Definition of non-conservative force

Question

In defining conservative force, we say that

"The potential energy difference is path independent."

However, as far as I understand, potential energy only exists when there is a force field.

People say one example of non-conservative force.

By definition, non-conservative force should be the one in which the difference in potential energy is path dependent. But where is potential energy for friction which is not a force field?

Can you give a reference? Potential energy is something we can define for conservative forces, but you are right, if they are not conservative then there is no potential energy associated with them — BioPhysicist, Jul 15 '19 at 15:45
Hint: The correct definition refers to work, not potential energy. — Qmechanic, Jul 15 '19 at 15:50
Possible duplicate of What causes a force field to be "non-conservative?" — BioPhysicist, Jul 15 '19 at 15:57

score 1 · Answer 1 · answered Jul 15 '19 at 15:53

I think you mean to say a conservative force $\mathbf F$ is one where we can define a potential energy $U$ such that $$\mathbf F=-\nabla U$$

Then the work done by that force is independent of the path and only depends on the endpoints of the path. In other words, the work is given by: $$W=\int\mathbf F\cdot\text d\mathbf l=\int(-\nabla U)\cdot\text d\mathbf l=U_{\text{start}}-U_{\text{end}}$$ by the fundamental theorem of calculus.

On the other hand, we cannot express a non-conservative force in terms of a potential energy. Therefore, we cannot apply the fundamental theorem of calculus to the work integral, and therefore there is a path dependence on the work.

Thank you very much for edit my question (con - "with"). Thank you again. — Sebastiano, Jul 19 '19 at 08:08

Definition of non-conservative force

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