# Conservative force

Conservative forces are those that possess certain properties[1]:

1. The work it does on a particle is independent of its trajectory.

2. The work done on a particle that moves along a closed trajectory (where the initial and final positions are the same, or di = df) = 0) is zero.

3. The force can be written as the negative of the gradient of a potential energy function, i.e. $\vec F = - \nabla U$.

When the only forces present in a system are conservative, mechanical energy is conserved.

Examples of conservative forces:

Example of a non-conservative force:

## References

1. Serway and Beichner, Physics for Scientists and Engineers, Fifth Edition