The studio explores the conservation of energy using the Interrupted Pendulum ap

Question

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.

Figure 1:

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

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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. 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. What is the minimum distance dmin (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?) Will the ball be able to make a complete circle about the peg if d = 0.5L? yes or no?

Explanation / Answer

A peg is located a distance h directly below the point of attachment of the cord. If h = 0.840 m, what will be the speed of the ball when it reaches the top of its circular path about the peg?
Yea!
Another conservation of energy problem

The potential energy of the ball is converted into Kinetic energy as it falls.
PE = mass * gravity * height
We will say h = 0 when the ball is at its lowest point
h = 1.24 at the beginning of this trip

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