines that are connected to electric generators.
Some hydroelectric power plants simply depend upon the natural
flow of water in a river. But most modern plants, such as the one shown
in Figure 17, rely on dams built across rivers. A dam blocks the flow of
water, storing potential energy that is converted into kinetic energy
when the water is released. The m ajor advantages of hydroelectric
energy include its low cost to produce and lack of pollution. Dams,
however, cause a variety of environm ental problems. For example,
dams hamper the run of fish upriver for spawning. Also, in the United
States many of the most suitable sites for hydroelectric plants are
already in use.
Figure 17 Hoover Dam was built
across the Colorado River on the
Arizona-Nevada border. This 221meter-tall structure can generate
over 2 million kilowatts of power.
Applying Concepts What type
o f energy conversion is involved
in a hydroelectric plant?
W o r ld E n e r g y U s e ( x 1 0 15 B t u )
1991
2000
136.47
154.28
Coal
88.35
94.22
Natural gas
76.03
90.15
Hydroelectric power
23.13
27.80
Nuclear fission
21.29
25.66
1.82
2.99
Source
Petroleum
Which energy resources are most com m only used
around the world? How is energy use changing
over time? The table shows total world energy use
in 1991 and 2000. Energy use is measured in
British thermal units, or Btu (1 Btu = 1055 J). Note
that petroleum includes oil and related fuels.
Other
1. Using Tables W hat was the world's largest
source of energy in 1991 ? In 2000?
4. Analyzing Data W hat percentage of world
energy use in 2000 was accounted for by
fossil fuels?
2 . Analyzing Data In general, how did usage
change from 1991 to 2000?
3.
Graphing Make a circle graph of world
energy use by source for the year 2000.
5.
Predicting How m ight total world energy use
be different in 2020? Explain.
Energy
463
Solar Energy Sunlight that is converted into usable
energy is called solar energy. Passive solar designs use sunlight to heat a building w ithout using machinery. For
example, sunlight passing through the windows of a house
may be absorbed by thick walls that then radiate thermal
energy to warm the house.
In an active solar energy system, sunlight heats flat collection plates through which water flows. The heated water
may be used directly for the buildings hot water needs, or it
maybe used to heat the house. Sunlight can also be converted
directly into electrical energy by means of solar cells, also
known as photovoltaic cells. Many small devices such as calculators now run on solar cells. A few large solar electric
plants, like the one shown in Figure 18A, use mirrors that concentrate sunlight to produce electricity.
The benefits of solar energy depend on the climate. Solar
energy is nonpolluting, but for areas where cloudy days are
frequent, solar energy is less practical.
Geothermal Energy Geothermal energy is thermal
energy beneath Earth’s surface. In some regions, especially
near volcanoes, geothermal energy is used to generate electicity. The geothermal power plant in Figure 18B pumps water
into the ground, where it turns into steam. The steam is then
used to drive electric generators. Geothermal energy is nonpolluting, but is not widely available.
Figure 18 Solar and geothermal
energy plants use renewable
resources to generate electricity.
A A solar electric plant uses solar
cells to convert sunlight into
electricity. B A geothermal plant
in California uses Earth's thermal
energy to generate electricity.
Comparing and Contrasting
What are some similarities and
differences betw een solar energy
and geothermal energy?
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464
Chapter 15
Other Renewable Resources Sunlight causes plants to grow,
converting electromagnetic energy into chemical energy. The chemical energy stored in living things is called biomass energy. Biomass
can be converted directly into therm al energy. For example, many
people around the world burn wood or peat to heat their homes or for
cooking. Also, agricultural wastes such as corn stalks can be converted
into a high-energy alcohol fuel that can be added to gasoline for cars.
A hydrogen fuel cell generates electricity by reacting hydrogen
with oxygen. Hydrogen fuel cells can be used to convert energy from
renewable resources. For example, hydrogen fuel can be extracted from
water using electricity from solar cells. The end product of fuel cells is
water, so they offer a nonpolluting means for transporting energy.
