Conservation of Energy

1
Conservation of Energy

• ITS THE

LAW
2
Lifting a Ball

• When you lift a ball to a certain height you do
  work on it.
• This work (W) is equal to the weight of the ball
  (wmg) times the height (h).
• The work done to lift the ball is stored as
  potential energy.

PE W mgh
h
W Fd wh mgh
3
Lifting a Ball

• The ball now has potential energy stored in it.
• This means the ball has the potential to do work
  if you drop it on something.
• But before it can do that work it must convert
  the PE to another form of energy called kinetic
  energy energy of motion

PE mgh
h
Kinetic Energy Energy of Motion
4
Kinetic Energy

• Kinetic Energy (KE) is energy of motion.
• Kinetic Energy depends on the moving objects
  mass (m) and the square of its speed (v).

5
Lifting a Ball

• As the ball falls
• Its Potential Energy decreases because its height
  decreases.
• Its Kinetic Energy increases because it speeds
  up.
• It turns out the amount of potential energy lost
  as the ball falls is the same as the amount of
  kinetic energy the ball gains!!!!

PE mgh
h
Kinetic Energy Energy of Motion
6
The Law of Conservation of Energy

• Energy cannot be created nor destroyed, it can
  just be transformed from one form to another, or
  transferred from one object to another.
• If we ignore any losses in energy to sound or
  heat (two big sources) this means that PE KE
  will always remain constant.

7
Mechanical Energy
The sum of all the potential energy and the
kinetic energy of a system is defined as its
mechanical energy.
 
Conservation of Mechanical Energy
In an isolated, closed system, if there are no
losses in energy in the form of sound or heat,
then the mechanical energy of a system is
conserved.
8
A Falling BallA 2-kg ball falls from a height of
5-m. Trace its PE KE as it falls.
PE (2)(10)(5) 100-J
Since the ball isnt moving, KE 0-J!!!!
Height PEmgh KE ME
5-m
4-m
3-m
2-m
1-m
0-m
100-J
0-J
100-J
100-J
PE KE 100 0 100-J
100-J
5-m
100-J
Conservation of Energy says ME will always be
100-J the entire time the ball falls!!!!!
100-J
100-J
9
A Falling BallA 2-kg ball falls from a height of
5-m. Trace its PE KE as it falls.
Height PEmgh KE ME
5-m
4-m
3-m
2-m
1-m
0-m
PE (2)(10)(4) 80-J
100-J
0-J
100-J
KE 100 80 20-J
100-J
80-J
20-J
100-J
4-m
100-J
100-J
100-J
10
A Falling BallA 2-kg ball falls from a height of
5-m. Trace its PE KE as it falls.
Height PEmgh KE ME
5-m
4-m
3-m
2-m
1-m
0-m
100-J
0-J
100-J
PE (2)(10)(3) 60-J
100-J
80-J
20-J
100-J
40-J
60-J
100-J
KE 100 60 40-J
3-m
100-J
100-J
11
A Falling BallA 2-kg ball falls from a height of
5-m. Trace its PE KE as it falls.
Height PEmgh KE ME
5-m
4-m
3-m
2-m
1-m
0-m
100-J
0-J
100-J
100-J
80-J
20-J
100-J
40-J
60-J
PE (2)(10)(2) 40-J
60-J
100-J
40-J
100-J
KE 100 40 60-J
2-m
100-J
12
A Falling BallA 2-kg ball falls from a height of
5-m. Trace its PE KE as it falls.
Height PEmgh KE ME
5-m
4-m
3-m
2-m
1-m
0-m
100-J
0-J
100-J
100-J
80-J
20-J
100-J
40-J
60-J
KE 100 20 80-J
60-J
100-J
40-J
PE (2)(10)(1) 20-J
20-J
80-J
100-J
100-J
1-m
13
A Falling BallA 2-kg ball falls from a height of
5-m. Trace its PE KE as it falls.
Height PEmgh KE ME
5-m
4-m
3-m
2-m
1-m
0-m
100-J
0-J
100-J
100-J
80-J
20-J
100-J
40-J
60-J
60-J
100-J
40-J
KE 100 0 100-J
20-J
80-J
100-J
0-J
100-J
100-J
PE (2)(10)(0) 0-J
14
A Falling BallA 2-kg ball falls from a height of
5-m. Trace its PE KE as it falls.
Where does the ball have its maximum speed?
Height PEmgh KE ME
5-m
4-m
3-m
2-m
1-m
0-m
100-J
0-J
100-J
Just before it hits the ground --- WHERE ITS KE
IS LARGEST
100-J
80-J
20-J
100-J
40-J
60-J
60-J
100-J
40-J
20-J
80-J
100-J
0-J
100-J
100-J
15
A Falling BallA 2-kg ball falls from a height of
5-m. Trace its PE KE as it falls.
Height PEmgh KE ME
5-m
4-m
3-m
2-m
1-m
0-m
100-J
0-J
100-J
If the ball bounces back up, what height will it
reach?
100-J
80-J
20-J
100-J
40-J
60-J
Since it only has 100-J available, it will only
reach its original height of 5-m!!!!
60-J
100-J
40-J
20-J
80-J
100-J
0-J
100-J
100-J
16
A Falling BallA 2-kg ball falls from a height of
5-m. Trace its PE KE as it falls.
Height PEmgh KE ME
5-m
4-m
3-m
2-m
1-m
0-m
100-J
0-J
100-J
If the ball loses 20-J to heat (air resistance)
and sound, how high will it bounce?
100-J
80-J
20-J
100-J
40-J
60-J
Since it only has 80-J (100 20) available, it
will only reach a height of 4-m!!!!
60-J
100-J
40-J
20-J
80-J
100-J
0-J
100-J
100-J
17
Pendulums Roller Coasters

• Pendulums and Roller Coasters must follow the Law
  of Conservation of Energy
• ITS THE LAW
• This means that what ever potential energy is
  stored in each at the beginning is transferred
  back and forth between PE KE.
• If we are allowing for losses in energy from heat
  and sound, then this amount of energy slowly
  disappears.

18
A Pendulum
Maximum PE
Maximum PE
PE
KE
Maximum KE
Maximum Height
Maximum Height
Maximum Height?
Highest Speed
Highest Speed?
19
A Pendulum
If there are losses in energy to heat and sound,
then the height it reaches each swing gets lower
and lower until it stops swinging.
20
Roller Coasters

• Roller Coasters use the potential energy stored
  when it is at the top of a hill and converts it
  to kinetic energy throughout the ride.
• WEeeeeeeeee!!!!!!!!!