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Pendulum of length l with mass m at end swings over a peg

  1. Mar 30, 2009 #1
    1. The problem statement, all variables and given/known data

    A pendulum is formed from a small ball of mass m on a string of length L. As the figure shows, a peg is height h \,=\:L/3 above the pendulum's lowest point.

    From what minimum angle theta must the pendulum be released in order for the ball to go over the top of the peg without the string going slack?

    Figure similar to this one on this site: http://www.ece.umd.edu/gradhandbook/physics1.gif [Broken]


    2. Relevant equations

    Conservation of Energy: Ki+Ugi=Kf+Ugf
    Conservation of Momentum(because of peg and sting collision?):
    m1v1f+m2v2f = m1v1i+ m2v2i
    Force diagrams with tension: Lcos(theta)=Tension before peg
    Tension after=?


    3. The attempt at a solution
    I'm am confused on how it all fits together as a system. I know it begins with potential energy and gains kinetic while swinging around the peg, and then potential again. I also know that the angle is going to correspond with the tension in the rope after swinging around the peg. I am unsure how to manipulate the equations, however..
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Mar 30, 2009 #2
    Re: Pendulum

    One way to go about this is to find the kinetic energy of the bob right before it hits the peg and use that energy to analyze the new L/3 system.
     
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