Gravitational PE & conservation of energy

The big idea: Lift something up and it stores gravitational potential energy (PE) — energy because of its height.

Let it fall and that PE turns into kinetic energy (KE) — energy because of its motion.

No energy is lost: the PE the object loses becomes the KE it gains.

Spot it: Top of a fall = all PE, no KE. Bottom = all KE, no PE. At any height in between, PE + KE adds up to the same total — that total is the mechanical energy, and it stays constant.

The change in gravitational PE when an object moves up or down a height Δh is given in the data booklet:

What 'conservation of energy' means here: For a falling body with no air resistance, the mechanical energy (PE + KE) is conserved — it stays the same.

So the PE lost = the KE gained: mgΔh = ½mv².

The kinetic energy of a moving object is also given in the booklet:

How this is tested — falling-body energy comes up in two predictable forms:

The classic trap: The mass cancels — speed at the bottom doesn't depend on m. And falling half the height means only half the energy is KE so far, not all of it.

The ratio shortcut: Because KE gained = PE lost, an object that has fallen a fraction f of its total height has turned a fraction f of its starting PE into KE. Fall half the height → KE = ½ of the starting PE.