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Please verify my answer!

  1. Dec 4, 2007 #1
    1. The problem statement, all variables and given/known data
    Use W=Integral F.Tds
    To find workdone when a particle is moved along the helix x=cost, y=sint, z=2t from (1,0,0) to (1,0,4pi) against a force F(x,y,z)=-yi+xj+zk = -sinti+costj+2tk ( substituting above)

    2. Relevant equations



    3. The attempt at a solution

    Let rt = costi+sintj+2tk
    r't= -sinti+costj+2k

    Therefore W= Intergral(0tp4pi)[ <-sint,cost,2>.<-sint,cos t,2t>=Intergal[sin^2t+cos^2+2t] = [t+2t^2]from 0 to 4pi

    Giving the answer 4pi+32pi^2
     
    Last edited: Dec 4, 2007
  2. jcsd
  3. Dec 4, 2007 #2

    dynamicsolo

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  4. Dec 4, 2007 #3
    Please assist...I am lost
     
  5. Dec 4, 2007 #4

    dynamicsolo

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    You can't be all that lost: it looks like your work integral is set up correctly.

    The path that the particle travels on is a helix (an ascending circular spiral) starting at (1, 0, 0) and ending at (1, 0, 4·pi). The parametric equation for this path is given as x = cos t, y = sin t, z = 2t . You said you're starting the path integral at t = 0, which corresponds to x = cos 0 = 1 , y = sin 0 = 0 , z = 2·0 = 0 , which checks against the starting coordinates. So what value must t have for the ending coordinates? That is the value you would end your integration of the dot product (1 + 4t) at.
     
  6. Dec 4, 2007 #5
    I get the point, and I am now using 2pi as the ending coordinate. My next dump question is having (-1,0,4pi) not (1,0,4pi) when i apply 2pi to the parametric equations.
     
  7. Dec 4, 2007 #6

    dynamicsolo

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    cos(2·pi) = ?
     
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