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Hanging rope calc of variations

  1. Sep 27, 2008 #1
    1. The problem statement, all variables and given/known data
    My professor told me about this problem and I wanted to do it to practice for the test.

    A rope attached to two fixed points A and B will take the shape that minimizes the potential energy. Find the shape of the curve.


    2. Relevant equations
    mgy

    df/dy-d/dx(df/dy')=0


    3. The attempt at a solution
    The rope is an extended object and every point is at a different height. I started by considering the potential energy at one such point as dM*g*Y(x) where dM=row dx.

    I was going to intergrate with

    U=row*g[tex]\int y(x)*dx[/tex]
    then treat y(x) as my functional.

    Am I on the right path?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 27, 2008 #2
    never mind, I got it.
     
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