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Shogin that F=-grad(U) in a centrally cymmetric force field

  1. Oct 17, 2011 #1

    Uku

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    1. The problem statement, all variables and given/known data

    I need to show that
    [itex]\vec{F}=(\vec{r}-\vec{r_{0}})f(\left\|\vec{r}-\vec{r_{0}}\right\|)[/itex]
    in a centrally symmetric force field.

    where [itex]\vec{r_{0}}[/itex] is the force field center and [itex]f[/itex] some sort of function.

    2. Relevant equations

    Newt. II

    [itex]m\vec{\ddot{r}}=\vec{F}[/itex] and perhaps that in a central force field
    [itex]\vec{U(\vec{r})}=\vec{U(r)}[/itex]

    3. The attempt at a solution
    I can write:

    [itex]m\vec{\ddot{r}}=(\vec{r}-\vec{r_{0}})f(\left\|\vec{r}-\vec{r_{0}}\right\|)[/itex]

    Is this the right approach?
     
  2. jcsd
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