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Central Force Motion

  1. Jul 13, 2013 #1
    1. The problem statement, all variables and given/known data
    An object of mass M moves under the influence of an attractive central force F = - A r^4 \hat{r} where \hat{r} is a unit vector in the radial direction.
    If the object is in a circular orbit of radius R , find its speed v as a function of M,A, and,R.


    2. Relevant equations

    a=v^2/r

    3. The attempt at a solution

    I rearranged the above equation to v=sqrt(ar). I know that the radius is R but I dont know what the acceleration is. Help!
     
  2. jcsd
  3. Jul 13, 2013 #2

    rude man

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    What is the force necessary to keep a mass M in circular motion with radius R?

    Equate this force with the given force.
     
  4. Jul 13, 2013 #3
    I don't understand what you are saying.
     
  5. Jul 14, 2013 #4
    You need to think about the centripetal force.

    [itex]F=\frac{mv^2}{r}[/itex]

    That is the force needed to keep an object in circular motion. Equate this with your central force.
     
    Last edited: Jul 14, 2013
  6. Jul 14, 2013 #5

    D H

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    You also know the constant A, the radius R, and the mass M. So what's the acceleration?
     
  7. Jul 14, 2013 #6
    I still don't understand. Could you please give me a hint?
     
  8. Jul 14, 2013 #7

    D H

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    F=ma. Divide the force by the mass.
     
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