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Find the work done by the force field F on particle moving along path

  1. Dec 9, 2012 #1
    1. The problem statement, all variables and given/known data
    Find the work done by the force field F on particle moving along path

    F(x,y) = -xi + 6yj, <I>C</I>: y = x^3 from (0,0) to (6,216)

    3. The attempt at a solution
    Drew the graph in the xy plane (y = x^3 is upper limit, x = 0 is lower limit)
    W = F ° r'(t) dt
    Vector field is not conservative
    I want to find r'(t) but am confused as to how, just not sure where to go from here. I have a habit of over thinking problems and am probably doing so. Any assistance is greatly appreciated.
     
  2. jcsd
  3. Dec 9, 2012 #2

    pasmith

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    If you're given a path of the form [itex]y = f(x)[/itex], then you can always parametrize it as [itex](x(t),y(t)) = (t, f(t))[/itex].
     
  4. Dec 9, 2012 #3
    in that case, would I just evaluate the line integral?
    ∫ f(x(t),y(t))||r'||
     
  5. Dec 9, 2012 #4
    r(t) = _ i + _ j, _ <= t <= _

    r(t) = (t)i + (t^3)j, 0 <= t <= 6
    r'(t) = <1, 3t^2)

    am I on the right track?
     
  6. Dec 9, 2012 #5

    pasmith

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    You need to calculate
    [tex]\int_0^6 \mathbf{F}(\mathbf{r}(t)) \cdot \mathbf{r}'(t)\,\mathrm{d}t[/tex]

    Yes.
     
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