1. Conservation of Energy
The relationship between Potential and Kinetic Energy

2. Relationship between KE and PE
In many situations, there is a conversion between potential and kinetic energy.
The total amount of potential and kinetic energy in a system is called the mechanical energy.
Mechanical energy = PE + KE

3. Mechanical Energy Mechanical energy is due to the position
and motion of the object.
What happens to the mechanical
energy of an apple as it falls from
a tree?

4. Mechanical Energy
As the apple falls to the ground, its height decreases. Therefore, its GPE decreases.
The potential energy is not lost – it is converted into kinetic energy as the velocity of the apple increase.
What happens to the mechanical energy?

5. Mechanical Energy
The mechanical energy does not change because the loss in potential energy is simply transferred into kinetic energy.
The total amount of energy remains the same. Energy is conserved and transformed.
This is the Law of Conservation of Energy – energy is neither created or destroyed – the total energy is constant.

6. Conservation of Mechanical Energy
m = mass
v = velocity
g = gravitational acceleration
h = height
Oni, did you know that even though it was a bumpy ride, our energy remained constant!
Kinetic Energy
Potential Energy
Total Energy

7. Conservation of Mechanical Energy

8. Conservation of Mechanical Energy

9. Conservation of Mechanical Energy

10. Conservation of Mechanical Energy

11. Conservation of Mechanical Energy

12. Conservation of Mechanical Energy
Is the skater above the ground?
NO ; h = 0 m ; PE = 0 J
Position m v KE PE E 1
60 kg
8 m/s
1920 J
0 J
1920 J

13. Conservation of Mechanical Energy
Energy Before = Energy After
E = PE + KE
1920 J = (60)(9.8)(1) + ½60v2
1920 J = 588 J + ½ 60v2
1332 J = 30v2
44.4 = v2
6.66 m/s = v
Position m v KE PE E 1
60 kg
8 m/s
1920 J
0 J 2
6.66 m/s
1332 J
588 J
1920 J

14. Conservation of Mechanical Energy
Is the skater moving at the top?
NO, v = 0 m/s
Energy Before = Energy After
E = PE + KE
1920 J = (60)(9.8)h + 0
3.27 = h
Position m v KE PE E 1
60 kg
8 m/s
1920 J
0 J 2
6.66 m/s
1332 J
588 J 3
0 m/s
0 J
1920 J
1920 J