[Physics] Work done by a non-conservative force and change in potential energy

energynewtonian-mechanicspotential energywork

I know that the work done by a non-conservative force is equal to the change in total mechanical energy (from Work-Energy Theorem). But I read in a place that "Non-conservative forces don't affect PE".
So I am confused. How does the work done by a non-conservative force affect the potential energy?

Best Answer

Your question seems to arise from a problem in which there is both a conservative and a non-conservative force. When you say "PE" you must be referring to the PE of the conservative force (by definition there is no PE of a non-conservative force).

The work done by the conservative force does not depend on the path. Therefore you can define the potential as

$$\phi(x_0) - \phi(x) \equiv W_{x_0\to x}$$

Notice that:

  • The potential is defined up to a global offset: you can arbitrarily choose the value $\phi(x_0)$ but afterwards any value of $\phi(x)$ is defined.
  • This is a well posed definition just because $W_{x_0\to x}$ is a well defined quantity (depends only on $x_0$ and $x$, by definition of conservative force). This is not the case for the non conservative force.