# Pendulum and Peg

A point mass on a mass-less string of length L is supported as a pendulum. A peg of negligible radius is placed a distance d directly below the support point. The mass is released from a horizontal position (theta = 90 degrees). Find the minimum value of d (in terms of L) such that the mass will make a complete circle around the peg.

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#### Solution Preview

We can use conservation of energy. We choose the potential energy level equal to zero at the lowest point of the point mass (or it can be chosen zero at the starting point, it does not make a difference). Since the mass is released there its initial velocity is zero (there is no mention of initial velocity, and the word "released" ...

#### Solution Summary

Using conservation of energy we calculate the minimum distance we can place a peg directly below the support point of a pendulum, so that the point mass at the end of the pendulum makes a complete circle around the peg.