Kinetic and potential energy

Moving objects have energy in their kinetic store; raised objects have energy in their gravitational potential store. As something falls, energy moves from one store to the other.

Key facts

  • KE = ½mv².
  • GPE = mgh (g ≈ 9.8 N/kg on Earth).
  • Falling without air resistance: GPE lost = KE gained.
  • Doubling speed makes kinetic energy four times bigger.

Worked examples

Example 1

A 50 kg skier drops 20 m down a slope. Ignoring friction, how fast is she going at the bottom?

  1. GPE lost: 50 × 9.8 × 20 = 9800 J.
  2. ½ × 50 × v² = 9800 v² = 392
  3. v ≈ 19.8 m/s (the mass actually cancels).

Answer: 19.8 m/s

Example 2

Find the kinetic energy of a 1000 kg car at 15 m/s.

  1. ½ × 1000 × 15² = 112500 J

Answer: 112 500 J