7.3: Conservative Forces and Potential Energy

A non-conservative force is a force that depends on the path an object takes. In other words, a non-conservative force depends on how an object got from its initial state to its final state. Non-conservative forces change the amount of mechanical energy in a system. This differs from conservative forces, which do not depend on the path taken from initial to final state, and do not change the amount of mechanical energy in a system.

An important example of a non-conservative force is friction. We know that friction is the force between two surfaces. We see friction when rolling a ball on a carpet versus a hardwood floor. The ball rolls farther on the hardwood floor than it does on a carpet. This is because the fuzzy carpet has more friction than the smooth hardwood. Friction converts some of the kinetic energy of the ball to thermal energy, or heat. As kinetic energy is converted to thermal energy, the balls slows to a stop.

On the other hand, a conservative force is a force which does work that only depends on the beginning point and the end point of the system. The work done by a conservative force does not depend on the path the system takes to get from beginning to end. Conservative forces exist in ideal systems with no friction. An idealized spring that does not experience friction would be an example of conservative forces.