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The work integral (general question)

  1. Apr 15, 2013 #1
    I'm sure you're all familar with this forumla for work, [itex]
    W=\int_{s_i}^{s_f} \mathrm{\vec{F}}\cdot\,\mathrm{d}\vec{s}

    [/itex]

    I don't understand how to evaluate this integral. How do you antidifferentiate in terms of a vector? How do you evaluate the dot product when ds isn't an actual value?

    Thanks! :)
     
  2. jcsd
  3. Apr 15, 2013 #2
    It's done with something called vector calculus, more specifically, line integrals.
    http://en.wikipedia.org/wiki/Line_integral#Vector_calculus

    Depending on whether it's a scalar or vector field, it is calculated slightly differently. Nevertheless, we will do a dot product inside the integral while manipulating the integral into something more familiar, so only parallel components will count.
     
  4. Apr 15, 2013 #3
    So would we do the dot product of F and delta-s? If so, that would give us a scalar value (or perhaps a function), and what would we integrate that in terms of?
     
  5. Apr 15, 2013 #4

    SteamKing

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    Remember that ds can be broken down into components dx and dy just like F can be broken down into components Fx and Fy (Fx and Fy do not represent partial derivatives here).
     
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