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Vector Fields

  1. Nov 23, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the work done by the force field F(x, y, z) = 3xi +3yj + 7k on a particle that moves along the helix r(t) = 4 cos(t)i + 4 sin(t)j + 4tk, 0 ≤ t ≤ 2π (As in the previous problem, recall that the work of the force F on the helix corresponds to the circulation of this vector field along the curve).


    2. Relevant equations



    3. The attempt at a solution

    F(x, y, z) = 3xi +3yj + 7k
    r(t) = 4 cos(t)i + 4 sin(t)j + 4tk , 0 ≤ t ≤ 2π
    r'(t) = -4sin(t)i + 4cos(t)j + 4

    [tex]\int[/tex]F(dot)dr
    [tex]\int[/tex](-48cos(t)sin(t) + 48cos(t)sin(t) + 28)dt
    [tex]\int[/tex] (28)dt

    With the integral going from 0 to 2pi I thought the answer would be 48pi, but it's not.
     
  2. jcsd
  3. Nov 23, 2008 #2
    Nevermind, I got it, it's 28*2pi
     
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