Question

Why do conservative forces need to be path independent?

Answer 1

Answer:

They don't need to be a path dependant but due to some properties, they are path-dependent.

Explanation:

Conservative forces are the kind of forces which give us the potential energy. And the potential energy is defined for the initial and final position. So potential energy equals the integration of force over its path. So if force were to be path-dependent then we'll get the same potential energy for the same initial and final position because there are different paths to reach from initial to the final position. That's why conservative forces are path independent, just to make the potential energy come outright.