Re: The Rise and Fall of Simple Machines.

[brian whatcott <inet@INTELLISYS.NET>]

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.
 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.

>                          Y A
>                      k= -----
>                           L
>                                                         2
>                             1      2    1         / dL \
>                      PE  = --- k dL  = --- Y A L | ---- |
>                        e    2           2         \  L /
> equating to dQ:
>
>                          = c m dT = c rho A L dT
>
>                                           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

Geometrically, this seems closer to a number advanced by Ludwik's
studious persona, yet arithmetically it is closer to the number given
by Leigh's professorial persona (which it must be noted, would be quite
opposed in spirit to this 'spoon-feeding' of the physics babies,
that I advocate.)

I am forced to say that this dialog has proven immensely helpful to me.
  I was reminded of the need voiced by a list member to cement concepts
though suitable questions may seem pedestrian.


With thanks

brian whatcott <inet@intellisys.net>
Altus OK