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Homework Help: Atwood's machine with a cylinder

  1. Mar 22, 2010 #1
    1. The problem statement, all variables and given/known data
    a massless string of negligible thickness is wrapped around a uniform cylinder of mass m and raidus r. the string passes up over a massless pulley and is tied to a block of mass m at its other end.
    the system is released from rest. what are the accelerations of the block and the cylinder? assume that the string does not slip with respect to the cylinder.
    Use conservation of energy (after applying a quick F=ma argument to show that the two objects move downward with the same acceleration)


    2. Relevant equations
    F=ma
    K=[tex]\frac{1}{2}[/tex]mv2+[tex]\frac{1}{2}[/tex]Iw2
    P=mgd
    where w=angular frequency
    and I=[tex]\frac{1}{2}[/tex]mr2 is the moment of inertia.

    3. The attempt at a solution
    I wrote an F=ma equation for each mass, and because they are the same mass should undergo the same acceleration
    I wasn't sure if that was as in depth as the question required.

    Then i wrote a conservation of energy equation for the system
    mgd + mgd = [tex]\frac{1}{2}[/tex]mv2 + [tex]\frac{1}{2}[/tex]mv2 + [tex]\frac{1}{2}[/tex]Iw2

    and solved for velocity, where i used the kinematics equation
    v2=2ad
    to solve for the acceleration, which i found to be
    [tex]\frac{4}{5}[/tex]g

    the problem is i really have no idea if i'm right, or if there was an error in my reasoning.
    any feed back would be appreciated.
    Thanks.
     
  2. jcsd
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