# Conservation of Energy of an Interrupted Pendulum

The studio explores the conservation of energy using the Interrupted Pendulum apparatus shown in (Figure 1). A ball is attached to a horizontal cord of length L whose other end is fixed. A peg is located at a distance d directly below the fixed end of the cord. The ball is released from rest when the string is horizontal, as shown in the figure, and follows the dashed trajectory in a fashion similar to a pendulum until the peg interrupts it, which causes the ball to suddenly follow a tighter circular trajectory.

Image: http://session.masteringphysics.com/problemAsset/1000232220/3/peg.jpg

1) If d = 0.75L, find the speed of the ball when it reaches the top of the circular path about the peg, in terms of L and g.

2) What is the minimum distance d_min (expressed as a fraction of L) such that the ball will be able to make a complete circle around the peg after the string catches on the peg? (Hint: what speed does the ball need to have at the top of its arc if it is to just barely continue to move in a circle?)

3) Will the ball be able to make a complete circle about the peg if d = 0.5L?

Attempt at solving the equation:

I'm not sure where to start, but I thought about using d=V_0*sqrt(m/k). Any explanations would be great! Thanks!

Simon Bridge
Homework Helper
Have you tried starting with the conservation of energy?