# Is the relation between change in potential energy and work by internal conservative force can be used even in presence of non conservative forces?

We know that work done by internal conservative forces is the negative of change in potential energy of the system stored in conservative force field. But does this logic still hold when there are non-conservative forces like friction or resistance?

Do the non-conservative forces only withdraw from the kinetic energy part and not affect the potential energy in any way? Consider for an example a system of two charges having some mass kept at a finite distance and both are free to move over a rough surface and released.

## 1 Answer

Non-conservative forces change the total mechanical energy of the system, since $$W_\text{nc}=\Delta E=\Delta K+\Delta U$$ assuming all conservative forces are internal to the system.

However, nothing from this tells us how the kinetic and potential energies change. More information is needed. For example, with a mass sliding on a horizontal surface with friction, the non-conservative work only changes the kinetic energy as the mass slows down. However, if you set up the mass to slide down an incline with friction at a constant speed then only the potential energy is changing. In each case we have the same non-conservative force, but the changes in kinetic and potential energies are different.

Of course one could argue that in the incline case that the potential energy is being converted into kinetic energy that is instantly removed from the system by friction, but at that point it's just a difference in interpretation that yields the same result.

• should we use the potential energy work relation of internal conservative forces in such situations. – Shrish Srivastava Nov 21 '19 at 5:27
• @ShrishSrivastava Usually it's easier to work with potential energy than work done by the conservative force (which is why potential energy is even used at all), but since they are equivalent I will say take it on a case-by-case basis – BioPhysicist Nov 21 '19 at 7:59