potential energy

Potential energy is the energy a system holds in reserve by virtue of its configuration. A brick held aloft has gravitational potential energy; a compressed spring has elastic potential energy; a stretched rubber band, a charged capacitor, a drawn bow — all are potential-energy reservoirs. Release the constraint and the stored energy converts to kinetic energy of the moving parts.

Mathematically, a potential energy function U(r) exists whenever the force on a body can be derived as F = −∇U — that is, whenever the force is conservative. Gravity near the Earth's surface (U = m·g·h), Hookean springs (U = ½·k·x²), electrostatic attraction (U = k·q₁·q₂/r), and universal gravitation (U = −G·m₁·m₂/r) are all described by potential-energy functions. Friction and air drag are not — they are dissipative, and the energy they take cannot be retrieved by reversing the motion.

The zero of potential energy is arbitrary; only differences matter physically. What the concept buys you is the conservation of total mechanical energy ½·m·v² + U(r), a running constant along the motion. In the absence of dissipation, the universe keeps strict count of how much is kinetic and how much is potential, and the total never changes.