Conservation of EnergyConservation of Energy

IT’S THEIT’S THE

LAWLAW

Lifting a BallLifting a Ball

When you lift a ball to a When you lift a ball to a certain height you do certain height you do work on it.work on it.

This work (W) is equal This work (W) is equal to the weight of the ball to the weight of the ball (w=mg) times the height (w=mg) times the height (h).(h).

The work done to lift the The work done to lift the ball is stored as potential ball is stored as potential energy.energy.

h

W = Fd =wh = mgh

PE = W = mgh

Lifting a BallLifting a BallAs the ball falls:As the ball falls: Its Potential Energy Its Potential Energy

decreases because its decreases because its height decreases.height decreases.

Its Kinetic Energy Its Kinetic Energy increases because it speeds increases because it speeds up.up.

It turns out the amount of It turns out the amount of potential energy lost as the potential energy lost as the ball falls is the same as the ball falls is the same as the amount of kinetic energy amount of kinetic energy the ball gains!!!!the ball gains!!!!

h

PE = mgh

Kinetic EnergyEnergy of Motion

The Law of Conservation of EnergyThe Law of Conservation of Energy

Energy cannot be created nor destroyed, it Energy cannot be created nor destroyed, it can just be transformed from one form to can just be transformed from one form to another, or transferred from one object to another, or transferred from one object to

another.another.

If we ignore any losses in energy to sound or If we ignore any losses in energy to sound or heat (two big sources) this means that PE + heat (two big sources) this means that PE +

KE will always remain constant.KE will always remain constant.

A Falling BallA Falling BallA 2-kg ball falls from a height of 5-m. Trace its PE & KE as A 2-kg ball falls from a height of 5-m. Trace its PE & KE as it falls.it falls.

5-m

HeightHeight PE=mghPE=mgh KEKE PE+KEPE+KE

5-m5-m

4-m4-m

3-m3-m

2-m2-m

1-m1-m

0-m0-m

100-J100-J 0-J0-J

100-J100-J

100-J100-J

100-J100-J

100-J100-J

100-J100-J

100-J100-J

PE = (2)(10)(5)=100-J

Since the ball isn’t moving,

KE = 0-J!!!!

PE + KE =100 + 0 =

100-J

Conservation of Energy says PE + KE will always be 100-J the entire time the

ball falls!!!!!

A Falling BallA Falling BallA 2-kg ball falls from a height of 5-m. Trace its PE & KE as A 2-kg ball falls from a height of 5-m. Trace its PE & KE as it falls.it falls.

4-m

HeightHeight PE=mghPE=mgh KEKE PE+KEPE+KE

5-m5-m

4-m4-m

3-m3-m

2-m2-m

1-m1-m

0-m0-m

100-J100-J 0-J0-J

100-J100-J

100-J100-J

80-J80-J 20-J20-J

PE = (2)(10)(4)=80-J

KE = 100 – 80 = 20-J

100-J100-J

100-J100-J

100-J100-J

100-J100-J

A Falling BallA Falling BallA 2-kg ball falls from a height of 5-m. Trace its PE & KE as A 2-kg ball falls from a height of 5-m. Trace its PE & KE as it falls.it falls.

3-m

HeightHeight PE=mghPE=mgh KEKE PE+KEPE+KE

5-m5-m

4-m4-m

3-m3-m

2-m2-m

1-m1-m

0-m0-m

100-J100-J 0-J0-J

100-J100-J

100-J100-J

80-J80-J 20-J20-JPE = (2)(10)(3)

=60-J

KE = 100 – 60 = 40-J

100-J100-J

100-J100-J

100-J100-J

100-J100-J

40-J40-J60-J60-J

A Falling BallA Falling BallA 2-kg ball falls from a height of 5-m. Trace its PE & KE as A 2-kg ball falls from a height of 5-m. Trace its PE & KE as it falls.it falls.

2-m

HeightHeight PE=mghPE=mgh KEKE PE+KEPE+KE

5-m5-m

4-m4-m

3-m3-m

2-m2-m

1-m1-m

0-m0-m

100-J100-J 0-J0-J

100-J100-J

100-J100-J

80-J80-J 20-J20-J

PE = (2)(10)(2)=40-J

KE = 100 – 40 = 60-J

100-J100-J

100-J100-J

100-J100-J

100-J100-J

40-J40-J60-J60-J

40-J40-J 60-J60-J

A Falling BallA Falling BallA 2-kg ball falls from a height of 5-m. Trace its PE & KE as A 2-kg ball falls from a height of 5-m. Trace its PE & KE as it falls.it falls.

