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Work, Energy, and Energy Bar Charts
By:
Jane Wang, Amber Sweeton, and Diane Zhou
Period: 5-6
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Introduction
Energy is all around us: it is what makes cars run, what makes objects move, what
lets forests grow, and what operates all our electronics. You can not see it, but its still
there. Energy enables you to perform actions and to move. In this chapter, we will
explore the concepts of energy and work using free-body diagrams and mathematical
representations.
Objectives for this chapter:
By the end of this chapter, you should…
o Understand what work and energy are in a basic sense
o Comprehend the concepts of negative, positive, and 0 work and be able to give
examples of each
o Know what the basic types of energy are (KE, GPE, EPE, IE)
o Know that energy is conserved in a system and that energy can not be created or
destroyed
o Be able to both interpret and draw energy bar charts
o Understand how the equations for GPE and KE are derived
o Be able to mathematically represent energy
o Be able to solve basic work/energy problems
Experiments That You Can Do at Home
Chalk Experiments:
These experiments will model various energy conversions and show you that
energy is conserved in all cases. With common household materials, we will investigate
exactly how energy conversions occur as well as the various types of energy. Some of
these are gravitational potential energy (GPE), kinetic energy (KE), elastic potential
energy (EPE), and internal energy (IE). These concepts will also be explained later in the
chapter.
Materials:
 Sticks of chalk
 A heavy object (ex. a book)
 A slingshot/rubber band
 A large toy car
Procedure:
Modeling a Change from GPE to KE
1. Place one piece of chalk flat on a smooth surface.
 This might be a messy experiment. Get parental permission before trying.
2. Lift your heavy object a short distance above the stick of chalk
 Observe that it requires a little work (effort) to lift the object.
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3. Drop the object.
 The chalk should not break or should only crack slightly. This is because
you gave the object only a little bit of GPE when you lifted it is slight
distance.
4. Replace the chalk with a new piece. Lift the heavy object once again, only much
higher above the chalk. Drop the object.
 Observe that it requires more work (effort) to lift the object this time, and
that the object gained more speed when falling.
 The chalk should crack or break.
What did we observe?
It takes more work to lift an object a higher distance and give it more GPE. When
an object has more GPE, it has more capacity for motion when it is dropped and applies a
greater force on the chalk, causing it to break
You could represent this experiment using an energy bar chart:
KE GPE EPE IE
KE GPE EPE IE
At the left is an energy bar chart depicting
this scenario (from the moment the object
is dropped to the moment before it hits the
chalk). Assume negligible air resistance.
Notice that the heights of the bars before
and after are the same. This shows that no
energy is created or destroyed. All energy
has been changed from GPE to KE.
Modeling a Change from EPE to KE
1. Take your rubber band and stretch it between two of your fingers.
2. Place a piece of chalk on the rubber band and stretch it back a bit; release chalk.
(Do not aim chalk at others, animals, or fragile objects; get parental permission
before firing)
 Observe that this does not take much work.
 The chalk does not go far, because it started out with very little EPE
3. Repeat step two, but stretch the rubber band father
 Observe that this takes more work.
 The chalk goes farther and faster, because you originally gave it more EPE.
What did we observe?
It takes more work to stretch a rubber band farther and to give it more EPE.
However, when you do so, the EPE transfers to KE and more motion is achieved. EPE is
energy that an object has when it is stretched or compressed.
You could also represent this using an energy bar chart:
This energy bar chart shows the change in
types of energy from right when the chalk
is released from the rubber band to when
the chalk is at the peak of its flight. Assume
that there is negligible air resistance and
that the chalk is released from a height off
the ground and angled upwards when fired.
KE GPE EPE IE
KE GPE EPE IE
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The energy converts from being GPE/EPE
to KE/GPE. The total amount of energy
remains the same before and after.
Modeling a Change from Work to KE and KE → IE
1. Stand a piece of chalk against a wall. (Get parental permission and do this
experiment on an easy to clean surface)
2. Place your toy car a fixed distance away from the chalk. Give it a small push.
 You have just done a little work on the car (you are not a part of the
system). This work changed to KE and resulted in a little motion.
 Notice how the car slows down after a while. This is because the KE is
changing into IE (heat, sound, etc.) because of friction.
3. Place your toy car the same distance away from the chalk. Give it a larger push.
 You have added more work into the system, so therefore it changes into
more KE and the car moves at a faster speed.
 The chalk might break this time or crack more than when only a little work
was added.
What did we observe?
