gravitational potential energy

Meaning: Gravitational potential energy (U) is energy stored by an object because of its position in a gravitational field. Lifting a mass at constant speed takes work against gravity, which is stored as U; when the object falls, U converts to kinetic energy. Gravity is conservative, so ΔU depends only on start and end heights, not path. The zero level is arbitrary, so only ΔU matters.

Equation: U = mgh near Earth's surface, where m is mass (kg), g is 9.8 m/s², and h is height above the chosen zero level (m); U is in joules. For large distances, U = −GMm/r, with G = 6.67 × 10⁻¹¹ N·m²/kg², M the central mass (kg) and r the center-to-center distance (m).

On the MCAT: Ramps, pendulums, roller coasters and falling objects are solved by energy conservation: with no friction, mgh at the top equals ½mv² at the bottom, so speed is independent of mass. With friction, some mechanical energy becomes thermal energy. Work done by gravity equals −ΔU.

Common confusion: Use vertical height, not distance along a ramp (h = L sinθ). Also, U can be negative; −GMm/r is negative, and it rises toward zero as r increases.