1-m

HeightHeight PE=mghPE=mgh KEKE PE+KEPE+KE

5-m5-m

4-m4-m

3-m3-m

2-m2-m

1-m1-m

0-m0-m

100-J100-J 0-J0-J

100-J100-J

100-J100-J

80-J80-J 20-J20-J

PE = (2)(10)(1)=20-J

KE = 100 – 20 = 80-J

100-J100-J

100-J100-J

100-J100-J

100-J100-J

40-J40-J60-J60-J

40-J40-J 60-J60-J

20-J20-J 80-J80-J

A Falling BallA Falling BallA 2-kg ball falls from a height of 5-m. Trace its PE & KE as A 2-kg ball falls from a height of 5-m. Trace its PE & KE as it falls.it falls.

HeightHeight PE=mghPE=mgh KEKE PE+KEPE+KE

5-m5-m

4-m4-m

3-m3-m

2-m2-m

1-m1-m

0-m0-m

100-J100-J 0-J0-J

100-J100-J

100-J100-J

80-J80-J 20-J20-J

PE = (2)(10)(0)=0-J

KE = 100 –0 = 100-J

100-J100-J

100-J100-J

100-J100-J

100-J100-J

40-J40-J60-J60-J

40-J40-J 60-J60-J

20-J20-J 80-J80-J

0-J0-J 100-J100-J

A Falling BallA Falling BallA 2-kg ball falls from a height of 5-m. Trace its PE & KE as A 2-kg ball falls from a height of 5-m. Trace its PE & KE as it falls.it falls.

HeightHeight PE=mghPE=mgh KEKE PE+KEPE+KE

5-m5-m

4-m4-m

3-m3-m

2-m2-m

1-m1-m

0-m0-m

100-J100-J 0-J0-J

100-J100-J

100-J100-J

80-J80-J 20-J20-J

100-J100-J

100-J100-J

100-J100-J

100-J100-J

40-J40-J60-J60-J

40-J40-J 60-J60-J

20-J20-J 80-J80-J

0-J0-J 100-J100-J

Where does the ball have its maximum speed?

Just before it hits the ground --- WHERE

ITS KE IS LARGEST

A Falling BallA Falling BallA 2-kg ball falls from a height of 5-m. Trace its PE & KE as A 2-kg ball falls from a height of 5-m. Trace its PE & KE as it falls.it falls.

HeightHeight PE=mghPE=mgh KEKE PE+KEPE+KE

5-m5-m

4-m4-m

3-m3-m

2-m2-m

1-m1-m

0-m0-m

100-J100-J 0-J0-J

100-J100-J

100-J100-J

80-J80-J 20-J20-J

100-J100-J

100-J100-J

100-J100-J

100-J100-J

40-J40-J60-J60-J

40-J40-J 60-J60-J

20-J20-J 80-J80-J

0-J0-J 100-J100-J

If the ball bounces back up, what height will it

reach?

Since it only has 100-J available, it will only

reach its original height of 5-m!!!!

A Falling BallA Falling BallA 2-kg ball falls from a height of 5-m. Trace its PE & KE as A 2-kg ball falls from a height of 5-m. Trace its PE & KE as it falls.it falls.

HeightHeight PE=mghPE=mgh KEKE PE+KEPE+KE

5-m5-m

4-m4-m

3-m3-m

2-m2-m

1-m1-m

0-m0-m

100-J100-J 0-J0-J

100-J100-J

100-J100-J

80-J80-J 20-J20-J

100-J100-J

100-J100-J

100-J100-J

100-J100-J

40-J40-J60-J60-J

40-J40-J 60-J60-J

20-J20-J 80-J80-J

0-J0-J 100-J100-J

If the ball loses 20-J to heat (air resistance) and sound, how high will it

bounce?

Since it only has 80-J (100 – 20) available, it

will only reach a height of 4-m!!!!

Pendulums & Roller CoastersPendulums & Roller Coasters

Pendulums and Roller Coasters must follow Pendulums and Roller Coasters must follow the Law of Conservation of Energythe Law of Conservation of Energy

IT’S THE LAWIT’S THE LAW This means that what ever potential energy is This means that what ever potential energy is

stored in each at the beginning is transferred stored in each at the beginning is transferred back and forth between PE & KE.back and forth between PE & KE.

If we are allowing for losses in energy from If we are allowing for losses in energy from heat and sound, then this amount of energy heat and sound, then this amount of energy slowly disappears.slowly disappears.

A PendulumA Pendulum

PE KE

A PendulumA PendulumIf there are losses in energy to heat and sound, then the height it reaches each swing gets lower and lower until it stops swinging.

Roller CoastersRoller Coasters Roller Coasters use the potential energy Roller Coasters use the potential energy

stored when it is at the top of a hill and stored when it is at the top of a hill and converts it to kinetic energy throughout the converts it to kinetic energy throughout the ride.ride.

WEeeeeeeeee!!!!!!!!!WEeeeeeeeee!!!!!!!!!