conservative forces

Meaning: A conservative force does work that depends on the starting and ending positions, not the path taken. Equivalently, the net work over a closed loop is zero, and the work can be stored as potential energy and recovered. Standard examples are gravity, the ideal spring force and the electrostatic force. Friction and air resistance are nonconservative: they depend on path and convert mechanical energy to thermal energy.

Equation: Wc = −ΔU, where Wc is the work done by the conservative force (J) and ΔU is the change in potential energy (J). Over a closed loop, Wc = 0.

On the MCAT: Passages use a frictionless ramp, pendulum, roller coaster or charge in a field. If only conservative forces do work, KE + U stays constant, so speed at a given height is the same whatever the path's shape. Add friction and mechanical energy falls by the magnitude of the work done by friction, which grows with path length.

Common confusion: Path independence does not mean zero work. Gravity does work mgh on a falling object; only a closed loop gives zero. Also, normal force and tension in a pendulum are not conservative forces, but they are perpendicular to the motion, do no work, and leave mechanical energy unchanged.