Conservation of Energy

Slide 90 / 122

Conservation of Energy

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Slide 91 / 122

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?

https://sites.google.com/a/ttsd.k12.or.us/tuhsphysics/home/htp-ib-physics/work-and-energy/ib-a6-2-conservation-of-energy

Practice conservation of mass

Slide 92 / 122

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

Slide 93 / 122

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!

Slide 94 / 122

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

Slide 95 / 122

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

Slide 96 / 122

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

Slide 97 / 122

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

Slide 98 / 122

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

Multiple Choice

At what position in the diagram does the object has just gravitational energY?

• W

• X

• Y

• Z

Slide 99 (Answer) / 122

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

[This object is a pull
tab]

Answer

A

Multiple Choice

At what position in the diagram does the object has only kinetic energy?

• W

• X

• Y

• Z

Slide 101 / 122

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

Multiple Choice

At what position in the diagram does the object has both kinetic and potential energy?

• W

• X

• Y

• Z

• Both Y and Z

Slide 101 (Answer) / 122

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

[This object is a pull
tab]

Answer

C and D

Slide 102 / 122

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

Slide 103 / 122

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

Slide 104 / 122

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 Non-Mechanical Energy). If we
consider the ball and the ground to be a
closed system, then the system's total
energy stays the same!

Slide 105 / 122

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.

Slide 106 / 122

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 block-spring system is
entirely due to the elastic potential
energy in the spring.

Slide 107 / 122

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

A

B

C

Slide 107 (Answer) / 122

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

A

B

C

[This object is a pull
tab]

Answer

C

Slide 108 / 122

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

A

B

C

Slide 108 (Answer) / 122

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

A

B

C

[This object is a pull
tab]

Answer

B

Slide 109 / 122

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

A

B

C

Slide 109 (Answer) / 122

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

A

B

C

[This object is a pull
tab]

Answer

A

Slide 110 / 122

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?

Slide 111 / 122

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?