Chapter 13: Work and Energy 425
potential energy p. 426
kinetic energy p. 426
mechanical energy p. 429
conservation of energy
p. 430
BEFORE, you learned
•Work is the use of force to
move an object
•Work can be calculated
NOW, you will learn
How work and energy
are related
How to calculate mechanical,
kinetic, and potential energy
What the conservation of
energy means
Energy is transferred
when work is done.
How is energy transferred?
School carnivals sometimes
include dunk tanks. The goal
is to hit a target with a ball,
causing a person sitting over
a tank of water to fall into the
water. You do work on the
ball as you throw with your
arm. If your aim is good, the
ball does work on the target. How do
you transfer your energy to the ball?
Work transfers energy.
When you change the position and speed of the ball in the carnival
game, you transfer energy to the ball. Energy is the ability of a person
or an object to do work or to cause a change. When you do work on an
object, some of your energy is transferred to the object. You can think
of work as the transfer of energy. In fact, both work and energy are
measured in the same unit, the joule.
The man in the photograph above converts one form of energy
into another form when he uses his muscles to toss the ball. You can
think of the man and the ball as a system, or a group of objects that
affect one another. Energy can be transferred from the man to the
ball, but the total amount of energy in the system does not change.
check your reading How are work and energy related?
Remember to add boxes
to your main idea web
as you read.
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426 Unit 3: Motion and Forces
Work changes potential and kinetic energy.
When you throw a ball, you transfer energy to it and it moves.
By doing work on the ball, you can give it (kuh-
NEHT-ihk), which is the energy of motion. Any moving object
has some kinetic energy. The faster an object moves, the more
kinetic energy it has.
When you do work to lift a ball from the ground, you give the
ball a different type of energy, called potential energy.
is stored energy, or the energy an object has due to its position or
its shape. The ball’s position in your hand above the ground means
that it has the potential to fall to the ground. The higher you lift
the ball, the more work you do, and the more potential energy
the ball has.
You can also give some objects potential energy by changing
their shape. For example, if you are holding a spring, you can do
work on the spring by squeezing it. After you do the work, the
spring has potential energy because it is compressed. This type of
potential energy is called elastic potential energy. Just as position
gives the spring the potential to fall, compression gives the spring
the potential to expand.
Potential energy
kinetic energy
reading tip
The word potential comes
from the Latin word
potentia, which means
power.” The word kinetic
comes from the Greek
word kinetos, which
means “moving.”
Potential and Kinetic Energy
The trampoline has potential
energy because it is stretched.
As the boy falls, his potential
energy changes into kinetic
energy, and he moves faster.
Potential Energy Kinetic Energy Potential Energy
The boy has potential energy
based on his position because
gravity will pull him back down.
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The formula for gravitational potential energy is similar to the
formula for work (W Fd). The formula for GPE also has a force
(mg) multiplied by a distance (h). To understand why mg is a force,
remember two things: force equals mass times acceleration, and g is
the acceleration due to Earths gravity.
Calculating Gravitational Potential Energy
Potential energy caused by gravity is called gravitational potential
energy. Scientists must take gravitational potential energy into account
when launching a spacecraft. Designers of roller coasters must make
sure that roller-coaster cars have enough potential energy at the top of a
hill to reach the top of the next hill. You can use the following formula
to calculate the gravitational potential energy of an object:
Gravitational Potential Energy = mass · gravitational acceleration · height
GPE = mgh
Recall that g is the acceleration due to Earths gravity. It is equal to
9.8 m/s
at Earths surface.
The diver in the photograph below has given herself gravitational
potential energy by climbing to the diving board. If you know her mass
and the height of the board, you can calculate her potential energy.
Sample Problem
Practice the Math
Calculating Potential Energy
What is the gravitational potential energy of a girl who has a mass
of 40 kg and is standing on the edge of a diving board that is 5 m
above the water?
What do you know? mass = 40 kg, gravitational acceleration =
9.8 m/s
, height = 5 m
What do you want to find out? Gravitational Potential Energy
Write the formula: GPE = mgh
Substitute into the formula: GPE = 40 kg p 9.8 m/s
p 5 m
Calculate and simplify: GPE = 1960 kg m
Check that your units agree: kg m
= kg p m/s
p m = Npm = J
Unit of energy is J. Units agree.
Answer: GPE = 1960 J
1. An apple with a mass of 0.1 kg is attached to a branch of an apple tree
4 m from the ground. How much gravitational potential energy does the
apple have?
