Kinetic and potential energy: the formulas

Mechanical energy has two forms: kinetic (from motion) and potential (from position/height).

Potential energy

E_p = m · g · h — mass (kg) × gravity (9.8 m/s²) × height (m). A body up high has "stored" energy.

Kinetic energy

E_k = ½ · m · v² — it depends on the square of speed, so doubling the speed quadruples the energy.

One becomes the other (conservation)

In a fall, potential turns into kinetic, but total mechanical energy is conserved (no friction). That's why impact speed is v = √(2·g·h) — the same that sets ½mv² equal to mgh.

Step-by-step example

A 2 kg ball at 10 m (g = 9.8):

• Potential: 2 × 9.8 × 10 = 196 J
• On landing, that becomes kinetic: ½ × 2 × v² = 196 → v ≈ 14 m/s

FAQ

Why does doubling speed quadruple energy? Because kinetic energy depends on v². It's why a car at 100 km/h has 4× the energy (and damage) of one at 50.

Does potential energy depend on the "zero"? Yes. Height is measured from a reference you choose; what matters physically is the height difference.