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Work/Line Integrals

  1. Nov 20, 2005 #1
    Why does work equal: [tex] W = \int^{P_{2}}_{P_{1}} F\cos\phi dl = \int_{P_{1}}^{P_{2}} F_{||} dl = \int^{P_{2}}_{P_{1}} F\bullet dl [/tex]?
    Thanks
     
  2. jcsd
  3. Nov 20, 2005 #2

    BobG

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    Are you asking how they got from the first equation to the last? That comes from the definition for a dot product:
    [tex]cos \phi = \frac{F \cdot dl}{F * dl}[/tex]
    If you substitute that for [tex]cos \phi[/tex] in the first, the problem simplifies to the last.
     
  4. Nov 20, 2005 #3
    Work is defined as the line integral over some path L of the scalar product of r and F. Now a scalar product of two vectors r and F is equal to
    [tex]\vec{r} \cdot \vec{F} = ||\vec{r}||*||\vec {F}||* cos( \theta)[/tex]


    The product of F with the cosine of the angle theta between r and F denotes the component of F parallel with vector r.


    marlon
     
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