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Work done by General Variable force

  1. Mar 10, 2012 #1
    1. The problem statement, all variables and given/known data

    The force on a particle is directed along an x-axis and is given by F = F0(x/x0 - 1).

    Find the work done by the force in moving the particle from x = 0 to x = 2x0
    2. Relevant equations



    3. The attempt at a solution

    It looks like the force is a recurrence relation or something...

    [itex]W = \int^{2x_{0}}_{0} F_{0}(x/x_{0}-1) dx[/itex]

    I don't really understand.. unless I just take x0 to be the lower limit of integration, 0, and then 2x0 is just also 0, leaving me integrating from 0 to 0... which is just 0, but that seems to render this an absurdly stupid question.
     
    Last edited: Mar 10, 2012
  2. jcsd
  3. Mar 10, 2012 #2

    ehild

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    F0 and x0 are undetermined constant.

    ehild
     
  4. Mar 10, 2012 #3
    So x0 is could not be described as lower limit of integration? I see it as integrating from original x position to two times original x position, which in this case is 0 to 0, which means the integral is 0?

    How do you view it?
     
  5. Mar 10, 2012 #4

    ehild

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    X0 is just a number and the upper limit of integration is 2X0, the lover limit is zero.

    Yes, the integral is 0. The antiderivative is F0(x2/(2x0)-x), which returns 0 between the limits.

    ehild
     
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