A form of hydrogen is also the most likely raw material for another
future source of energy, nuclear fusion. The process of fusion will probably produce little pollution or radioactive waste. Scientists have been
working on sustained fusion for years, but many challenges remain.
Wind Turbine
W ind turbines convert the kinetic energy in the horizontal
movement o f w ind into rotational energy of the turbine's
rotor shaft. Rotational energy is then converted into
electrical energy using an electric generator. The output of a
w ind turbine depends on the turbine's size and the wind's
W ind farm
Enormous wind farms like this
one in California can generate as
much power as a large power
plant (without any air pollution).
speed. In terp retin g D ia g ra m s What is the purpose o f
the gearbox?
Blades The shape and angle of the
blades are designed to extract as much
energy as possible from the horizontal
movement of the wind.
Gearbox The rotor
shaft itself rotates
fairly slowly at about
20-30 revolutions per
minute. The gearbox
converts this to a
rotation some 50 times
faster—about 1500
revolutions per minute.
Rotor shaft
Generator The shaft
from the gearbox enters
I the generator, which
converts the kinetic
energy of the shaft into
electrical energy.
The anemometer
measures wind
speed.
Wind
vane
Direction o f
rotation
Wind
direction
A yaw ring
changes the
direction o f
the turbine.
Electrical energy
passes to the
local grid.
I Yaw drive
mechanism
Control unit This
computer-operated
unit controls the yaw
drive mechanism,
ensuring that the
turbine always faces
directly into the wind.
Energy
465
Conserving Energy Resources
Figure 19 Mass transportation
systems include buses, trains, and
streetcars such as the one shown
here. In fe rrin g How can the
use o f mass transportation
save energy?
Fossil fuel supplies may become increasingly scarce and expensive in
the future. An im portant way to make these energy resources last
longer is to use them more slowly.
Energy resources can be
conserved by reducing energy needs and by increasing the efficiency
of energy use. Finding ways to use less energy or to use energy more
efficiently is known as energy conservation.
It’s easy to forget that the energy you use often comes at the
expense of resources that are being used up forever. People can reduce
the use of these resources by making energy-saving decisions, for
example turning off lights when they are not being used. Because conventional cars consume an enormous am ount of energy, the decisions
that people make about transportation are very important. Walking
or biking on short trips and carpooling can save considerable energy.
Using mass transportation, such as the streetcar shown in Figure 19,
can also reduce energy use.
Making appliances, cars, and even light bulbs more energy efficient
is a way of reducing energy use while still enjoying its benefits. Much
has already been done to make appliances more energy efficient. Light
bulbs have been developed that provide superior lighting at a lower
energy cost. The technology for further improvement, including more
fuel-efficient cars, is already known in many cases. However, the initial
cost of energy efficiency can be an obstacle for manufacturers and for
consumers. Energy-efficient purchases often cost more initially, but
can save money in fuel costs over time.
Section 15.3 Assessment
Reviewing Concepts
1. ® List the major nonrenewable and
renewable sources of energy.
5. Comparing and Contrasting How
are passive and active solar energy
systems different?
2. ® W hat could be done to make present
energy resources last longer?
6. Applying Concepts Describe three ways
that you used energy resources today.
3. W hy are coal, oil, and natural gas called
fossil fuels?
Science )-------------
Critical Thinking
4. Applying Concepts You are looking for the
best place to build a hydroelectric plant along
a river. Would you locate the plant along a
steep or flat section of the river? Explain.
466
Chapter 15
W riting to Persuade Suppose you are an
energy planner who is concerned about the
possibility of future shortages of electricity.
Write a paragraph describing one or two pro­
posals that you think would help to avoid this
potential problem.
Investigating a Spring Clip
There are many ways to use potential energy. A
spring clip is a device used to hold weights on a
barbell. The spring clip stores energy when you
compress it. In this lab, you will determine how the
distance you compress a spring clip is related to the
force you apply and to the spring's potential energy.
Problem
How does the force you apply to a
spring clip affect its elastic potential energy?
