Path independence of energy change

Path independence of changes in potential energy.

Gravitation is often the context for conservation of energy problems on comprehensive exams. The work a conservative force performs on an object in moving it from A to B is does not depend on the path. Gravity is a conservative force. With gravitation, the work does not depend on the path taken. It depends only on the end points of the motion.

Let's talk about an important consequence. If the work performed were not path independent, a circular path could be conceived which would dissipate energy, but on the contrary, because gravity is a conservative force, any path which ends in the same initial position must necessary result in no change in potential energy state. This means that for an isolated gravitational system, the total energy must be be the same everywhere. And because or an initial state has both kinetic and potential energy, this total energy value gives the total of the kinetic energy plus the potential energy for all other possible states, regardless of the path between states, as long as only gravitational force is involved.