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Homework Help: Rotational Dynamics Question

  1. Jan 31, 2007 #1
    1. The problem statement, all variables and given/known data

    Problem: A massless string is wrapped around a solid cylinder as shown in the diagram at the right. A block of mass m = 2.0 kg hangs from the string. When released, the block falls a distance of 82 cm in 2.0 s. Starting with a free-body diagram, calculate the mass of the cylinder.

    2. Relevant equations

    d = Vot + 0.5at^2
    Tension = ma - mg
    Torque = (I)(alpha) = F(r)

    3. The attempt at a solution

    Conceptually, I figure I need to find the force being exerted on the wheel, and the acceleration. That will leave nothing but the mass to be determined. But the fact that it's rotational, throws a wrench into it, especially since no radius is provided.

    using d = Vot + 0.5at^2 we get a = 0.41 m/s^2 for the block.
    Tension is therefore, 18.78 N in the opposite direction of the block's movement and is the force being exerted on the wheel (I think).

    Torque = 18.78(r) = 0.5Mr^2(a/r)

    If my approach is right, I need M, but r is in the way. What to do?
     
    Last edited: Jan 31, 2007
  2. jcsd
  3. Jan 31, 2007 #2
    Wait a minute... the radii all cancel... therefore M = 37.56/0.41 = 91.6 kg

    Did I figure it out, or did I just dig myself into a deeper hole? Help please!
     
  4. Jan 31, 2007 #3

    Pyrrhus

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    Homework Helper

    Could you give more information about the geometry?
     
  5. Jan 31, 2007 #4
    I don't really know where I could attach a photo of it, but it essentially looks like a string hanging off a pulley with a mass on the end.

    Any suggestions on how I can show it to you?
     
    Last edited: Jan 31, 2007
  6. Jan 31, 2007 #5

    Pyrrhus

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    Homework Helper

    When you make a new reply below "submit reply" look for a button called "Manage Attachments".
     
  7. Jan 31, 2007 #6
    Sweet thanks! Here it is:
     

    Attached Files:

  8. Jan 31, 2007 #7
  9. Feb 1, 2007 #8
    I'm new to this forum but just a general hint i post my pictures on photobucket.com and then just click the image button where i want it in the post and paste in the link ...
     
  10. Feb 1, 2007 #9
  11. Feb 1, 2007 #10
    Anything guys (or ladies)?

    The attachment's been approved. So does anyone have any ideas?
     
  12. Feb 1, 2007 #11

    Doc Al

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    Staff: Mentor

    Your solution looks good to me.
     
  13. Feb 1, 2007 #12
    Alright then! Thanks a lot!
     
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