Mechanical energy and free fall

Kinetic energy and potential energy

During free fall, two forms of energy are involved:

• kinetic energy: Ec = (1/2)mv^2
• gravitational potential energy: Ep = mgh

where m is the mass (kg), v is the velocity (m/s), and h is the height relative to a reference level (m).

Conservation of mechanical energy

Since there is no friction, the mechanical energy Em = Ec + Ep is conserved during the fall: the potential energy lost (as the object descends) is entirely converted into kinetic energy (as the object accelerates).

Example: an object of mass m = 2 kg is dropped from a height h = 10 m (v₀ = 0).

• Initial Ep = mgh = 2 * 9.8 * 10 = 196 J
• Initial Ec = 0 J
• At ground level (h = 0): Potential energy (Ep) = 0 J, so final kinetic energy (Ec) = 196 J, which gives v = √(2 × 196/2) = 14 m/s.

Summary table

Time	Ep (J)	Ec (J)	Em (J)
Start (h=10 m)	196	0	196
Finish (h=0 m)	0	196	196

Pitfall to avoid

This conservation of mechanical energy only holds true if friction is negligible. As soon as there is air resistance (e.g. parachute, falling with an umbrella, etc.), some of the energy is dissipated as heat and Em decreases over time.