Gravitational potential energy and kinetic energy (5.2)

What is gravitational potential energy?

Gravitational potential energy - the energy stored in mass due to its position in a gravitational field

How do you derive the equation for GPE?

1) Consider a mass m lifted up a height h

2) Thus mg is the weight of the mass where g is the gravitational energy

3) W = Fd = mg x change in height

4) So ΔGPE = mgΔh

What is kinetic energy?

Kinetic energy - energy an object has due to motion

How do you derive the equation for KE?

1) Consider a mass m at rest which accelerates to a speed v over distance d

2) Recall W = Fd and F = ma

3) Using v² = u² + 2as, plug in values so u = 0 and s = d

4) Rearrange v² = 2ad for a. a= v²/2d

5) Plug back into F=ma. So F=mv²/2d

6) Plug into W = Fd = ½ x mv²/d x d = E

7) The d cancels so E = ½ x m x v²