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Re: Weird question...



On Sat, 24 Aug 1996, Delissa Souder wrote:

If 2 people are 2 light years apart. Person 1 wants to signal Person 2.
Person 1 has a laser and a rigid stick that is just a few inches short of
2 light years in length (almost touching Person 2). At the exact same
time, the laser is shown at Person 2 and the rigid pole is pushed into
Person 2. Which will reach Person 2 first?

Assume the pole is rigid and there is no sideway flexing.

Easy answer: mechanical energy travels as low frequency sound waves.
Therefor, when you push on a long rod, the force propagates at the speed
of sound (in steel? wood? neutronium? Depends on the composition of your
rod.) The light will reach Person 2 first. The mechanical energy will
arrive many years later.

I had an 'Aha!' experience in school years ago. I was wondering what
Mechanical energy really is, and suffered an extreme paradigm shift.
Mechanical energy is an entity which appears on the acoustic spectrum! At
high frequencies we call it "sound", (usually "sound in solids") At low
frequencies we call it "work," "joules," etc. In the same way that light,
radio, and electrical energy are simply various frequencies on the EM
spectrum, "work" and "sound" are various frequencies on the acoustic
spectrum. I went around accosting roommates and babbling that "work is
sound!"

A similar viewpoint: if the wavelength of the Mechanical energy is much
longer than the size of the object, (small objects, slow changes,) we call
it "work". If the wavelength is shorter than the object (large objects,
sudden changes,) we call it "sound." We think in these terms because in
the regime of low-frequency mechanical energy, the ENTIRE OBJECT moves as
a unit. Grab a ball and lift it, and we perceive it as behaving as an
object and not like a medium through which waves are propagating. But
grab and lift one end of a stretched rope, or a huge block of jello, and
the wave-nature of mechanical energy becomes obvious. Yet the wave nature
is always there whether the object is a book or is a 2ft cube of jello.

Whenever we grab and move an object, we act only on the part in contact
with our hand. This part of the object acts on deeper parts, the deeper
parts act on yet deeper parts, etc. An object can never really move as a
unit, if it did then the "wave of initiation of motion" would travel
instantaneously. This wave instead travels at the speed of sound in that
material. All solid objects are like jello, when we grab and lift them we
send waves of force and motion propagating through them, although usually
these waves die out in a small fraction of a second. An average behavior,
"moving as a unit," quickly comes to dominate the observed behavior.

I don't own Physics Simulation software, and I've always wanted to build
some "real" objects and then watch them interact. To do this, take four,
nine, etc. point masses and connect them into a square array with springs.
Build two of these "crystal" objects. Then throw the one at the other.
Not only will you see the expected collision mechanics, but you should
also see all the fascinating wave-propagation effects which we tend to
ignore in our manipulation of objects in the real world.

How many springs and point masses can various software packages tolerate?
Would it be possible to build numerous square 16-mass array-objects and
then perform experiments such as 3-body linear collisions, "Newton's
Cradle", etc. What will you see when Obj5 hits the row of Objs 1-4 below?
Obj 1 should fly off the end, but what will you see DURING the collision?
A simulation like this should answer the perennial student question, "What
REALLY happens when one penny crashes into the end of a row of pennies?"

O--O--O O--O--O O--O--O O--O--O O--O--O
| | | | | | | | | | | | | | |
O--O--O O--O--O O--O--O O--O--O <-- O--O--O
| | | | | | | | | | | | | | |
O--O--O O--O--O O--O--O O--O--O O--O--O
Obj 1 Obj 2 Obj 3 Obj 4 Obj 5

......................uuuu / oo \ uuuu........,.............................
William Beaty voice:206-781-3320 bbs:206-789-0775 cserv:71241,3623
EE/Programmer/Science exhibit designer http://www.eskimo.com/~billb/
Seattle, WA 98117 billb@eskimo.com SCIENCE HOBBYIST web page