2. If you lift a 2 kg box of toys to the top shelf of a closet, which is 3 m high,
how much gravitational potential energy will the box of toys have?
A newton (N) is a kg m/s
and a joule (J) is a N
Chapter 13: Work and Energy 427
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428 Unit 3: Motion and Forces
Calculating Kinetic Energy
The girl on the swing at left has kinetic energy. To find out how much
kinetic energy she has at the bottom of the swing’s arc, you must
know her mass and her velocity. Kinetic energy can be calculated
using the following formula:
Kinetic Energy =
KE =
Notice that velocity is squared while mass is not. Increasing the
velocityofan object has a greater effect on the object’s kinetic energy
than increasing the mass of the object. If you double the mass of an
object, you double its kinetic energy. Because velocity is squared, if
you double the objects velocity, its kinetic energy is four times greater.
Sample Problem
Practice the Math
Calculating Kinetic Energy
What is the kinetic energy of a girl who has a mass of 40 kg and a
velocity of 3 m/s?
What do you know? mass = 40 kg, velocity = 3 m/s
What do you want to find out? Kinetic Energy
Write the formula: KE =
Substitute into the formula: KE = p 40 kg p (3 m/s)
Calculate and simplify: KE = p 40 kg p
= 180 kg p m
Check that your units agree: = p m = Npm = J
Unit of energy is J. Units agree.
Answer: KE = 180 J
1. A grasshopper with a mass of 0.002 kg jumps up at a speed of 15 m/s.
What is the kinetic energy of the grasshopper?
2. A truck with a mass of 6000 kg is traveling north on a highway at a speed
of 17 m/s. A car with a mass of 2000 kg is traveling south on the same
highway at a speed of 30 m/s. Which vehicle has more kinetic energy?
kg p m
kg p m
360 kg p m
2 s
9 m
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Calculating Mechanical Energy
is the energy possessed by an object due to its
motion or position—in other words, it is the objects combined
potential energy and kinetic energy. A thrown baseball has mechanical
energy as a result of both its motion (kinetic energy) and its position
above the ground (gravitational potential energy). Any object that has
mechanical energy can do work on another object.
Once you calculate an object’s kinetic and potential energy, you
can add the two values together to find the object’s mechanical energy.
Mechanical Energy = Potential Energy + Kinetic Energy
ME = PE + KE
For example, a skateboarder has a potential energy of 200 joules due
to his position at the top of a hill and a kinetic energy of 100 joules
due to his motion. His total mechanical energy is 300 joules.
check your reading How is mechanical energy related to kinetic and potential energy?
Mechanical energy
How does mechanical energy change?
Find and record the mass of the ball.
Build a ramp with the board and books. Measure and record the height of
the ramp. You will place the ball at the top of the ramp, so calculate the
ball’s potential energy at the top of the ramp using mass and height.
Mark a line on the floor with tape 30 cm from the bottom of the ramp.
Place the ball at the top of the ramp and release it without pushing. Time how
long the ball takes to travel from the end of the ramp to the tape.
Calculate the ball’s speed using the time you measured in step 4. Use this speed
to calculate the ball’s kinetic energy after it rolled down the ramp.
•At the top of the ramp, how much potential energy did the ball
have? kinetic energy? mechanical energy?
Compare the ball’s mechanical energy at the top of the ramp with
its mechanical energy at the bottom of the ramp. Are they the
same? Why or why not?
CHALLENGE Other than gravity, what forces could have affected
the movement of the ball?
Mechanical Energy
Mechanical Energy
Analyzing data
20 minutes
Chapter 13: Work and Energy 429
Use a vocabulary strategy
to help you remember
mechanical energy.
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430 Unit 3: Motion and Forces
The total amount of energy is constant.
You know that energy is transferred when work is done. No matter
how energy is transferred or transformed, all of the energy is still
present somewhere in one form or another. This is known as the
As long as you account for all the
different forms of energy involved in any process, you will find that
the total amount of energy never changes.
Conserving Mechanical Energy
Look at the photograph of the in-line skater on page 431. As she rolls
down the ramp, the amounts of kinetic energy and potential energy
change. However, the total—or the mechanical energy—stays the
same. In this example, energy lost to friction is ignored.
At the top of the ramp, the skater has potential energy because
gravity can pull her downward. She has no velocity; therefore,
she has no kinetic energy.
