# Potential Energy and Conservation of Energy

Here's a brief review of the idea behind potential energy:

One of the most common examples of potential energy is Gravitational Potential Energy (GPE). And the most fun you can have (legally) with gravitational potential energy is ... using it in rollercoasters!

Let's make a little rollercoaster and see if all this theory actually works ...

Some problems can be attacked either via forces or via energy ....

If you finish early, consider this rather slippery problem.

• You sit on top of a perfect hemisphere of ice, balanced perfectly on the very top. A gust of wind blows you forward, and you slide without friction downwards along the curved surface. At what angle from the top of the hemisphere will you fly off the ice and fall through the air?

Hint: draw a big picture, and assign symbolic values like m, R, etc., to any quantities that you think might be relevant. Consider both conservation of energy and the motion of an object in a circular path ...