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Masses Over a Uniform Cylindrical Pulley

  1. Oct 28, 2016 #1
    ηϖ1. The problem statement, all variables and given/known data
    EmvCBrU.jpg

    2. Relevant equations
    I=½MR2
    PE=mgh

    3. The attempt at a solution

    The first thing that jumped out at me was "uniform cylinder" so I went ahead and calculated the moment of inertia for the cylinder and got I=½(4.4)(.4)2 = .352 and held onto that.

    Then, I calculated the forces due to gravity of each mass that is pulling down on the string.
    Fmb = 48kg×9.8m/s2 = 470.4N
    I'm not sure if I do the same for ma because it's resting on the table, so is there a force pulling on the string creating tension?

    But the next thing I did was find the gravitational potential energy of mb:
    PE = mgh = 48kg×9.8m/s2×2.5m = 1176 J.

    I'm not sure if torque is needed, but I went ahead and calculated it anyways:

    T=F×r = 470.4N×.4m = 188.16

    And that is all I can think to do. I'm not sure how the radius, inertia, mass, and other properties of the pulley affect the masses A and B that move up and down via the string over that pulley.

    Could I take the 1176 J of potential energy and set it equal to ½mv2? But what mass would I use? Mass of the system (A + B)? Solve for V? That seems too simple for this section, because we are learning about angular kinematics, torque...etc. I think I'm missing something.

    Thank you for your time and advice!
     
  2. jcsd
  3. Oct 28, 2016 #2

    BvU

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    Science Advisor
    Homework Helper
    Gold Member

    Hi there,

    The hint in the exercise is pretty clear: use energy considerations. So list off all the energies (my clue: there's more than you mentioned so far, but you are thinking in the right direction) at t=0 at at t = bump.

    Extra tip: does the ##\bf I## you calculated have any influence ? (Imagine a huge R0 to decide)
     
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