As the skater rolls down the ramp, her potential energy decreases
because the elevation decreases. Her kinetic energy increases
because her velocity increases. The potential energy lost as the
skater gets closer to the ground is converted into kinetic energy.
Halfway down the ramp, half of her potential energy has been
converted to kinetic energy.
At the bottom of the ramp, all of the skater’s energy is kinetic.
Gravity cannot pull her down any farther, so she has no more
gravitational potential energy. Her mechanical energy—the total
of her potential and kinetic energy—stays the same throughout.
Losing Mechanical Energy
A pendulum is an object that is suspended from a fixed support so that
it swings freely back and forth under the influence of gravity. As a
pendulum swings, its potential energy is converted into kinetic energy
and then back to potential energy in a continuous cycle. Ideally, the
potential energy at the top of each swing would be the same as it was
the previous time. However, the height of the pendulums swing actually
decreases slightly each time, until finally the pendulum stops altogether.
In most energy transformations, some of the energy is transformed
into heat. In the case of the pendulum, there is friction between the
string and the support, as well as air resistance from the air around the
pendulum. The mechanical energy is used to do work against friction
and air resistance. This process transforms the mechanical energy into
heat. The mechanical energy has not been destroyed; it has simply
changed form and been transferred from the pendulum.
law of conservation of energy.
APPLY Energy must
occasionally be added to
a pendulum to keep it
swinging. What keeps a
grandfather clock’s
pendulum swinging
Observe how potential
and kinetic energy are
transferred on an
amusement park ride.
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The potential energy and kinetic energy in a system or
process may vary, but the total energy remains unchanged.
Conserving Mechanical Energy
At the top of the ramp, the
skater’s mechanical energy is
equal to her potential energy
because she has no velocity.
Fabiola da Silva is a professional
in-line skater who was born in Brazil
but now lives in California.
As the skater goes down the
ramp, she loses height but gains
speed. The potential energy
she loses is equal to the kinetic
energy she gains.
As the skater speeds along the
bottom of the ramp, all of the
potential energy has changed to
kinetic energy. Her mechanical
energy remains unchanged.
Top of Ramp
Halfway Down Ramp
Bottom of Ramp
How do the skater’s kinetic and potential energy change as she skates
up and down the ramp? (Assume she won’t lose any energy to friction.)
Chapter 13: Work and Energy 431
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432 Unit 3: Motion and Forces
1. Explain the relationship
between work and energy.
2. How are potential energy and
kinetic energy related to
mechanical energy?
3. When one form of energy
changes into one or more
other forms of energy, what
happens to the total amount
of energy?
4. Infer Debra used 250 J of
energy to roll a bowling ball.
When the ball arrived at the
end of the lane, it had only
200 J of energy. What hap-
pened to the other 50 J?
5. Calculate A satellite falling to
Earth has a kinetic energy of
182.2 billion J and a potential
energy of 1.6 billion J. What is
its mechanical energy?
6. Apply At what point in its
motion is the kinetic energy
of the end of a pendulum
greatest? At what point is its
potential energy greatest?
When its kinetic energy is half
its greatest value, how much
potential energy did it gain?
Forms of Energy
As you have seen, mechanical energy is a combination of kinetic
energy and potential energy. Other common forms of energy are
discussed below. Each of these forms of energy is also a combination
of kinetic energy and potential energy. Chemical energy, for example,
is potential energy when it is stored in bonds.
Thermal energy is the energy an object has due to the motion of its
molecules. The faster the molecules in an object move, the more
thermal energy the object has.
Chemical energy is the energy stored in chemical bonds that hold
chemical compounds together. If a molecule’s bonds are broken or
rearranged, energy is released or absorbed. Chemical energy is used to
light up fireworks displays. It is also stored in food and in matches.
Nuclear energy is the potential energy stored in the nucleus of an
atom. In a nuclear reaction, a tiny portion of an atoms mass is turned
into energy. The source of the Suns energy is nuclear energy. Nuclear
energy can be used to run power plants that provide electricity.
Electromagnetic energy is the energy associated with electrical
and magnetic interactions. Energy that is transferred by electric
charges or current is often called electrical energy. Another type of
electromagnetic energy is radiant energy, the energy carried by light,
infrared waves, and x-rays.
It is possible to transfer, or convert, one energy form into one or more
other forms. For example, when you rub your hands together on a
cold day, you convert mechanical energy to thermal energy. Your body
converts chemical energy stored in food to thermal and mechanical
energy (muscle movement).
Include common forms of
energy in your web.
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