Non-Conservative Forces

When no change in potential energy occurs, applying $\mathrm{KE}_{\mathrm{i}}+\mathrm{PE}_{\mathrm{i}}+W_{\mathrm{nc}}=\mathrm{KE}_{\mathrm{f}}+\mathrm{PE}_{\mathrm{f}}$ amounts to applying the work-energy theorem by setting the change in kinetic energy to be equal to the net work done on the system, which in the most general case includes both conservative and nonconservative forces. But when seeking instead to find a change in total mechanical energy in situations that involve changes in both potential and kinetic energy, the previous equation $\mathrm{KE}_{\mathrm{i}}+\mathrm{PE}_{\mathrm{i}}+W_{\mathrm{nc}}=\mathrm{KE}_{\mathrm{f}}+\mathrm{PE}_{\mathrm{f}}$ says that you can start by finding the change in mechanical energy that would have resulted from just the conservative forces, including the potential energy changes, and add to it the work done, with the proper sign, by any nonconservative forces involved.