Materials
•
•
•
•
clamp
spring clip
masking tape
metric ruler
50-newton spring
scale
graph paper
For the probeware version of this lab, see
the Probeware Lab Manual, Lab 6.
Skills
Measuring, Using Tables and Graphs
Procedure
1. Make a data table with three columns. Label
the columns Force (N ), Position of Handle
(cm ), and Total Distance Moved (cm ).
2. Using the clam p, firm ly attach one handle of
the spring clip to a tabletop, with the other
handle facing up and away from the table as
shown. CA U TIO N Be careful not to pinch your
fingers with the clamp or spring clip.
3. Remove the plastic cover from the upper
handle of the spring clip. Hook the spring
scale to the spring clip handle as shown and
use masking tape to secure it. Have your
teacher check your setup for safety
before proceeding.
4. Have a classmate hold the ruler next to the
spring clip as shown. Record the starting
position of the handle. (The reading on the
spring scale should be zero.)
5. Slowly pull the spring scale down at a right
angle to the upper handle until the upper
handle moves 0.1 cm . Record the force and
the position of the upper handle. Slowly
release the scale back to the starting position.
6. Repeat Step 5, this time pulling the handle
0.2 cm from the starting position.
7. Repeat Step 5 a few more times, pulling the
handle 0.1 cm farther each time. Continue until
the spring scale reaches its maximum force.
8. Calculate the total distance the handle moved
each time you pulled it and record these
values in your data table. Graph your data.
Place distance on the horizontal axis and force
on the vertical axis.
A n a ly z e a n d C o n c lu d e
1. Using Graphs W hat is the approximate
relationship between the total distance you
compressed the spring clip and the force you
applied to it?
2. Classifying W hat type of energy transfer did
you use to compress the spring clip? What
type of energy did the spring clip gain when it
was compressed?
3. Drawing Conclusions W hat relationship
exists between the distance the spring clip was
compressed and its potential energy? (Hint:
The elastic potential energy of the spring clip
equals the work done on it.)
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Energy
467
CHAPTER
15
■ Study Guide
15.1 Energy and Its Forms
15.3 Energy Resources
(^ K e y Concepts
( ^ K e y Concepts
• Work is the transfer of energy.
• Nonrenewable energy resources include oil,
natural gas, coal, and uranium.
• The kinetic energy of any moving object depends
on its mass and speed.
• An object's gravitational potential energy depends
on its mass, its height, and the acceleration
due to gravity.
• The major forms of energy are mechanical energy,
thermal energy, chemical energy, electrical energy,
electromagnetic energy, and nuclear energy.
Vocabulary
energy,
• Energy resources can be conserved by reducing
our energy needs and by increasing the efficiency
of energy use.
Vocabulary
nonrenewable energy resources,
p. 447
fossil fuels,
p. 447
potential energy, p. 448
kinetic energy,
elastic potential energy,
hydroelectric energy,
p. 449
p. 450
p. 450
mechanical energy,
p. 451
chemical energy, p. 451
electrical energy, p. 452
thermal energy,
electromagnetic energy,
p. 452
p. 452
p. 462
p. 462
renewable energy resources,
gravitational potential energy,
nuclear energy,
• Renewable energy resources include hydroelectric,
solar, geothermal, w ind, biomass, and, possibly in
the future, nuclear fusion.
solar energy,
p. 463
p. 463
p. 464
p. 464
p. 464
hydrogen fuel cell, p. 464
energy conservation, p. 466
geothermal energy,
biomass energy,
Th in kin g Visually
Comparing and Contrasting Copy the partially
15.2 Energy Conversion and
Conservation
completed table below. Complete it to compare the
major forms of energy.
C ^ K ey Concepts
Form of Energy
Definition
Example
• Energy can be converted from one form
to another.
M echanical
Energy o f motion and
position o f everyday
objects
Bouncing ball
Lightning
• The law of conservation of energy states that
energy cannot be created or destroyed.
a.
?
b.
• The gravitational potential energy of an object is
converted to the kinetic energy of motion as the
object falls.
c.
?
Energy stored in
chemical bonds
d.
?
