Any child who's played on a swing set can explain the physics of a pendulum. Children know how hard they have to push off to get going and how many times they need to drag their feet to stop. They have experienced that brief moment where they sat motionless in mid-air as the swing changed direction. A playground swing set is only one of many pendulums we encounter every day.
Definition
The American Heritage Science Dictionary defines a pendulum as a "mass hung from a fixed support so that it is able to swing freely under the influence of gravity." Another quality of a pendulum is that the mass of the string or rod on which the pendulum mass is suspended is typically negligible.
Potential Energy
A pendulum starts its motion when it is pulled back to some height, giving it potential energy. Potential energy, in the case of the pendulum, is defined as the pendulum mass times the acceleration of gravity times the height to which the pendulum mass is raised above its original position. Mathematically, it is written as PE = mgh.
Kinetic Energy
When a pendulum is released, the force of gravity works to convert the initial potential energy into kinetic energy. Kinetic energy is the energy of motion and is defined as one half the pendulum mass times the square of the velocity. Mathematically, it is written KE = 0.5mV^2
Equation of Motion
According to the principle of conservation of energy, the total amount of energy at any given point in the path of a pendulum is constant. This means as velocity, and therefore kinetic energy, increases, the potential energy must decrease. As the height, and therefore the potential energy increases, the kinetic energy must decrease. Mathematically, this is written as C = mgh + 0.5mV^2.
You can calculate the total energy in the system by determining it at a point where either the potential or kinetic energy equals zero. When the mass is at its lowest point, "h" equals zero, so the potential energy is zero, and total energy is equal to the kinetic energy. When the pendulum mass is at the top of its swing, "V" equals zero, so the kinetic energy is zero, and the total energy is equal to the potential energy.
Examples
A playground swing is an example of a simple pendulum, and a tether ball is an example of a conical pendulum. Wall clocks, cuckoo clocks and grandfather clocks all contain pendulums that are assisted by the internal clockworks to drive the hands of the clock. A metronome operates on similar principles. Finally, in the field of ballistics, a pendulum is used to determine the velocity of a bullet.
Tags: pendulum mass, kinetic energy, potential energy, equals zero, total energy