This experiment uses a pendulum to demonstrate the conservation of energy.
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A pendulum has potential energy due to the gravitational attraction of the earth. The equation for this potential energy (U) is
U = mgh
where m is the mass of the pendulum bob, g is the acceleration due to gravity, and h is the bob's height, measured from some arbitrary reference point.
If the pendulum is swinging, it also has kinetic energy. The equation for kinetic energy (T) is
T = (1/2)mv2
where v is the pendulum bob's velocity.
The total mechanical energy of the pendulum is E = T + U, or the sum of the potential energy and the kinetic energy. If the pendulum is left to swing freely (that is, without air resistance or friction, and without being pushed), then the total energy is conserved. It doesn't change. Potential energy can be converted to kinetic energy as the bob loses height and gains speed, or kinetic energy may be converted to potential energy as the bob swings higher and slows to a stop. Nonetheless, at every point in the pendulum's swing T + U is the same.
If the pendulum is raised to a height A and is then released from rest, at the instant of its release U = mgA and T = 0, so the total energy is
E = T + U = 0 + mgA = mgA
Since energy is conserved, T + U = mgA for the rest of the swing as well. This means that whenever the pendulum swings out and comes to rest again, it will do so at a height of A... no higher and no lower *.
* In a perfect situation, with no air resistance or friction on the pendulum's pivot point, this would happen. In real situations, the pendulum swings to a height lower than its starting height.
If the pendulum is again raised to a height of A, but is now given a slight push, Uagain equals mgA, but T is greater then zero. The pendulum will have enough total energy, not only to swing to a height of A, but to swing still higher. Each time the pendulum swings back again, it will come to a stop at a stop at a point higher than A.