Energy is always conserved in a system. This is shown when more work resulted
in more KE. Internal energy is energy that results from friction and turns into heat, light,
sound, etc.
This can also be represented using an energy bar chart:
+
KE GPE EPE IE
W
KE GPE EPE IE
KE GPE EPE IE
This energy bar chart shows the change in types of energy in three stages: when the car is first
pushed, when you release the car and it begins moving, and when the car begins to slow down.
Assuming that the system includes the table, the chalk, and the car , your work is first
transferred all into KE. This KE is later converted into internal energy because of friction.
Super Happy Fun Ball Experiment:
This experiment will be discussed more in depth later in
the section. This explanation will be mainly for observational
purposes. You will observe that energy is conserved in a system.
The procedure of this experiment will be explained later in this
chapter; this is just a brief overview of the experiment.
The super happy fun ball snowman is a set of 3 rubber
balls stuck together with a pole sticking out of the top. There is
also a separate smaller ball with a hole through its center. This
ball can be placed on the rod and the snowman. Refer to the
figure at the right.
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Can
come
off
Stuck
Together
What can you observe?
When you drop the snowman from a certain height, it falls to the ground. When it
hits the ground, all of the kinetic energy is transferred into the small ball at the top. The
“super happy fun ball” flies off and jumps to a very high height.
This demonstrates a conservation of energy. When you were holding the
snowman above the ground, it had a certain amount of GPE. When the small ball was at
the highest point in its jump, it had the same amount of GPE. This aptly demonstrates a
property of the equation for GPE. GPE=mgh. Since the mass of the small ball is
significantly less than that of the snowman, and the GPE and g remain the same, the
height varies. When the mass is great, the height is small and when the mass is small, the
height is great. These variables are inversely proportional.
Simple Observations that You Can Make in Your Everyday World:
Energy is all around you and many of its properties can be observed by just
watching things and actions occur. For example, if you drop your pencil during class one
day, you can observe an energy conversion. How, you ask? Right before your pencil
leaves your hand, it has gravitational potential energy (it has the potential to move/fall).
When you let go of your pencil, it falls and all of the GPE that it originally had is
changed into KE. When it hits the ground, it stops moving. Why is this? It’s because all
of the KE that your pencil had previously had has been changed to internal energy (i.e.
sound, heat, etc.)
You can also make simple observations about work. When you have a book
sitting on the table, it has no kinetic energy since it is not moving. When you push it (add
work to the system), that work changes into kinetic energy and the object starts to move.
Elastic potential energy is also easy to observe. In addition to the rubber band and
chalk experiment explained above, you could also jump on your bed to demonstrate the
concept. At the lowest point of any jump (when your feet are on the bed and it is about to
spring you up again), all of the energy in your system (the bed and you) is elastic
potential energy. You are not moving at that time. Soon after that point, all of that
elastic potential energy turns into gravitational potential and kinetic energy and you are
moving again.
Work, Energy, and Energy Bar Charts
What is energy?
Energy is the capacity to do work. Energy is what you have. Work is what you
do. (Work is explained in more detail in “What is Work?”) Both work and energy are
measured in joules.
KE GPE EPE IE
Figure 1
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KE GPE EPE IE
This is an energy bar chart. Energy bar charts are used to represent the changing
of energy. The left part represents the energy that the object started out with. The right
part represents how the energy changed. Sometimes more than two energy bar charts are
needed to represent all the energy transfers in a situation.
In an energy bar chart, the energy amounts on both sides of the arrow must add
up. In the example above, the initial KE is the sum of the resulting KE and GPE. This is
because energy can not be created or destroyed. The amount of energy in a system will
always stay constant. The fact that the energy in a system will always remain constant is
known as the Work-Energy Theorem.
To draw an energy bar chart, draw two perpendicular lines and draw the bars of
energy inside. Label them so that their type can be identified. Most of the time, energy
bar charts are qualitative, not quantitative, so the size of the bars doesn’t have to be exact.
As long as they’re roughly correct and both sides of the arrow add up to each other, it’s
fine. The dotted lines on the energy bar chart are like interval markers on a graph. They
help to make your chart more exact, but they’re not always necessary.
There are many kinds of energy that can be represented in Energy Bar Charts. In
the graph above, the object starts out with KE. KE represents the object’s Kinetic
Energy. Kinetic energy is the energy an object has as a result of its movement. GPE
represents Gravitational Potential Energy, which an object has as long as it is above the
“0” point. The 0 point is whatever you determine it to be. For example, the 0 point can
be defined as sea level, or it can be defined as the ground on which a person is standing,
depending on the situation.
