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Billiard ball rotating and slipping

  1. Nov 24, 2009 #1
    . The problem statement, all variables and given/known data
    A ball radius "a" and mass "m" initially spinning counterclockwise with angular speed w=-v0/a with a forward speed vo. The coefficient kinetic friction between the ball and the billiard table is Mu, [Given a,m,vo,mu]
    Determine the work lost to friction while slipping using two methods (they should be equal)
    W=-Ffs where s the distance ball slips not travels
    W= delta Kt + delta Kr


    2. Relevant equations
    F=ma
    Torque= I*alpha
    W=v/r
    V=vo+at
    W=Wo+alpha*t



    3. The attempt at a solution

    I found a from equation F= ma where F=-Ff
    Then plug in a to eq V=Vo+at

    I also found alpha from eq Torque= I alpha
    then plug in alpha to eq W=Wo+ alpha t

    set V=RW i got T where the slipping becomes rolling without slipping.

    The questions are
    1. Can i use this t and plug it in to eq X=Xo+Vot+0.5at^2 to find The distance the ball SLIPS??
    2. If i cant use that equation, then How can i find the distance the ball slips?
    3. In finding W= delta Kt + delta Kr, Do I have to use final angular and forward speed that i found from previous calculation or Do i have to find them?

    Thank you for your help.
     
  2. jcsd
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