• Einstein's equation shows that energy and mass are
equivalent, and can be converted into each other.
Electrom agnetic
e.
?
f.
?
Nuclear
g.
?
Fission
Therm al
h.
?
i.
Vocabulary
energy conversion,
468
Chapter 15
p. 454
?
?
Assessment
Reviewing Content
Interactive textbook with
assessment at PHSchool.com
10.
Most renewable energy originates from
a. fossil fuels.
b. the ground,
c. the sun.
d. uranium.
Choose the letter that best answers the question or
completes the statement.
1. The energy of a moving object is
a. kinetic energy.
b. potential energy,
c. chemical energy.
d. nuclear energy.
2. If the speed of an object doubles, its kinetic energy
a. doubles.
b. quadruples,
d. is halved.
c. stays the same.
3. An example of an object having elastic potential
energy is
a. a stretched spring, b. books on a shelf,
c. a moving arrow.
d. a falling oyster.
4. An example of electromagnetic energy is
a. a falling rock.
b. a stretched spring,
c. a speeding train.
d. sunlight.
5. Energy stored in the bonds between atoms
is called
a. kinetic energy.
b. mechanical energy,
c. chemical energy.
d. thermal energy.
6. Mechanical energy is
a. found in machinery only.
b. usually measured at the atomic level.
c. the sum of the chemical and thermal
energy of an object.
d. the sum of the kinetic and potential
energy of an object.
7. An example of the conversion of gravitational
potential energy into kinetic energy is
a. a falling raindrop.
b. a gasoline-powered engine.
c. striking a match.
d. a hockey puck sliding on ice.
8. The law of conservation of energy states that
a. energy cannot be converted from one
form to another.
b. energy cannot be created or destroyed.
c. energy resources must be used efficiently.
d. energy is constantly being lost to friction.
9. Which of the following energy resources accounts
for most of the world's present energy use?
a. uranium
b. solar energy
d. wind energy
c. fossil fuels
U nderstanding Concepts
11. W hat is energy?
12. How are kinetic energy and potential
energy different?
13. How does the potential energy of an object
change when its height is tripled?
14. Look at the graphs below. One of the graphs is a
plot of kinetic energy vs. mass for a set of objects
with different masses, all moving at the same
speed. The other graph is a plot of kinetic energy
vs. speed for a set of objects with the same mass,
all moving at different speeds. Identify each
graph and explain how can you tell which graph
is w hich.
15. W hat happens to the atoms of an object if its
thermal energy is increased?
16. Explain the energy conversions that occur as a
basketball falls, hits the ground, and bounces
back up. Ignore frictional forces.
17. W hat force is acting when the kinetic energy of a
moving object is converted into thermal energy?
18. Explain how energy is converted as a
pendulum swings.
19. Is mechanical energy always conserved? Explain
w h y or w h y not.
20. Explain the meaning and the importance of the
formula E = me2.
21. W hy are coal, oil, and natural gas considered to
be nonrenewable energy resources?
22. W hat is the source of geothermal energy?
Energy
469
CHAPTER
15
Assessment
C ritical Thinkin g
(continued)
Concepts in A ction
23. Calculating A small meteoroid is approaching
Earth. It has a mass of 100.0 kg and a speed of
10.0 km/s. How much kinetic energy does the
meteoroid have? (Hint: 1 km = 1000 m)
24. Designing an Experiment Design an
experiment to find out how much elastic potential
energy is in a compressed spring. In addition to
the spring, you may use a small metal ball, a ruler,
and a scale for measuring mass.
25. Calculating A 0.15-kg ball is dropped from the
top of a 150-m building. W hat is the kinetic
energy of the ball when it passes the sixteenth
floor at a height of 63 m? (Ignore air resistance.)
30. Using Graphs A soccer ball is kicked from the
ground into the air. Describe two graphs that show
how the potential energy and kinetic energy
change between the time the ball is kicked and
when it lands. (Hint: Make time the x-axis.)
31. inferring When a falling object reaches a
speed called terminal velocity, its speed no
longer increases. The object is losing
gravitational potential energy but not gaining
kinetic energy. Since energy must be conserved,
where must the gravitational potential energy be
going?
