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Re: Simple explanations. Was: what are the labs for?



At 10:30 2/8/98 -0500, you wrote:
... Maybe some of you can enlighten me.
....
Stand on a lecture desk, holding one end of a Slinky (TM) spring. Wait
till the spring quits bouncing....
what will be the motion of the lower end.

a) The lower end rises as the upper end falls, the center of mass
falling, and when the spring fully closes the whole thing falls with
acceleration g.

b) The lower end remains at the same level, while the upper end falls.
When the spring fully closes it falls with acceleration g.

c) All parts of the spring fall, the spring closing as it falls. The upper
end falls faster than the lower end until the spring closes.

Now for the analysis. Why does the spring behave this way and not some
other way? Simple, yet correct, analysis, please. Would the same result be
seen with two balls on the end of a spring made of stretched rubber bands?
Would the rubber band demo behave the same if the two balls were of
different mass? What if just one ball is at the lower end of a string of
rubber bands? In this case the result is quite different than it was for
the Slinky. Even with the slinky, does the spring constant matter? Would
we get the same result with a limp spring as with a stiff one? Must the
particular spring constant, length, and mass of the slinky be exactly
right for the observed result?

And, if you think you've got this one licked, try an explanation of this:
A heavy rubber band is stretched horizontally between two nails on a
board. A cm or so beyond nail A a light object is placed. Stretch the
other end (B) of the band back, let it go. It it stopped by the nail B, of
course, but does the end of the band at the other nail (A):

a) Remain in contact with the nail until the band stops.

b) Move forward as the band contracts, knocking over the light object.

c) Move forward, knocking over the object, till the rear end contacts its
nail (B), then the band contracts.

....
-- Donald

I was hoping that someone would connect these interesting demonstrations
with the scaffolding which Maxwell erected ( and soon completely obliterated)
in connection with his celebrated system of EM equations.

Maxwell at least could use the concept of mechanical vibrations using
longitudinal waves as a metaphor for the transverse waves that he was
describing. He spoke of helices and whorls, if I remember...

Similarly, I find it helpful to consider Donald's systems as mechanical
transmission lines: this allows me to fall back on prior concepts like
mechanical characteristic impedence, and transmission rate at some fraction
of a characateristic speed - in this case the speed of sound.

I ponder on how mismatching of source and termination can vary the
displacement wave in both the mirror sense (for a low impedence
termination) and in the additive sense for a high impedance terminal.

Sincerely,
brian whatcott <inet@intellisys.net>
Altus OK