How Do Non-Conservative Forces Affect Potential Energy?

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Homework Help Overview

The discussion revolves around the concept of non-conservative forces and their relationship with potential energy. Participants are exploring the implications of path dependence in the context of work done by these forces and questioning why potential energy is defined primarily for conservative forces.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to understand the definition of non-conservative forces and their characteristics, particularly focusing on path dependence and its implications for potential energy. Questions are raised about the equivalence of path dependence and undefined potential energy, with references to calculus concepts.

Discussion Status

The discussion is ongoing, with participants providing insights into the mathematical foundations of the topic. Some guidance has been offered regarding the relationship between force, work, and potential energy, though there is no explicit consensus on the explanations provided.

Contextual Notes

There are indications that some participants may have varying levels of familiarity with calculus, which could affect the depth of discussion regarding the mathematical proofs involved.

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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