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Force and potential

  1. Dec 7, 2006 #1
    Just studying for an exam and the following question appeared on the sample exam:
    Given the force: [tex]F=-c(x-y)^2(\hat{i}-\hat{j})[/tex] where i and j are the unit vectors.
    a) Show the force is conservative
    b) Show the potential energy is given by [tex]V(x,y) = \frac{c}{3(x-y)^3)}[/tex] assuming V(0,0) =0.


    So for a) it is simple to show using the curl of F. but for b i am not sure how to get the potential energy function given the force. [tex]F=-\nabla V[/tex] will give the force easily if i have the potential function, but im not sure how to go the other direction. perhaps for the exam to show it i could just take the negative gradient, (which appears to be wrong for the potential given in this question) but i would like to just know how to go the other way for knowledge. thanks
     
    Last edited: Dec 7, 2006
  2. jcsd
  3. Dec 7, 2006 #2
    if a field is conservative, then the work done against the field on a object from point a to point b is conserved and equals to the change in potential. Well, basically, if you know the work done alone a path, you know the potential function.
     
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