The work done by a conservative force is (by definition) path-independent; that means that in particular the work done when moving along any closed path must be zero. For a conservative force, we can ...The work done by a conservative force is (by definition) path-independent; that means that in particular the work done when moving along any closed path must be zero. For a conservative force, we can thus define a potential energy difference between points 1 and 2 as the work necessary to move an object from point 1 to point 2.