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Race between different shapes

  1. Feb 19, 2013 #1
    1. The problem statement, all variables and given/known data
    Three uniform objects: a ring, a disk, and a sphere all have identical masses and radii. They are released simultaneously from the top of a ramp 3.80 meters in LENGTH. If the ramp is inclined at θ= 17.0°, use conservation of energy to calculate the linear speed of the ring, disk and sphere.


    2. Relevant equations
    Ei=Ef
    Iring = mr2
    Idisk = (mr2)/2
    Isphere = (2mr2)/5


    3. The attempt at a solution
    Ui + Ki = Uf + Kf
    mgh = (1/2)Iω2f + (1/)mv2f <--initial K and final U are zero

    then substituting I for Iring
    mgh = (1/2)((mr2)(vf)/(r)) + (mv2f)
    masses cancel, pulled out 1/2
    gh = (1/2)(rvf + v2f)

    But that's as far as I can get before I can't understand it.
     
  2. jcsd
  3. Feb 19, 2013 #2

    TSny

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    Homework Helper
    Gold Member

    Note that ωf is squared.
     
  4. Feb 20, 2013 #3
    I always end up asking questions on here because of stupid mistakes like that, haha. That made much more sense, with the radii canceling out. Thanks so much.
     
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