Conservative and Non-Conservative Forces

If the work done is path independent, the underlying force is conservative.

Example: the force of gravity:    dWgrav = mg • dr = - mg dy
Wgrav = - mg(yf-yi) = - mg Δ y

Because the work done depends only on the endpoints and not on the path the underlying external force is conservative.

Examples of conservative force:   gravity, springs.
Example of non-conservative force:   friction.

For an arbitrary conservative force:   Wcons = - (Uf - Ui)

Energy Conservation Statement:

Start with our previous connection between kinetic energy and work:

W = Δ K   →   Wcons + Wnon-cons = Δ K

Ui - Uf + Wnc           = Kf - Ki

Ki + Ui + Wnc = Kf + Uf