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My students are building and racing mag-lev racers down a track that is at a 10 degree angle and then again at a 20 degree angle. We will then compare the actual acceleration to the theoretical acceleration. How should the relationship between the theoretical and actual acceleration change as the angle of incline increases? Will the ratio between them increase, decrease, or stay the same? More importantly why does the ratio change?
- J. Mack (age 49)
Las Vegas, NV, USA
There are several sources of friction that are nearly linear in velocity. These include air friction at very low speeds and electromagnetic eddy-current friction. Their effects should simply scale proportional to the ideal acceleration, leaving the ratio of actual to ideal friction unchanged. (I prefer the word "ideal" to "theoretical", since our theory obviously can take friction into account, as we are doing now.)
The most important friction, however, is air friction after the racer is going fairly fast. That goes approximately as the square of the speed. So it becomes proportionately more important at high speeds. I bet you find bigger fractional deviations from the ideal with the larger slope.
(published on 05/31/2011)
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