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Fundamental Theorem of Line Integration

  1. Mar 5, 2013 #1
    1. The problem statement, all variables and given/known data
    Suppose that F is the inverse square force field below, where c is a constant.
    F(r) = c*r/(|r|)^3
    r = x i + y j + z k
    (a) Find the work done by F in moving an object from a point P1 along a path to a point P2 in terms of the distances d1 and d2 from these points to the origin.


    2. Relevant equations



    3. The attempt at a solution

    Well this is a conservative force because it is dealing with gravity. So i know that the solution is going to be something like F(d2-d1). But how do i write that out? I think that |r| just equals d1 or d2 depending on which one is selected. But how do i get r?
     
  2. jcsd
  3. Mar 5, 2013 #2
    I also thought something like (c*P2)/(d2)^3-(c*P1)/(d1)^3..but thats not right, so i must be missing something
     
  4. Mar 5, 2013 #3

    Dick

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    Try and guess a potential function that gives you that vector field as a gradient. If you know something about gravity, you might already know the form of the potential function.
     
  5. Mar 5, 2013 #4
    So apparently I know nothing about gravity because i can't guess the potential function. I would think that all the vectors would point in towards the more massive object. (in this case towards the origin)
     
  6. Mar 5, 2013 #5

    Dick

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    Which direction they point depends on the sign of c. Try computing the gradient of 1/|r|. Does it look anything like your vector field?
     
  7. Mar 5, 2013 #6
    since r(t)=xi+yj+zk isn't lrl=sqrt(3). That isn't the gradient is it..because del f is like (fx,fy,fz,..etc) ...
     
  8. Mar 5, 2013 #7

    Dick

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    |r|=sqrt(x^2+y^2+z^2). How is that sqrt(3)?
     
  9. Mar 6, 2013 #8
    sorry i meant lr'(t)l
     
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