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Mass Pulley System, Acceleration

  1. Jun 12, 2015 #1
    1. The problem statement, all variables and given/known data
    A block of 1kg is resting on an incline of 20° that has a coefficient of friction μk=0.45 with the surface. It is connected with a mass less string to a friction-less pulley of mass 0.10 kg to a hanging block of 2 kg. What is the acceleration of the system without ignoring rotational inertia. Model the pulley as a disk.


    2. Relevant equations

    First we need newtons 2nd law, ΣF=ma
    Also for rotational motion ΣF=Iα
    and friction is ƒk=μN where N is the normal force.

    3. The attempt at a solution

    After drawing my free body diagrams, I was left with this :

    But I'm stumped there, I feel like I'm missing something obvious.

    I want to plug the two equations for the tensions into the pulley equation, but then I'm still missing the radius of the pulley.

    pDYs1xT.jpg



    EDIT: The -m2g in the last equation on the right should be m2a

    EDIT #2: I forgot the R on the (T2-T1)=IAlpha, I solved it. Thanks.
     
    Last edited: Jun 12, 2015
  2. jcsd
  3. Jun 13, 2015 #2

    Simon Bridge

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    Well done ... and good work doing all the algebra before subbing in the values.
     
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