- #1

FaraDazed

- 347

- 2

## Homework Statement

I need the derivations of gravitational potential energy and kinetic energy (without using calculus)

## Homework Equations

[itex]

PE = mgh \\

KE = {1 \over 2}mv^2

[/itex]

## The Attempt at a Solution

Potential Energy:

Work done = [itex]Fs[/itex]

But... [itex]F=ma[/itex]

So substituting that in becomes [itex] mas [/itex]

where a is the acceleration due to gravity (the g in mgh), and s is the height in mgh.Kinetic Energy (this is I am a lot less sure on):

Work done = [itex]Fs[/itex]

But... [itex]F=ma[/itex]

So substituting that in becomes [itex] mas [/itex]

And when u=0 [itex]v^2 = 0 + 2as[/itex]

Which can be arranged to [itex]a = {v^2 \over 2s}[/itex]

So substituting that in becomes [itex] = m \times {v^2 \over 2s} \times s[/itex]

Which can apparently (so I was told) be rearranged to become [itex]{1 \over 2}mv^2[/itex]

Can anyone let me know if these are correct, if not any advice is appreciated and if they are correct, any advice on how to word it correctly is also appreciated.

Thanks.