Exploring the Relationship Between Non Conservative Forces and Potential Energy

In summary, Non-conservative forces, such as friction, have a path dependence, meaning that the work done depends on the path taken. This is due to the absence of potential energy for these forces. This equivalence is proved in calculus through the study of multivariate calculus and path integrals. This may not be easily understandable without prior knowledge of these subjects.
  • #1
andyrk
658
5
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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  • #2
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.
 
  • #3
How is path dependence equivalent to undefined potential energy?
 
  • #4
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.
 
  • #5
Is the calculus part you are talking about made for the high school level ?
 
  • #6
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.
 

Related to Exploring the Relationship Between Non Conservative Forces and Potential Energy

1. What are non-conservative forces?

Non-conservative forces are forces that do work on an object that is dependent on the path taken. Examples of non-conservative forces include friction, air resistance, and tension in a string.

2. How do non-conservative forces affect an object's motion?

Non-conservative forces can cause an object to slow down or change direction due to the work they do on the object. This work can be positive or negative, depending on the direction of the force and the displacement of the object.

3. Can non-conservative forces do positive work?

Yes, non-conservative forces can do positive work. For example, a person sliding down a slide experiences positive work from the force of friction between their body and the slide.

4. How do non-conservative forces affect an object's mechanical energy?

Non-conservative forces can cause a change in an object's mechanical energy by doing work on the object. This change can result in a decrease in kinetic energy or an increase in potential energy.

5. Can non-conservative forces be conservative?

No, non-conservative forces cannot be conservative. Conservative forces are those that do not depend on the path taken and can be completely described by a potential energy function. Non-conservative forces, on the other hand, depend on the path and cannot be described by a potential energy function.

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