8.5:
Conservative Forces
Forces can be categorized as conservative and non-conservative forces.
Gravitational, electrostatic, and elastic restoring forces are a few examples of conservative forces.
For example, a car at rest possesses potential energy while its kinetic energy is zero. When the car starts moving, its potential energy is converted to kinetic energy, and when it stops, its kinetic energy converts back to potential energy provided there is no friction.
As these energies are interconverting from one form to another, the sum of kinetic and potential energy remains the same throughout the path. This interconversion of energies is governed by conservative forces.
The work done by the conservative forces is consistently reversible and does not depend on the path taken by the object. It depends only on the start and the end points, and can be expressed as the difference in the potential energies at these points.
However, for a closed path, the work done will be zero.
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.