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Bobbin on incline

  1. Jun 26, 2010 #1
    1. The problem statement, all variables and given/known data

    A bobbin of M = 3 kg consists of a central cylinder of radius r = 5 cm and two end plates of radius R = 6 cm. It is placed on a slotted incline on which it will roll but not slip, and a mass m = 4.5 kg is suspended from a cord wound around the bobbin. It is observed that the system is in static equilibrium. What is the angle of tilt θ of the incline?


    2. Relevant equations
    F=ma
    Torque is force times arm perpendicular to the force.

    3. The attempt at a solution
    I know the torque being exerted by mass m is the force (mg) times the distance r; t=mgr.
    This torque must be equal to the torque being exerted by the mass. How do I find that torque?
     

    Attached Files:

  2. jcsd
  3. Jun 26, 2010 #2
    How about a free body diagram of the bobbin, and your equations of static equilibrium?
    Include the reactions of the ramp on the bobbin.
     
  4. Jun 27, 2010 #3
    tvavanasd is right. U need to draw a free body diagram. And since it will roll on the incline u must take into account of the frictional forces.
    for translational equilibrium the required equation will be
    (M+m)gsinθ= µ(M+m)gcosθ.......(1)
    For rotational equilibrium the equation is
    mgr=µ(M+m)gRcosθ......(2)
    Divide equation 1 by 2 and u will get ur answer.
     
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