Conservative force

If a force is conservative, it is possible to assign a numerical value for the potential at any point and conversely, when an object moves from one location to another, the force changes the potential energy of the object by an amount that does not depend on the path taken, contributing to the mechanical energy and the overall conservation of energy.

If the force is not conservative, then defining a scalar potential is not possible, because taking different paths would lead to conflicting potential differences between the start and end points.

Though the particle may still be moving, at that instant when it passes point A again, it has traveled a closed path.

If the net work done by F at this point is 0, then F passes the closed path test.

The work done by a conservative force is equal to the negative of change in potential energy during that process.

Despite conservation of total energy, non-conservative forces can arise in classical physics due to neglected degrees of freedom or from time-dependent potentials.

[8] For instance, friction may be treated without violating conservation of energy by considering the motion of individual molecules; however, that means every molecule's motion must be considered rather than handling it through statistical methods.

For macroscopic systems the non-conservative approximation is far easier to deal with than millions of degrees of freedom.

Examples of non-conservative forces are friction and non-elastic material stress.

Friction has the effect of transferring some of the energy from the large-scale motion of the bodies to small-scale movements in their interior, and therefore appear non-conservative on a large scale.

[8] General relativity is non-conservative, as seen in the anomalous precession of Mercury's orbit.