Conservation of Energy Notes

90

Conservation of Energy

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Section 3

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What we have looked at so far is that an object has kinetic energy if
the object is in motion. The faster that the object is going, the more
kinetic energy it has.

In order for an object's kinetic energy to increase, it must get energy
from somewhere. But where would it get that energy?

Conservation of Energy

Hint: think back to the roller
coaster. What kind of
energy did it have at the
top of the hill?

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This is called the Conservation of Energy.

initial Total Energy = final Total Energy

TEi = TEf

In order for an object's kinetic energy to increase, it must take
energy from its stored energy, which we call potential energy.
When this happens, the potential energy that an object
possesses decreases.

Even though kinetic and potential energy are changing, the Total
Energy (TE) in that closed system contains does not change.

Conservation of Energy

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When energy is conserved, no energy is added or taken away from
the system. The total energy you start with is the total energy you
end with.

TEi = TEf

In other words, energy can not be created or destroyed. It can only
be transformed from one form to another.

Conservation of Energy

Click here to see conservation of energy
explained in roller coasters!

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When looking at the mechanical energy of a system, the total
energy possible is the Potential Energy (PE) and the Kinetic
Energy (KE) added together. Therefore, another way to write
conservation of energy is like this:

(PE + KE)i = (PE + KE)f

Conservation of Energy

When would PE be zero?

• the object is on the
ground (GPE)

• when a spring or other
elastic material is not
stretched or compressed
(EPE)

When would KE be zero?

• the object is not moving

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Conservation of Energy

Let's see if we can determine the total energy of a ball that is dropped
from rest. The figure below shows the ball at different positions as it
falls, starting with when it's at rest at 1 m before being dropped. Use
the idea of conservation of energy to determine the missing values.

v= 0 m/s
Height = 1 m

Height = 0.5 m

Height = 0 m

Remember that the total
mechanical energy at
that position is the sum of
the two individual
energies: (PE + KE)

TE = 0.5 J
PE = 0.5 J
KE = 0 J
TE = 0.5 J
PE = 0.25 J
KE = 0.25 J

TE = 0.5 J
PE = 0 J
KE = 0.5 J

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At position A in the diagram below, the roller coaster car has 40 J of
total energy and has a velocity equal to 0 m/s.

40 J

15 J
25 J

How much kinetic energy does the car possess at Point A?

0 J

How much gravitational potential energy does the car possess at
Point A?

40 J

since velocity is zero

KE is also zero

if KE is zero and the
TOTAL must equal
40 that means GPE must be 40 J

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At position B in the diagram below, the roller coaster car has a
gravitational potential energy equal to 15 J.

40 J

15 J
25 J

How much total energy does the car possess at Point B?

40 J

How much kinetic energy does the car possess at Point B?

25 J

the TOTAL is still 40 b/c

total energy CANNOT CHANGE

if GPE is now 15

and GPE + KE
must equal the total,

then KE is now 25 J

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At position C in the diagram below, the roller coaster car has a
gravitational potential energy equal to 25 J.

40 J

15 J
25 J

How much total energy does the car possess at Point C?

40 J

How much kinetic energy does the car possess at Point C?

15 J

the TOTAL is still 40 J b/c

total energy CANNOT CHANGE

if GPE is now 25
and GPE + KE needs

to equal 40 total, that
means KE is now 15 J

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36 At what position in the diagram below does the object
have only gravitational potential energy?

A W

B X

C Y

D Z

E None of the above

h = 0 m

Answer

*not moving yet

to ONLY have GPE it needs to HAVE HEIGHT but NOT BE MOVING

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37 At what position in the diagram below does the object
have only kinetic energy?

A W

B X

C Y

D Z

E None of the above

h = 0 m

Answer

*not moving yet

to ONLY have KE it needs to BE MOVING and HAVE NO HEIGHT

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38 At what position in the diagram below does the
object have both gravitational potential and kinetic
energy? Choose all that apply.

A W

B X

C Y

D Z

E None of the above

h = 0 m

Answer

at these points, it has both height and speed

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Transfer of Kinetic Energy to Potential
Energy

The total energy of the object must always be the
same due to conservation of energy. Let's look at the
ball that is dropped from 1 m again. Suppose the ball
bounces after it hits the ground. What will happen to
the KE?

Just as potential energy can be transferred to kinetic energy, kinetic
energy can be transferred into potential energy.

v= 0 m/s
Height = 1 m

Height = 0.5 m

Height = 0 m

TE = 0.5 J
PE = 0.5 J
KE = 0 J
TE = 0.5 J
PE = 0.25 J
KE = 0.25 J

TE = 0.5 J
PE = 0 J
KE = 0.5 J

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Transfer of Kinetic Energy to Potential
Energy
The kinetic energy at the bottom will be transferred to gravitational
potential energy as the ball gains height. Because of conservation of
energy, the total energy stays the same!

v= 0 m/s
Height = 1 m

Height = 0.5 m

Height = 0 m

TE = 0.5 J
PE = 0.5 J
KE = 0 J

TE = 0.5 J
PE = 0.25 J
KE = 0.25 J

TE = 0.5 J
PE = 0 J
KE = 0.5 J

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Transfer of Kinetic Energy to Potential
Energy
In reality, the ball will not bounce as high as it was dropped. Does this
mean energy was lost?

v= 0 m/s
Height < 1 m

TE = 0.5 J
PE = 0 J
KE = 0.5 J

NME = 0.10 J

NME=0.10 J

TE = 0.5 J
PE = 0.25 J
KE = 0.15 J

TE = 0.5 J
PE = 0.4 J
KE = 0 J

Sound Energy!

