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Homework Help: Uniform Circular Motion of an object

  1. Nov 19, 2007 #1
    1. The problem statement, all variables and given/known data
    A horizontal force of 210N is exerted on a 2.0kg object as it rotates uniformly on a horizontal plane with a radius of 0.9m. Calculate the speed of the object.


    2. Relevant equations
    I THINK the relevant equations for this problem are v=2[tex]\Pi[/tex]r/T and ar=v^2/r.


    3. The attempt at a solution
    v=2[tex]\pi[/tex]0.9/???
    ar=???/0.9

    My biggest problem is that for the life of me, I can't figure out how to find either the T or the v. If I knew how to do that, I could figure out the problem. I've also drawn a diagram of the problem.
     
  2. jcsd
  3. Nov 19, 2007 #2
    You won't need to find T. Use your equation for "ar" as you suggest, but remember Newton's Second Law... F = ma. Since you know the Force, v can be calculated. No T needed, but if you are curious, T can be calculated now that you know v!!!
     
  4. Nov 19, 2007 #3

    PhanthomJay

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    All you need to know is that the radial acceleration (or centripetal acceleration ) is v^2/r, as you have noted. Then use newton's 2nd law in the radial (centripetal) direction to calculate v, the tangential speed .
     
  5. Nov 19, 2007 #4
    In this case, would my F=m(a) be 2.0(210)?

    I'm thinking I need to find "a" first... perhaps a=Fnet/m?
     
    Last edited: Nov 19, 2007
  6. Nov 19, 2007 #5
    No...F = 210, m = 2.0, a is given by the equation you have stated...v^2/r
     
  7. Nov 20, 2007 #6
    Hmmm...

    F=ma and a=v^2/r... F=m(v^2/r)

    v^2/r=F/m

    v^2=Fr/m

    v=sqrtFr/m

    v=sqrt 210(.9)/2.0

    v= 9.7 m/s^2
     
  8. Nov 20, 2007 #7
    Right!!
     
  9. Nov 20, 2007 #8
    thank you guys so much :D
     
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