Nonconservative Force

  • #1
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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  • #2
cnh1995
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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.
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.
 
  • #3
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.
 
  • #4
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The frictional force is not a vector field. You cannot take the curl of it.
 
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  • #5
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?
 
  • #6
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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?
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.
 
  • #7
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
 
  • #9
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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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