How the energy formulas work
An object's kinetic energy depends on how fast it moves and how heavy it is:
KE = ½ × m × v²
Its gravitational potential energy depends on how high it is raised relative to a chosen reference level:
PE = m × g × h
where g ≈ 9.81 m/s² near Earth's surface. The total mechanical energy is KE + PE, and the central idea of classical mechanics is that in a system with no friction or air resistance, this total stays constant as the object moves — a falling ball trades potential energy for kinetic energy one-for-one, and lands with exactly the speed that height predicted.
Worked example
A 10 kg object moving at 5 m/s and held 20 m up has KE = ½ × 10 × 25 = 125 J and PE = 10 × 9.81 × 20 = 1,962 J, so mechanical energy is 2,087 J — only about 6% is kinetic. If the object is released, the 1,962 J of potential energy converts to kinetic as it falls: v = √(2gh) = √(392) ≈ 19.8 m/s at the reference level, and the KE then equals the PE it lost. Notice the v² in the kinetic formula — doubling speed quadruples the energy, which is why small speed increases cost so much more fuel.
Where the energy goes in the real world
The "no friction" assumption is the idealisation. In practice some energy becomes heat (air resistance, engine friction), sound, and deformation. That is why a bouncing ball never returns to its original height: each bounce loses a fraction of its energy to the air and the impact, and the bounces get shorter and weaker until it stops. In a pendulum, the same ideal conservation gives a clean exchange between height and speed at every swing.