Freefall Without Secured Rope
(the illustration of mechanics principles through a stunt)
A spectacular video entitled ``Freefall Without Secured Rope'' (Fritt fall uten sikret tau) is well worth watching:
In a carefully planned stunt to test the laws of physics, Norwegian physicist and television host Andreas Wahl is seen hanging 15 meters above the ground, attached by his harness to a rope which is allowed to slide over a horizontal, cantilevered pole. The other strand of the rope is attached horizontally to a secured hook, while supporting a counterweight of only a few kilograms. Upon release of the rope from its attachment point, Wahl is seen to drop while the counterweight winds around the horizontal pole. After a few turns, the rope quickly tightens around the pole, decelerating the drop and leading Wahl to a complete stop, safely above the ground. Watch the video to get a sense of the experiment and to appreciate the risks involved (no safety net can be seen).
We can identify at least three principles of mechanics at play in this “experiment”:
- conservation of angular momentum: as the rope winds around the horizontal mast, the small counterweight is seen to accelerate rotationally. The effect of the centrifugal inertial force becomes increasingly dominant over that of gravity.
- the friction force exerted on the rope around the support: the rope quickly stops slipping after a few turns thanks to exponentially increasing friction (Euler-Eytelwein equation).
- the elasticity of the rope: the stuntman is seen bouncing at the end of the drop, which is a good thing. Without an elastic rope, he would probably not survive the sudden stop.
This would be an excellent problem to model mathematically. As with most problems in mechanics, a solution will require a numerical model.