Conservative and non-conservative forces

We said that potential energy can be introduced in certain systems. What conditions does the system have to meet in order for potential energy to be able to be incorporated into it?

Potential energy is an energy due to position. Unlike work, it characterises a position and not a process. Consequently, it can only be associated with forces whose work is independent of the path and only depends on the initial and the final position. We call these forces conservative forces.

Conservative and non-conservative forces

Conservative forces

We call a force conservative if the work it does on any object depends only on the initial position and the final position of the object and not on the path between. Consequently, the work done by a conservative force along a closed path is always zero.

Non-conservative forces

A force is non-conservative if the work it does on an object does depend on the actual path followed by the object. A conservative force does non-zero work along a closed path.

Consider the paths shown in the figure. If the object moves from position A to position B under the effect of a conservative force, the work the force does will be the same in the green path (through point C) and in the red path (through point D), or any other path in between positions A and B, regardless of the shape or the length of the path. If the object starts from A and arrives back to A, the total work will be zero. By contrast, if the force is non-conservative, the work along the green path will be different to the work along the red path, and the work along a closed path will not be zero.

The force of gravity, the force exerted by a spring, the electrostatic force all conservative and thus we can associate potential energy with them. The forces of friction or the drag force, by contrast, are non-conservative and no potential energy can be defined for them.