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Difficult energy conservation/rotational energy problem

  1. Apr 21, 2016 #1
    1. The problem statement, all variables and given/known data
    In the figure below, the hanging object has a mass of m1 = 0.405 kg; the sliding block has a mass of m2 = 0.825 kg; and the pulley is a hollow cylinder with a mass of M = 0.350 kg, an inner radius of R1 = 0.020 0 m, and an outer radius of R2 = 0.030 0 m. Assume the mass of the spokes is negligible. The coefficient of kinetic friction between the block and the horizontal surface isμk = 0.250. The pulley turns without friction on its axle. The light cord does not stretch and does not slip on the pulley. The block has a velocity of vi = 0.820 m/s toward the pulley when it passes a reference point on the table.
    10-p-049.gif

    2. Relevant equations
    KE = 1/2Iw^2
    KE = 1/2mv^2
    PE = mgh
    Non-conservative work = (delta)KE + (delta)PE

    3. The attempt at a solution
    The left side has negative work because of friction. On the right side, I put the KE of each as well as the potential energy (ONLY on m1, I believe?)

    I think my only problem is the moment of inertia for the two pulleys. I don't understand how to implement the two radii. The answer shows that there is a combination of both. I have no idea why. Parallel axis theorem maybe?
     
  2. jcsd
  3. Apr 21, 2016 #2

    Orodruin

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    There is only one pulley. It has a hollow cylinder with inner radius ##R_1## and outer radius ##R_2##. You need to compute its moment of inertia ##I##.

    You also have not stated the actual problem, i.e., what you are asked to find, only the setup.
     
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