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Mechanics - Show Forces Are Conservative

  1. Nov 11, 2008 #1
    1. The problem statement, all variables and given/known data
    Show that the following forces are conservative:

    a) [tex]\vec{F}[/tex]=c([tex]\vec{\omega}[/tex]x([tex]\vec{\omega}[/tex]x[tex]\vec{r}[/tex]))
    b) [tex]\vec{F}[/tex]=d([tex]\vec{\omega}[/tex]x[tex]\vec{v}[/tex])

    where c and d are constants.

    2. Relevant equations
    There are probably more but I think helpful ones include:
    [tex]\vec{\nabla}[/tex]x[tex]\vec{F}[/tex]=0
    [tex]\vec{v}[/tex]dt=d[tex]\vec{r}[/tex]

    3. The attempt at a solution
    First I think equation a is just the Centrifugal force in the force equation for a rotating system and equation b is the Coriolis force. I could be wrong though.

    We were told for part a that we should just evaluate for the x-component and assume symmetry for the rest. I think for part a the curl should first be calculated.

    For part b I believe it would be helpful to show that the force along any path would be zero first. But I'm not sure how to go about this.

    Thank you for your time and help!
     
  2. jcsd
  3. May 24, 2009 #2
    Sorry, this is the wrong thread. Sorry bout that.
     
    Last edited: May 24, 2009
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