How Do Non-Conservative Forces Affect Potential Energy?

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Non-conservative forces, such as friction, have work done that depends on the path taken, unlike conservative forces where work is path-independent. This path dependence indicates that potential energy cannot be defined for non-conservative force fields. The relationship between path dependence and undefined potential energy is established through calculus, particularly in multivariate calculus and path integrals. While some aspects of this equivalence are straightforward, others require more complex mathematical proofs. Understanding these concepts is essential for grasping the fundamental differences between conservative and non-conservative forces.
andyrk
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Can you tell me more about Non Conservative Forces? In non conservative forces like friction work done is dependent on the path that we take to reach one position to the other position but how? And why does potential energy have a meaning only for conservative force field and not non-conservative force field?
 
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Path dependence is pretty much a definition of a non-conservative force. And path dependence is equivalent with absence of potential energy for the force. The equivalence is rigorously proved in calculus.
 
How is path dependence equivalent to undefined potential energy?
 
andyrk said:
How is path dependence equivalent to undefined potential energy?

Like I said: this is studied in calculus. If you have studied multivariate calculus and path integrals, you should know. If you have not, I won't be able to explain that in a post on a forum. Sorry.
 
Is the calculus part you are talking about made for the high school level ?
 
One part of the equivalence is rather trivial, though. If force F has potential energy U(x), then the work of force between x = a and x = b is U(a) - U(b), which is independent of the path.

The proof of the other part is more involved.
 

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