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Rotational motion on pulley system

  1. Apr 17, 2013 #1
    1. The problem statement, all variables and given/known data
    A string passing over a pulley has a 3.80-kg mass hanging from one end and a 3.15-kg mass hanging from the other end. The pulley is a uniform solid cylinder of radius 4.0 cm and mass 0.80 kg. If the bearings of they pulley were frictionless, what would be the acceleration of the two masses?


    2. Relevant equations
    I=0.5mr2
    a=rα
    Ʃτ=Iα
    τ=Fr
    T1-mAg=mAa
    mBg-T2=mBa

    3. The attempt at a solution
    I tried rearranging the bottom two equations into the form:
    a=(T1-mAg)/mA
    a=(mBg-T2)/mB

    I then plugged variables into the following equation:
    Ʃτ=0.5mr2α
    (T2-T1)r=0.5mr2α
    (T2-T1)r=0.5mr2(a/r)

    This equation then simplifies to:
    a=(2T2-2T1)/m

    This is where I'm stuck. How do I proceed from here? Thanks.
     
  2. jcsd
  3. Apr 18, 2013 #2

    ehild

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    Homework Helper
    Gold Member

    Isolate T1 from 1 and T2 from 2 and substitute them into the last equation.

    ehild
     
  4. Apr 18, 2013 #3
    Okay, I can do that but then how do I solve for T1 and T2?
     
  5. Apr 18, 2013 #4

    ehild

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    Homework Helper
    Gold Member

    Substitute the numerical value for a in equations 1) and 2).

    ehild
     
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