An Equation for Every Occasion by John M. Henshaw

Author:John M. Henshaw
Language: eng
Format: epub
Publisher: Johns Hopkins University Press
Published: 2014-08-14T16:00:00+00:00

29. Love Is a Roller Coaster

* * *

One Form of Faraday’s Law of Induction

The equation quantifies the electromotive force, emf, that is generated by the rate at which a magnetic field, ΦB, is changing with respect to time, t. The minus sign signifies, in accordance with Lenz’s law, that the induced electromotive force and the change in magnetic flux have opposite signs.

* * *

Folks sure are passionate about their roller coasters and other amusement park rides. They’ll stand in line for hours to ride them. Part of the thrill of these rides comes from the sensation of motion as you hurtle down the track through impossible twists, turns, and loops. But let’s be honest: part of the thrill comes from the danger involved. Amusement park rides have a pretty good safety record, but it’s not perfect, a fact that has to be in the back of your mind as they strap you in to that padded steel cage.

One thing that helps keep you safe on many of those rides is a braking system with no moving parts. The braking systems on almost all wheeled vehicles—cars, bicycles, and even airplanes (on the ground)—are based on friction. When you step on the brake pedal in your car, you cause a component that is rotating with the wheel to come into contact with other components that aren’t rotating. The resulting friction transforms the kinetic energy (the energy of motion) of the car into thermal energy (heat). And so you slow down.

Friction-based braking systems have been under development for hundreds of years, and they work pretty darn well. And they have plenty of applications on amusement park rides such as roller coasters. But because these rides travel on tracks, they are especially amenable to another braking system based on a completely different concept: that of magnetic induction. In amusement parks, magnetic induction braking is most commonly used on so-called “free-fall” rides. On such rides, the track structure contains built-in copper plates. The freely falling car or cabin contains (along with you and your friends) a set of powerful permanent magnets. As the passenger car falls, the magnets pass by very close to the copper plates. This induces a powerful force that opposes the motion of the car, and the car slows down.

This effect can be very easily demonstrated. (An early demonstration is attributed to the French physicist François Arago [1786–1853].) One way to do it is with a straight piece of copper tubing about a foot long, a solid cylindrical magnet that just fits inside the tube, and a cylindrical piece of steel the same size as the magnet. Hold the copper tube vertical, and drop the magnet into it. Repeat with the piece of steel. You should notice that the steel descends through the tube much more rapidly than the magnet.

The more powerful the magnet you use and the closer its diameter is to the inside diameter of the copper tube, the more convincing your demonstration will be. That is, the greater the braking effect will be on the magnet as it drops through the tube.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.