Potential energy

Stretch the band of a catapult (slingshot) or bend an archer's bow, then let go: the stone or arrow flies off. The work you did stretching it was stored, and on release it turns into kinetic energy.

This stored energy is potential energy. It can be stored in two ways:

• By changing shape: a stretched band, a bent bow, a squashed or stretched spring.
• By position: two objects that pull or push each other, held apart or together. Unlike magnetic poles held apart, opposite charges held apart, a ball held up above the Earth. Let go, and they rush together, gaining kinetic energy.

Gravitational potential energy. To lift a mass m slowly up a height h, you must push up with a force equal to its weight, mg. The work you do is force × height:

U = mgh

(counting the ground as zero). That work is stored in the raised object.

Seeing it: drop a ball into sand from 2 m, then from 1 m. From 2 m it makes a deeper dent: it had more stored energy.

Careful: it's height above the ground, not how far it has fallen. A 2 kg box sits on a shelf 10 m up: U = 2 × 10 × 10 = 200 J. It falls 4 m. Its height is now 6 m, not 4 m, so U = 2 × 10 × 6 = 120 J.

Two limits:

• U = mgh works only near the Earth's surface. Far away, g gets smaller.
• Work done against friction is not stored. Push a box along the floor and the work turns into heat; you can't get it back.