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Math Help - Finding the Circulation of a force vector around a cone

  1. #1
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    Finding the Circulation of a force vector around a cone

    I'm tring to find the circulation of F=<x2-y, 4z, x2> around the curve, C which is the plane z = 2 intersects z = Sqrt(x2+y2)
    All help appreciated guys!
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  2. #2
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    Re: Finding the Circulation of a force vector around a cone

    Have you at least determined what the curve is?
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  3. #3
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    Re: Finding the Circulation of a force vector around a cone

    circ = \int [C] Fdr = \int [C] { (x−y)dx+4zdy+xdz }

    Simplify integral first if you can to reduce work

    \int [C] 4zdy = 8 \int [C] dy = 0 since C is closed

    \int [C] xdz = 0

    \int [C] xdx = 0

    \int [C] Fdr = \int [C] −ydx

    To find this set x=2cosθ, y=2sinθ, 0≤θ≤2π (ac/w from above)
    <br />
\int [C] −ydx = \int (−2sinθ)(−2sinθdθ), [θ=0,2π]

    = \int 4sinθdθ, [θ=0,2π] = \int 2(1−cos2θ)dθ, [θ=0,2π] = 4π

    Alternatively, \int [C] ydx =area within C by Greens Theorem = π2
    Last edited by TheIntegrator; April 27th 2012 at 09:01 AM.
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