Conservative force

Conservative forces are those that possess certain properties:

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 d_i = d_f) = 0) is zero.

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

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

Examples of Conservative forces:

• Gravitational force
• force performed by a spring