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Statics with an engine regulator

  1. Jul 2, 2011 #1
    1. The problem statement, all variables and given/known data
    [PLAIN]http://img15.imageshack.us/img15/7379/unledtzc.png [Broken]
    (The rods are of length L, there is no friction, massless rods, yadee yadee yada)
    At a certain angular speed [itex]\omega[/itex], the counterweight performs uniform circular motion. Show that [itex]\omega[/itex] and [itex]\theta[/itex] are related as follows:

    [itex]\omega^2 \cos{\theta} = (1 + \frac{2m'}{m}) \frac{g}{L}[/itex]
    2. Relevant equations
    [itex]T_1 = L m \omega^2[/itex]
    [itex]\cos{\theta} (T_1 - T_2) = g (m + m')[/itex]

    3. The attempt at a solution
    (Working backwards) Combined above to get
    [itex]T_2 \cos{\theta} = m' g[/itex]

    which makes a lot of sense, but i'm not sure if the procedure was right
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Jul 2, 2011 #2

    tiny-tim

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    welcome to pf!

    hi hurrfdurrf! welcome to pf! :wink:

    you need vertical equations for mass m and for mass m' (separately) …

    what do you get? :smile:
     
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