## October 4, 2011

Understand how conservation of energy produces a link between gravitational potential energy, kinetic energy and work

Conservation of Energy
As a reminder; the conservation of energy states that the total amount of energy in a system is constant over time (i.e. if you put 5J in you get 5J out). A consequence of this is that energy can neither be created nor be destroyed; and can only be transformed from one state to another.

We can write the principle of conservation of energy as a formula:

Calculation
The Diagram below shows a man at the top of a building, calculate how much energy he has at the start and hence show how much energy he has at the end.
Energy at the top GPE = mgh
GPE = 50 x 10 x 20
GPE = 10,000J

KE = 0J (He isn’t currently moving)

Total Energy = KE + GPE
Total Energy = 0 + 10,000
Total Energy at start = 10,000J

Energy at the bottom GPE = 0J

Total energy Start = Total energy End
Total energy end = KE + GPE
10,000J = KE + 0J
KE = 10,000J

KE = ½ mv2
10,000 = ½ x 50 x v2
v = 20m/s