Nylon Springs
Introduction
After the second world war Dupont invented a great force Visualizer, this device showed the force it was exerting as a vector, with both magnitude and direction. The device is a nylon stocking.
Material
To Do and Notice
Hold one stocking by its top, notice how long it is.
Drop one global into the toe and notice how far it stretches.
Drop a second global in the toe and notice the additional stretch.
Note that the length of the stocking increases as the force it exerts increases.
Gravity pulls down on the balls with an invisible force. The stocking pulls upward equal and opposite to gravity, but you can see the stretch of the stocking.
Swing the nylon with one global in the toe in a horizontal circle. Notice the stretch of the stocking. To make the ball move in a circle a force is needed to pull the ball toward the center, the centripetal or "center pulling" force.
Swing the ball around more rapidly and notice that the stocking stretches to a longer length. A higher force is needed to hold the faster ball in its circular orbit.
Math Root
The centripetal force needed to hold a mass, m, in a circular orbit of radius, r, at a speed v is Fc = mv^{2}/r.
Etc.
In a circular orbit, the centripetal force is provided by gravity. The relationship between the kinetic energy and potential energy in a circular orbit is provided by the centripetal force. The kinetic energy is 1/2 of the potential energy and opposite in sign. If you remove total energy from an orbiting satellite, for example when it collides with the atmosphere, the satellite speeds up increasing its kinetic energy as it loses twice as much potential energy.
Scientific Explorations with Paul Doherty 

21 August 2003 