Gravitational Potential Energy

Lift a book onto a shelf and you push against gravity the whole way up. That push, applied over the distance you lift it, is work, and it does not vanish once your hand lets go. It gets filed away as gravitational potential energy, energy that belongs to the book-and-Earth system because of how far apart they now are. Let the book fall and that stored energy converts back into kinetic energy, which is why it feels like cashing in savings: you deposited work on the way up, you withdraw it as motion on the way down.

The mechanism is just bookkeeping. The work done lifting an object at constant speed equals the force needed to support it, mg, times the height risen, h. So PE = mgh. Nothing here cares about the path you took to get the book up there, only the net height gained, because gravity is a conservative force. This is also why the zero of potential energy is a choice, not a fact: PE measures height relative to some reference level you pick, like the floor or the ceiling, and nature only cares about changes in PE, not the number itself. Pick a different floor and every PE value shifts by a constant, but every change in PE, and so every change in kinetic energy, comes out identical.

This sets up the energy bar charts coming next: PE and KE are just two entries in the same ledger, and total mechanical energy stays constant when only gravity does work. Potential energy is also where this unit starts replacing force diagrams with a scalar story: instead of tracking vectors through a fall, you track one number, energy, and let it shuffle between kinetic and potential forms.