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

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SUMMARY

The discussion focuses on determining the minimum release angle, theta, for a pendulum with mass m and string length L to successfully swing over a peg positioned at height h = L/3 without the string going slack. Key principles include the Conservation of Energy, which states that the initial kinetic energy plus gravitational potential energy equals the final kinetic energy plus final potential energy. Additionally, the Conservation of Momentum is relevant due to the interaction with the peg. The tension in the string before and after the peg's collision is crucial for solving the problem.

PREREQUISITES
  • Understanding of Conservation of Energy principles
  • Familiarity with Conservation of Momentum equations
  • Knowledge of force diagrams and tension in strings
  • Basic trigonometry for angle calculations
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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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