# Pendulum and Peg

Demonstrates conservation of energy. The pendulum’s swing is obstructed at its equilibrium position by a peg but the ball continues to rise to its original height.

Equipment:

• Pendulum and peg set-up (ball, string, and backboard are included)

Demo:

Pull the ball up to different heights and release, note that the ball will always rise up to the same height on the opposite side.

Note that for initial heights that are above the peg, the problem gets more complicated. For more information on this particular problem, research “Interrupted Pendulum.”

Explanation:
The total energy of the system is conserved. Let us take the potential energy as U = 0 at the bottom of the ball’s trajectory.

1. Initially, the ball is released at a height h1 with potential energy U = mgh1 and kinetic energy K = 0. The total energy is E = K + U = mgh1.

2. At the bottom of its trajectory, the ball has K = ½mv2 and U = 0. The total energy remains unchanged: E = 0 + ½mv2 = mgh1. Some of the gravitational potential energy has been converted to kinetic energy.

3. At the peak of its trajectory on the other side, the ball will again have U = mgh1 and K = 0. The total energy is E = mgh1. The peg does not affect the final height of the ball for starting heights less than that of the peg.