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Math Help - finding work by integrals

  1. #1
    s7b
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    finding work by integrals

    Find the work done by the force F from (0,0,0) to (1,1,1) over the following path:

    The path of the line segment from (0,0,0) to (1,1,0) followed by the line segment from (1,1,0) to (1,1,1) where the Force F=(1/(x^2+1))j


    How do I set up this integral??
    Please help me out if you know how!
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  2. #2
    MHF Contributor
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    Work done by variable force

    Hello s7b
    Quote Originally Posted by s7b View Post
    Find the work done by the force F from (0,0,0) to (1,1,1) over the following path:

    The path of the line segment from (0,0,0) to (1,1,0) followed by the line segment from (1,1,0) to (1,1,1) where the Force F=(1/(x^2+1))j


    How do I set up this integral??
    Please help me out if you know how!
    The first line segment is in the plane z=0; the force is in the direction of the y-axis, and it moves along the line y = x in the plane from (0,0) to (1,1). So as the point of application of the force moves from (x,y) to (x+\delta x,y+\delta y), \delta y = \delta x \Rightarrow work done = F\delta y = F\delta x.

    To find the work done, then, you'll need to evaluate \int_0^1F\,dx, where F = \frac{1}{x^2+1}

    The second part of the movement is parallel to the z-axis, and is therefore at right angles to the force. So it does a zero amount of work.

    Grandad
    Last edited by Grandad; March 23rd 2009 at 02:21 PM. Reason: Corrected solution
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