No. It just means that some of the KE that
the ball had when it first hits the ground was
transferred to the ground as heat and sound
energy (aka Non­Mechanical Energy). If we
consider the ball and the ground to be a
closed system, then the system's total
energy stays the same!

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Transfer of Kinetic Energy to Potential
Energy

Conservation of energy of
still applies, which means the
total energy remains
constant.

Let's consider a system that
is composed of a block and a
spring as shown to the right.

Kinetic energy can also be transferred to elastic potential energy.

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Transfer of Kinetic Energy to Elastic
Potential Energy

In the top picture, the block is travelling
at 10 m/s, meaning that it has kinetic
energy. The spring is relaxed and
therefore has no elastic potential
energy. The total energy of the block­
spring system is entirely due to the KE
of the block right now.

In the bottom picture, the block has
compressed the spring and is no
longer moving. The block has
transferred its kinetic energy to elastic
potential energy in the spring. The total
energy of the block­spring system is
entirely due to the elastic potential
energy in the spring.

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39 In which position of the block would the system have
only EPE?

A

B

C

Answer

to ONLY have EPE it would have to be stretched or compressed

WITHOUT MOVING - C would be the only place this happens when
the spring is compressed all the way to the board

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40 In which position of the block would the system have
both KE and EPE?

A

B

C

Answer

to have BOTH KE and EPE, the spring needs to be compressed a little

AND be moving, which is only happening at spot B

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41 In which position of the block would the system have
only KE?

A

B

C

Answer

to ONLY have KE, the block needs to be moving but the spring should

be still in its relaxed state of zero, which only occurs at spot A before
the spring is even touched

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If the total amount of energy that we start with, Ei, does not equal
the total amount of energy that we end up with, "Ef", then energy
was not conserved
TEi TEf

This means that there was an outside force that acted on the
system. Let's look at the dropping ball again. Last time we
considered the ball and the ground as the system together. What if
we just considered the ball as the system by itself?

What if the Total Energy is not
equal at the beginning and the end?

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v= 0 m/s
Height < 1 m

TE = 0.5 J
PE = 0 J
KE = 0.5 J

NME = 0.10 J

NME=0.10 J

TE = 0.4 J
PE = 0.25 J
KE = 0.15 J

TE = 0.4 J
PE = 0.4 J
KE = 0 J

Sound Energy!

TE = 0.5 J

The total energy of the ball before the bounce and after the bounce
would be different. This is because the ground would now be an
outside force acting on the system, the ball.

What if the Total Energy is not
equal at the beginning and the end?

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Types of Energy Resources

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113

Electrical energy can be produced through the conservation of
energy by using the mechanical energy contained in energy
resources.

Energy resources can be broken down into two categories:
Renewable and Non­Renewable.

Renewable Energy Resources are natural resources that can
replenish themselves over time.

Non­Renewable Energy Resources are natural energy resources
that exist in limited supply and cannot be replenished in a timely
manner.

Energy Resources

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Types of Energy Resources

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Energy Production from the Sun

Solar energy is a renewable form of
energy that is produced when
photons that are contained in sunlight
are absorbed by specially designed
plates that are angled towards the
sun.

When the photons hit the solar panels, charged particles are free to
move which causes a current to be produced. This current is
converted to usable electricity by the home.

Solar energy is converted to electrical energy!

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Energy Production from the Wind

Wind is a renewable energy resource
that is used to create electricity by
wind turbines, such as in the Alta
Wind Energy Center in California, the
world's largest wind farm.

As the wind blows past the blades of
the turbine, the kinetic energy of the
wind is transferred to the blades.
Inside the column of the turbine,
there is a drive shaft which is
connected to a generator.

As the blades spin, it spins the drive shaft that is connected to a
generator. The generator converts the kinetic energy (mechanical
energy) into electrical energy!

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Energy Production From Water

Water is a renewable resource that can be used to
create electricity in dams such as the Hoover Dam.

Gravitational potential energy is stored in elevated
water. When the water is released downward
towards a turbine, the GPE is converted to kinetic
energy and spins the turbine.

The turbine is connected to a generator that
converts this mechanical energy to electrical
energy!

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Energy Production from Fossil Fuels

Fossil fuels are a non­renewable energy
resource that can be used to produce
electricity when it is burned.

Fossil fuels include: natural gas, oil, and coal
(shown to the right).

When the fuel is burned, the heat
turns water into steam which turn
the blades of a turbine (kinetic
energy!). The turbine is connected
to a generator that converts the
mechanical energy into electrical
energy!

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Effects of Using Fossil Fuels As An Energy
Resource

Fossil fuels are non­renewable
energy resources due to how long
it takes for them to be produced
compared to how much is used to
create energy.

Fossil fuels take millions of years
to be produced.

Fossil fuels are also not considered
"Clean" energy resources as they
produce Carbon Dioxide (CO2) when
burned. Carbon dioxide is
considered a greenhouse gas, which
many believe is a cause global
warming.

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42 Which of the following is not considered a renewable
energy resource?

A Solar

B Wind

C Hydroelectric (water)

D Fossil Fuels

Answer