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

AI Thread Summary
To determine the minimum angle theta for a pendulum with mass m and length L to swing over a peg at height h = L/3 without the string going slack, conservation of energy principles must be applied. The pendulum starts with potential energy, which converts to kinetic energy as it swings down, and then back to potential energy after passing the peg. The tension in the string plays a crucial role in maintaining the pendulum's motion, particularly after it passes the peg. The challenge lies in correctly manipulating the equations of energy and tension to find the relationship between the angle and the forces involved. Understanding these dynamics is essential for solving the problem effectively.
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Homework Statement



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


Homework 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=?


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..
 
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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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