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Circular motion - Which string breaks first?

  1. Mar 17, 2010 #1
    1. The problem statement, all variables and given/known data
    Basically, three different masses hanging on three strings of different lengths all different distances from the axis of rotation. They have a maximum tensile strength of 450 newtons. I have to solve in variable form first, and however... Well, okay. Just check the image below.

    http://i44.tinypic.com/ae4egk.jpg

    I just need to find an equation where I can vary the rotational speed and solve for the tension. Despite what I show in the image, for step two I really seem to need an equation where when given all the variables you can solve the function by changing "N" until you see it hits 450 newtons and the string breaks. The angle theta changes the radius which changes the velocity which then changes the acceleration and centripetal force so things just go bad really fast for me.


    2. Relevant equations
    v = (2piR/N)
    a = v^2/r
    F(c) = mv^2/r


    3. The attempt at a solution
    Well, based on the image I drew and posted... The corrected radius is the original radius plus the string length multiplied by the sin of theta. Using all that I wind up finding two functions from that picture that I think could apply for the tensions...... But I'm making a screwy mistake somewhere in one of these. (m*g*cos(theta) or just m*g the whole time?)

    T = mgcos(theta) + 4mpi^2(R+Lsin(theta)/N^2 = 450
    Or
    T = mg + 4mpi^2(R+Lsin(theta))/N^2 = 450

    If anyone can help me, that'd be great. I feel like such an idiot because this was on my last test. (Though my professor honestly didn't prepare us for questions like this. None of the homework or worksheets was nearly this hard... -_-)

    Oh! I accidentally labeled the opposite "H" in the diagram. I meant to say "O" for opposite. My bad...
     
    Last edited: Mar 17, 2010
  2. jcsd
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