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Re: [Phys-l] Help! An explanation for the laity



On 12/05/2007 01:01 PM, Carl Mungan wrote:
What he means is why is a log used

Because it's the inverse of an exponential.
Why is an exponential used?
Because it's the special function whose value is equal to its slope everywhere.
Why is that useful?
Because the rate of change of quantity y is proportional to the amount y left.

That's all good and true.

One might take it one line farther:

Why do we think the drag force is proportional to
velocity (which in turn is proportional to amplitude)?

Note that for many things of interest, including cars
and airplanes and even pitched baseballs, the drag
force scales like velocity /squared/.

Answer: Clock pendulums have a rather smaller Reynolds
number, which means they are in the non-turbulent regime
(unlike the just-mentioned examples) and therefore a
drag force proportional to velocity is nicely consistent
with everything else we know, including Stokes's law:
http://en.wikipedia.org/wiki/Stokes'_law

Maybe the laity doesn't know about Reynolds numbers, but
they ought to be told (at least) that some things are
turbulent and some thing are not, and that life is very
different in the two cases.

====================

Reynolds numbers are an example of nondimensonal scaling,
and therefore provide yet another object lesson in why
dimensional analysis is not the answer to all the world's
problems.
http://www.av8n.com/physics/scaling.htm
http://www.av8n.com/physics/scaling.htm#sec-non-dimensional