# Potential Energy, Perfect Spring

Published on: Tue Mar 16 2010

I needed to keep my graphic from last lecture… We continued the problem, of a mass sliding down a slide, represented by an arc one quarter of a circle. So we were talking about how as the mass goes down the slide it makes these very small changes in distance, which are the same as making very small changes in the angle theta.
Total work done is equal to mass * gravity * radius.
So, looking at this graphic, we are able to say the **total work** done is equal to the **change in potential energy**, which is equal to one half mass * velocity squared at the bottom. This concept also applies for work which does not move in a smooth arch to the bottom.
How high should you start from in order to successfully make a loop-de-loop on a rollercoaster?
If you put a mass on a perfect spring, compress the spring and then release it, what is the potential energy in the spring at the top of the in the air fly time? k is the spring bounciness.
We briefly started to touch on momentum. Momentum is a vector, represented by the symbol “*p*”. It is mass times velocity. The professor noted how the conservation of energy does not actually happen to often. But conservation of momentum does tend to happen quite regularly.