Some other things you might encounter in energy bar charts include Work (W)
and Elastic Potential Energy (EPE). Work is explained below, in the section “What is
work?”. EPE is the energy an object has as a result of being stretched or compressed,
like a rubber band. In its original, un-stretched state, a rubber band has no EPE.
However, when you tug on both sides and stretch it out, it has the potential to snap back,
so it has Elastic Potential Energy.
Also, there is something known as Electrical Potential Energy (ELPE). ELPE
is an object’s potential to move based on its location, position, and charge in relation to
another object. If two objects that are held next to each other have a positive charge, they
have ELPE because they want to repel each other (likewise if they both have negative
charges). If one object has a positive charge and one has a negative charge and they’re
next to each other, they won’t have any ELPE because they attract each other anyway. If
they’re already next to each other, they don’t have any potential to move any further.
You may also see something called Internal Energy (IE). Internal energy is all
the other types of energy, such as heat, light, sound, etc. It can be a result of friction. For
example, if you rub your hands together very quickly, the friction will create heat and
they’ll feel warmer.
Now that you understand how to read the Energy Bar Chart, you can understand
the motion of the object.
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How is the object in Figure 1 moving?
It’s moving at a high speed because it has a lot of kinetic energy at first. Then the
KE goes down and the GPE goes up, so it must have slowed down, but also somehow
moved above the zero point. For example:
In the diagram the watermelon is running fast, and then he slows down as he goes
up a hill, just like the previous description.
There are many different situations that the chart in Figure 1 could represent. The
running watermelon is only one example.
As you can see, Energy Bar Charts are useful to understanding the transfer of
energy. Based on that information, you can get a rough idea of the object’s motion.
What is work?
As previously mentioned, work is what you do when you have energy. The more
energy you have, the more work you’re capable of doing. In science, it’s only considered
regular positive work when the object is moving in the same direction of the force. So, if
you stand still and hold a pineapple, it is not considered work, because you’re applying
force upward against gravity, but the pineapple is not moving up. It is staying still even
though your force goes up, so it isn’t work.
There are three types of work: positive, negative, and zero. Positive work is
when the work gives more energy to the object, such as pushing a shopping cart forward.
Negative work is when the force causes the object to have less energy, such as a person
catching a baseball that is thrown at them. Zero work is done when there is no change in
energy.
What is a system?
A system is the group of objects that a problem is taking into consideration.
Objects outside of the system can do work on objects within a system, but they are still
not considered a part of it. Therefore, Energy Bar Charts only take into consideration
how much energy is in the system.
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Derivations for KE and GPE:
Fstring → box
Use the force diagram at the right as a starting point for the following
derivation. A person is pulling a string attached to a box, while the earth
is pulling down on the box with an equal and opposite force.
For the following derivation, remember that:
Fearth → box
W = KE + GPE
Fs  box  Fe  box
m
F  box  mg
a s
m
a
F  am  mg
Start with the basic Newton’s second law equation. In this
example, a force (Fs) is being applied on an object upwards
while the earth is applying a force on it downwards (Fe).
The force of the earth on an object is equal to the mass of
the object x g (acceleration of gravity or 9.8 m/s2)
Multiply by m on both sides and move the mg to the other
side.
h( F )  h(am  mg )
Recall that: F  d  W
W  mah  mgh
Multiply by h on both sides of the equation. Recall that force
x distance/height = work
V f  Vi  2ah
2
2
V f  Vi
2
a
2h
mh(V f  Vi )
2
W 
W 
W 
Recall the equation listed at the right.
2
Subtract Vi2 from both sides and divide both sides by 2h.
2
2h
2
2
m(V f  Vi )
2
 mgh
 mgh
Plug this expression in for a.
Cancel out the h from the numerator and denominator of the
fraction.
mv 2
 mgh
2
Arrive at the final equation for work.
Notice a few key things about this equation:
1. This equation looks a lot like our previous equation, W = KE + GPE
2. Therefore, GPE = mgh
mv 2
3. KE would then equal
2
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Important Concepts to Grasp from this Section:
Work is equal to the sum of kinetic energy and gravitational potential energy.
Using equations that we had previously learned, you can derive and arrive at equations
for kinetic energy and gravitational potential energy:
KE 
mv 2
2
GPE  mgh
Using these equations, we will work to solve problems in later sections of this
chapter. In future sections, you will learn how to create generalized equations for a given
scenario as well as how to solve for specific variables.