32. Calculating Suppose a 200.0-kilogram dolphin
is lifted in the air to be placed into an aquarium
tank. How much energy is needed to lift the
dolphin 3.00 meters into the air?
M ath Skills
26. Converting Units Using mass in kg, velocity in
m/s, and height in m, show that the formulas for
kinetic energy and gravitational potential energy
result in energy values with the same units. W hat
is the energy unit called?
Questions 2 7 -2 9 refer to the data in the table below.
Three balls are thrown vertically into the air from
different heights above the ground. The data for
each ball are shown in the table below.
D ata Table
Object
Mass
(kg)
Initial Upward
Speed
(m/s)
Initial Height
Above Ground
(m)
Ball 1
1.00
8.00
15.00
Ball 2
2.00
1.00
10.00
Ball 3
3.00
4.00
5.00
27. Calculating How much kinetic energy does
each ball have when it is thrown?
33. Applying Concepts How is energy converted
as a car moves between the top and the bottom
of a roller coaster loop?
34. Making Judgments What are some
advantages and disadvantages of solar energy?
35. Applying Concepts How can electricity be
obtained from the wind?
36. Writing in Science Using your own words,
write a brief summ ary of the law of conservation
of energy. Include an example from your
everyday life.
Perform ance-Based Assessm ent
Applying Concepts Identify one practical w ay that
your fam ily or school could reduce energy use. Find
out how much energy is currently being used for the
purpose you choose, and estimate how much energy
your suggestion could save. Write a brief summary of
your recommendations.
28. Analyzing Data Which ball has the greatest
gravitational potential energy when it reaches
its maximum height? (Hint: Find the total energy
for each ball.)
29. Predicting Which ball hits the ground with the
most kinetic energy?
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Chapter 15
cGo i n l i n e
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Standardized Test Prep
Test-Taking Tip
Avoiding Careless Mistakes
Students often make mistakes when they fail to
examine a test question and possible answers
thoroughly. Read the question carefully and
underline key words that may change the mean­
ing of the question, such as not, except, exclud­
ing, and so on. After choosing an answer, reread
the question to check your selection.
Which statement about work and energy is
N OT correct?
(A)
(B)
(C )
(D)
Both can be expressed in joules.
Energy is the ability to do work.
Work done is always equal to energy input.
Energy input is always greater than
work output.
(E ) Energy is transferred in order to
accomplish work.
4. Friction causes kinetic energy to be converted into
(A) potential energy.
(B) thermal energy.
(C ) mechanical energy.
(D) electrical energy.
(E ) chemical energy.
5. Which of the following is N OT considered a
renewable energy resource?
(A) geothermal energy
(B) biomass
(C) hydroelectric energy
(D) uranium
(E ) wind energy
Use the figure below to answer Questions 6 and 7.
(Answer: C)
Choose the letter that best answers the question or
completes the statement.
1. Which form of energy does a plant store when
light is transformed during photosynthesis?
(A) chemical energy
(B) thermal energy
(C) mechanical energy
(D) electrical energy
(E ) nuclear energy
2. Which of the following is N OT an example
of kinetic energy being converted to
potential energy?
(A) a basketball player jumping for a rebound
(B) releasing a compressed spring
(C) squeezing a rubber ball
(D) pulling a sled up a hill
(E) a swing moving upward
3. A 50.0-kg wolf is running at 10.0 m/sec. W hat is
the wolf's kinetic energy?
(A) 5 j
(B) 500 j
(C) 5000 j
(D) 2 5 0 ]
(E ) 2 5 0 0 ]
A pendulum weight is released in position A. The
weight moves through positions B, C, D, and E.
6.
At which location(s) does the pendulum have
m axim um potential energy?
(A) A and B
(B) B and D
(C) C only
(D) D and E
(E) A and E
7.
At w hich location(s) does the pendulum have
m axim um kinetic energy?
(A) A and B
(B) B and D
(C) C only
(D) D and E
(E) A and E
Energy
471