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Thin Rod

  1. May 10, 2009 #1
    1. The problem statement, all variables and given/known data
    A thin, uniform rod of mass M is supported by two vertical strings. Find the tension
    in the remaining string immediately after one of the strings is severed

    2. Relevant equations


    I = 1/3MR^2 (thin rod rotating at end)

    3. The attempt at a solution

    So I was thinking:
    Torque = Moment of Inertia * angular accel

    R*Mg = (1/3*MR^2)(acm/R)

    3g = acm

    then F = ma
    macm = Mg - T


    Unfortunately this gives me the incorrect answer (it is supposed to be 1/4Mg).

    Does anyone see where I am going wrong? It seems like this should be a rather straightforward problem.
     
  2. jcsd
  3. May 10, 2009 #2
    I'll assume that the strings are attached to the ends of the rod, although that wasn't stated.

    Where you went wrong is that [R=length of rod], so force of gravity acts at the center of mass, which is at the center of the rod, which means it has an arm of R/2. So your equation of [net torque = I*alpha] should be:

    (R/2)*Mg = (1/3*MR^2)(acm/(R/2))

    Then just do the rest of the steps accordingly, and you get (T = 1/4*Mg).
    Hope that helped.
     
  4. May 10, 2009 #3
    Itshould be (R/2)*Mg = (1/3*MR^2)(acm/(R/2))
     
  5. May 10, 2009 #4
    Oh yes... Thanks guys!
     
  6. May 10, 2009 #5
    That's what she said (last post, title).

    Sorry, couldn't resist. Back me up here, guys.
     
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