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Homework Help: Potential Function from a simple conservative force

  1. Feb 22, 2010 #1

    K29

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    1. The problem statement, all variables and given/known data
    Find the potential functions for these conservative forces:

    (1)F=xi+yj

    (2)F=yi+xj

    2. Relevant equations
    F=-[tex]\nabla[/tex]V (Force = -del (Pot.energy))


    3. The attempt at a solution

    So, I'm guessing to get V I just need to integrate F. For the first equation that gets me the right answer hurray!

    However I think my method is wrong(or my general understanding the opposite of partial derivatives). Doing the same thing to eqn 2 leaves me with a slight problem.
    -([tex]\int[/tex]y dx +[tex]\int[/tex]x dy)leaves me with -2xy+C. The correct answer should be -xy+C

    (I checked and it is indeed a conservative force)

    Please enlighten me
    Thanks in advance
     
  2. jcsd
  3. Feb 22, 2010 #2

    ehild

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    Homework Helper

    For a conservative force, the work between two points is independent on the connecting path. Start to integrate from point (0,0) to point P(X,Y).
    You can follow the line along the x axis from x=0 to x=X and then a straigth line parallel to the y axis from (X,0) to (X,Y). The work done is

    [tex]V(0,0)-V(X,Y)=\int_{(0,0)}^{(X,Y)}{ydx+xdy}=\int_{(0,0)}^{(0,X)}{ydx}+\int_{(X,0)}^{(X,Y)}{xdy}[/tex]

    As y=0 along the first line, and x=X along the second one, the first integral is 0, the second one is XY.

    ehild
     
  4. Feb 24, 2010 #3

    K29

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    solved. thanks
     
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