8.5: Conservative Forces
According to the law of conservation of energy, any transition between kinetic and potential energy conserves the total energy of the system. Hence, the work done by a conservative force is completely reversible. It is path independent, which means that we can start and stop at any two points in the transition, and the total energy of the system (kinetic plus potential energy at these points) will remain conserved. This is characteristic of a conservative force. Some important examples of conservative forces include gravity, elastic, and static electric force.
The work done by a conservative force is independent of the path taken; in other words, it is the same for any path connecting two points. We can conclude that the work done is independent of the path by checking that the infinitesimal work is an exact differential. In a closed path, where the beginning and the ending points are identical, the work done by a conservative force on an object is zero.
This text is adapted from Openstax, University Physics Volume 1, Section 8.2: Conservative and Non-Conservative Forces.
