Lift an object and you store gravitational potential energy; let it fall and that store pours into kinetic energy. Two short formulas, each derived from mechanics you already know, capture the whole exchange.
The change in gravitational potential energy is ΔEₚ = mgΔh, from W = Fs with F = mg. Kinetic energy is Eₖ = ½mv², from the work done by a resultant force using v² = u² + 2as. With no resistance, GPE and KE interchange while their total is conserved.
Release the ball and watch the two energy bars trade: gravitational potential energy falls as kinetic energy rises, while the total stays fixed. The speed at the bottom comes from mgΔh = ½mv².
Both formulas come straight from work done by a force.
| Energy | Where it comes from |
|---|---|
| ΔEₚ = mgΔh | from W = Fs with F = mg over height Δh |
| Eₖ = ½mv² | from W = Fs = mas and v² = u² + 2as |
Four quick checks tied to this lesson. Each correct answer earns XP and lights this skill on your star map.
The change in gravitational potential energy when a mass m rises through a height Δh is:
The kinetic energy of a 2.0 kg object moving at 3.0 m s⁻¹ is:
An object falls freely from rest. As it falls, its gravitational potential energy is mainly converted into:
If the speed of a moving car doubles, its kinetic energy:
Energy conservation often lets the mass cancel and the path drop out.
Kinetic energy depends on v², not v, so doubling the speed quadruples the kinetic energy (and the braking distance). The change in gravitational potential energy uses the vertical height only, never the distance along a slope. And in free energy conversion the mass cancels, so a heavy and a light ball dropped from the same height reach the same speed.
Unlocks once the checks above are done. Worth more XP, written to AS Paper 1 and 2 standard.
A ball is dropped from rest from a height of 1.8 m. Ignoring air resistance and taking g = 9.8 m s⁻², its speed just before landing is:
A 0.50 kg ball is thrown straight up at 12 m s⁻¹. Using energy conservation (g = 9.8 m s⁻²), the maximum height reached is:
Two identical balls roll from rest from the same height down two frictionless slopes of different shapes. At the bottom their speeds are:
This skill is now lit gold on your star map. You have finished the lessons of Topic 5; the Paper 1 set awaits.