Nonconservative Force: Understanding Force of Friction

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Discussion Overview

The discussion revolves around the nature of the force of friction, particularly its classification as a nonconservative force and the implications of this classification on the application of curl in vector fields. Participants explore theoretical aspects, mathematical reasoning, and conceptual clarifications regarding friction as a vector field.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants express confusion about why the curl of a constant frictional force is not equal to zero, suggesting that this indicates the nonconservative nature of the force.
  • Others argue that friction opposes motion and that in conservative fields, forces can assist or oppose motion, leading to zero net work in a round trip.
  • One participant seeks to demonstrate the nonzero curl of the frictional force theoretically, as it is nonconservative.
  • Another participant claims that the frictional force is not a vector field, stating that curl cannot be applied to it.
  • Some participants propose that friction can be considered a vector field, noting that it varies in direction along a closed trajectory, which could validate its nonconservative nature.
  • One participant argues that the frictional force does not depend solely on location but also on velocity and other forces, complicating its classification as a vector field.
  • Another participant presents a counterpoint regarding circular friction, asserting that the work done is non-zero for a closed path, supporting the idea that friction is a vector field based on their calculations.
  • Some participants acknowledge the complexity of calculating curl in paths with abrupt changes, such as corners in a square trajectory.
  • One participant suggests that the underlying mechanism for friction might be better described as a tensor field rather than a simple vector field.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the frictional force can be classified as a vector field or on the implications of applying curl to it. Multiple competing views remain regarding the nature of friction and its mathematical treatment.

Contextual Notes

Participants highlight limitations in defining the frictional force, noting its dependence on various factors like velocity and external forces, which complicates its classification and the application of mathematical operations like curl.

Andres Latorre
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I not understand because why if I have a (constant) force of friction and I apply the curl, I finding that this not is equal to zero, since this force is non conservative.
 
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Andres Latorre said:
I not understand because why if I have a (constant) force of friction and I apply the curl, I finding that this not is equal to zero, since this force is non conservative.
Because friction will always "oppose" the motion. In conservative field, the force both assists and opposes the motion when you make a round trip, thus net work done is 0.
 
I understand that, but I want to know how to show this using the curl. Theoretically I should get the curl of the frictional force is nonzero because it not is conservative.
 
The frictional force is not a vector field. You cannot take the curl of it.
 
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Thank you Dale. You could say that the friction force is a vector field, since it is not defined in the entire space ?. For example, in the case of a closed square trajectory, by analyzing the frictional force is being defined with different direction in each of the faces of the square, that force is not the same throughout the path could validates be another reason?
 
Andres Latorre said:
Thank you Dale. You could say that the friction force is a vector field, since it is not defined in the entire space ?. For example, in the case of a closed square trajectory, by analyzing the frictional force is being defined with different direction in each of the faces of the square, that force is not the same throughout the path could validates be another reason?
So a vector field is a field which evaluates to a single vector at each point in space. You can certainly restrict the space to cover a smaller region, that is not the problem with frictional force.

The problem with friction the frictional force is that even within a restricted space there is not a mapping between the location and the force. The frictional force does not depend just on location, but also on things like velocity and the presence of other forces. So the frictional force is not a vector field.
 
I am not in complete agreement. I considered circular friction force a path as shown in the picture.
The friction force is clearly not conservative, then it is expected that their work is non-zero for the closed path, which is actually true as shown in the calculation. I think that it is a vector field because below I calculate the curl of force and is nonzero. I suspect that in the square path is not possible to calculate the curl because it is a path with tips because the frictional force changes abruptly at the corners.

https://drive.google.com/folderview?id=0BxhsA5VJDGFubkxIcnZObDI2LVE&usp=sharing
 
I guess you could say that the underlying mechanism for friction can be described as a vector field (or rather a tensor field).
 

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