The Super Happy Fun Ball Experiment
The super happy fun ball experiment can be used to
enhance one’s knowledge on the various equations for
acceleration, forces, and energy. The super happy fun ball
snowman is a set of three rubber balls stacked one on top of
another. A rod runs through the center of the three balls and all
of the balls are immobile. A smaller ball is also with a hole
through it is also slipped onto the rod. When dropped from a
certain height, the balls will fall together. However, when it hits
the floor and bounces back up, most of the energy will get
transferred to the little ball on top and it will shoot up to a great
height. Using the equations for acceleration, forces, and
Newton’s second law, the exact height that the small can reach
can be determined.
Can
come
off
Stuck
Together
Materials Needed:
o Super Happy Fun Ball Snowman
o Scale
o Meter stick
o Calculator
Procedure:
1. Measure the mass of your snowman using the scale
2. Measure the mass of just the little ball that can come off
3. Hold your snowman at a specific height (the height that you will drop it from);
measure this height with a meter stick
4. Drop the super happy fun ball snowman
5. Using the equation for GPE, figure out the final height of the small ball.
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The method for finding the maximum height:
In this example, we are using the following:
msmall ball = 4.2 g
msnowman = 87 g
hdrop = 1.25 m
Assume that the height of the snowman, friction, and air resistance are
negligible to the final height of the super happy fun ball.
Solving the Equation:
Remember that energy is conserved in a system. Therefore, the GPE of the snowman
(GPE1) when first dropped will equal the GPE of the super happy fun ball at the height of
its jump (GPE2).
GPE1  mgh
GPE1  (0.087 kg )(9.8 m s 2 )(1.25m)
GPE1  1.066J
GPE1  GPE2
GPE2  mgh
1.066J  (0.004kg) (9.8 m s 2 )( h)
h  27.19m
The final height of the small ball (if dropping it from 1.25 m) is 27.19 meters.
Model Problems
Sample Problem 1:
A 3 kg pineapple is thrown directly up into the air by a person who does 250 J of work on
it. How high will the pineapple fly? Assume negligible air resistance.
Energy Bar Chart…
+
KE GPE EPE IE
KE GPE EPE IE
W
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Solving the Problem…
The pineapple has no energy in the beginning of the problem (it has no height and
is not moving). Work is then done on it, causing it to shoot up. At the highest point of
its flight, it stops for a very brief moment, and all of its energy is GPE. Therefore, the
equation for this situation would be:
W  mgh
To solve for height, just plug in numbers for W, m, and g:
W  mgh


200J  (3kg) 9.8 m s 2 (h)
h  6.8m
Sample Problem 2:
A man drops a 4 kg bowling ball from the edge of a building. Assume negligible air
resistance. If the ball’s final velocity is 196 m/s, what is the height of the building from
which the bowling ball was dropped?
Energy Bar Chart…
KE GPE EPE IE
KE GPE EPE IE
Solving the problem…
When first dropping the ball, the only type of energy that the ball had was
gravitational potential energy (it was really high up, but was not moving). When it fell,
that GPE turned into KE. If its final velocity was 196 m/s, then all of the energy that it
had at that point would have been KE. Therefore, the equation for this would be
mgh= ½m(vf - vi)2
mv 2
KE 
2
(4kg)(196m/s ) 2
KE 
2
KE  392J
KE  GPE
GPE  mgh
392J  (4kg)(9.8m /s 2 )( h)
h  10m
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Sample Problem 3:
Mary weighs 50 kg and is swinging on a vine. At the lowest point of her swing,
she is going at a speed of 20 m/s. Considering that energy is conserved and assuming
that there is no negligible friction, what is the highest point of Mary’s swing?
For this problem, this is the energy bar chart if you consider Mary’s swing in
three stages: the top of her swing, when she’s going the fastest, and the top of her swing
on the other side.
KE GPE EPE IE
KE GPE EPE IE
KE GPE EPE IE
Solving the Problem…
Mary had all kinetic energy at the point in which she was swinging the fastest (in
a pendulum-like situation, the fastest speeds are achieved when the object is closest to the
ground). Therefore, she has all GPE at the highest point of her swing. Using that
information, the equation would be…
½m(vf - vi)2= mgh
From there, all you have to do is plug in numbers and solve the equation…
mv 2
KE 
2
(50kg)(10m/s) 2
KE 
2
KE  2500J
KE  GPE
GPE  mgh
2500J  (50kg)(9.8 m/s 2 )( h)
h  5.1m
Sample Problem 4:
Make an energy bar chart for the energy that the skier will have at all three points:
A, B, & C.
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Energy Bar Charts…
A.
