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Re: The Rise and Fall of Simple Machines.

At 17:17 11/23/99 -0800, Leigh wrote:

SOCRATIC DIALOG

You make me do the calculation myself (symbols
are the usual suspects):

Suspects can be the usual suspects to the constable
of long standing, but I fear there are no usual suspects
for the rookie.

True, but that was not part of the dialog. The present
sophisticated company will have assumed the same suspects
you did, I'm sure.

I could wish not only that numeric examples of
mind experiments be couched in successive prime numbers the
better to trace them, but that letters will no more adorn an
equation without an adjacent glossary, such as this:

"for Y = Young's modulus, the pressure for unit strain.
A = area
L = length
dL = extension
k = spring rate in force per extension
c = specific heat capacity in energy per (mass x change in temp)
m = mass
rho is mass per volume"

Even this begs the question of a compatible set of units for the
various quantities. I noticed earlier in this dialog, the juxtaposition
of the symbol m in its sense of mass with m in the sense of displacement
unit. This is poisonous to the understanding of novel relations, it
seems to me.

Still it is hard to impugn the present conversationalists, when every
physics text adopts just the same mode - a glossary given once in back,
whose symbols may or may not be relevant to a particular equation of
interest.

Since I was doing a quick & dirty (and, it turns out, incorrect)
calculation I didn't need to bother with that which I require of
my students.

2
Y / dL \
dT = ------- | ---- |
c rho \ L /

Using data from Hecht (handy) I get dT = 0.5 degrees C, much
more in line with my expectations. (Someone check my work.)...

Leigh

dT = 2E11/(500 7800) (0.01)^2 = 5K

Thanks, Brian. I guess I should have used a calculator. I like to
think that isn't necessary. This result is greater than I expected,
but 1% is a huge strain. It corresponds to a tensile stress of two
gigapascals (in pressure units), far beyond the tensile strength of
steel (0.4 GPa in Hecht). 0.2 % strain seems to be about as far as
you can go, which would bring the temperature rise down to 0.2
degrees C. It is clear that a steel-spring windup car will never
compete with battery electrics as a low emission vehicle.

Leigh