KE GPE EPE IE
B.
C.
KE GPE EPE IE
KE GPE EPE IE
Explanation…
A. For the energy bar chart, it is all Gravitational Potential Energy because the skier
is at the top of the hill and isn’t moving, so there is no Kinetic Energy.
B. It is two units of Kinetic Energy, one unit of Gravitational Potential and one unit
of Internal Energy. It is like this because the skier is moving, still above the zero
point, or ground, and there is friction beneath the skis on the snow.
C. There is all Internal Energy because it is not moving and not in the air but there is
still the heat on the skis that was made by the friction, which is Internal Energy.
Sample Problem 5:
Make an energy bar chart and a general Newton’s laws equation for a car traveling up a
hill and halfway up revs its engine and it goes faster and higher.
Energy Bar Charts…
+
KE GPE EPE IE
KE GPE EPE IE
W
½mv12
+ mgh1 + W =
½mv22
+ mgh2
First, there is Kinetic and Gravitational Potential Energy, then the engine, a force outside
of the system, does work. This then comes to all Kinetic and Gravitational Energy.
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Summary
In this chapter, we have learned about the different types of energy and about
work. Energy is the ability to do work. Energy is something you have, work is
something you do. Energy in a system is always conserved. The different types of energy
are once again:
 Gravitational Potential Energy (GPE): energy you have when you are
above the ground or 0 point.
 Kinetic Energy (KE): energy as a result of movement.
 Elastic Potential Energy (EPE): energy something has when it can be
stretched or compressed.
 Internal Energy (IE): all other types of energy like heat, light & sound.
Work is what you do when you have energy. You can do positive, negative &
zero work. Positive is when the work gives more energy to the object. Negative is when
a force causes the object to have less energy. Zero is when there is no change in energy.
Practice Questions
A
B
D
E
C
F
0 Point
Diagram for Questions 1-6
1. Does the cart have GPE or KE at Point A? Why?
2. Draw an energy bar chart for the cart at Point B.
3. Does the cart have any GPE at point C? Why or why not?
4. Draw the energy bar chart for the cart at Point D.
5. How is the energy bar chart for Point E different from the one at Point D? Why?
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6. What happened to the cart at Point F? Does it have any GPE or KE? If not, what
happened to all its energy?
7. A person has jumped off of a cliff, but he lands a conveniently placed obese pig
and is saved. What type of force does the obese pig exert on the person? Draw
energy bar charts for the person as soon as he jumped off and just before he hit
the pig.
8. An object is hanging in the air from a pulley and staying still. Then someone
pulls the other end of the pulley and the object moves up. Draw energy bar charts
to represent before and after the pull.
9. By how much does the gravitational potential energy of a 64 kg pole vaulter
change if his center of mass rises about 4 meters during the jump?\
10. A 55 kg hiker starts at an elevation of 1600 meters and climbs to the top of a 3100
meter peak. (a) What is the hiker’s change in potential energy? (b) What is the
minimum work required of the hiker? (c) Can the actual work done be more than
this?
11. If a box is initially at rest and is pulled up, make an energy bar chart and
Newton’s laws equation of the box ending up above the ground and moving.
12. How high will a 0.325 kg rock go if thrown straight up by someone who does 115
J of work on it? Neglect air resistance.
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Answer Key
1. GPE, because it’s not moving and it’s high above the zero point.
2.
KE GPE EPE IE
3. Yes, but not very much, because it’s just above the zero point.
4.
KE GPE EPE IE
5. For Point E, it has the same amount of GPE as point D, but it’s moving more
slowly, so it has less KE and more IE instead.
6. At Point F the cart has neither GPE nor KE because it’s at the zero point and it’s
not moving. All its energy has been converted into IE.
7. Negative force.
KE GPE EPE IE
KE GPE EPE IE
8.
+
KE GPE EPE IE
W
KE GPE EPE IE
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9. 2.5 x 103 J
GPE  mgh
GPE  (64kg)(9.8 m s 2 )( 4m)
GPE  2500
10. (a) 8.1 x 105 J
GPE  mgh
GPE  (55kg)(9.8 m s 2 )(1500m)
GPE  81000
(b) 8.1 x 105 J; it would be the same amount as the energy done.
(c) yes; it can account for internal energy as well.
11.
+
KE GPE EPE IE
KE GPE EPE IE
W
W = ½mv22 + mgh2
12. 36.1 m
GPE  mgh
115  (0.325kg)(9.8 m s 2 )( m)
GPE  36.1
Sources used: Physics: Principles with Applications, by Giancoli
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