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On Thu, 20 Sep 2001, Larry Woolf wrote:
Newton's balls
http://www.officeplayground.com/balanceballs.html
may be a nice demo of what John Denker stated:
Suppose I wrap one end of a long rope around a massive pulley, then I pull
upon the far end of the rope. In this way I can indirectly do work upon
the pulley. However, note that I am injecting mechanical energy into this
system on one end, and the energy appears at the other distant end.
Mechanical energy appears to move along the rope.
Is this really happening? Can "mechanical energy" flow? Well, imagine
that our rope is hundreds of feet long. If I suddenly pull upon one end,
that section of the rope pulls upon the next section, etc., and a wave of
motion moves visibly along the rope, finally causing the distant pulley to
turn. And if I suddenly stop pulling upon my end of the rope, a wave of
"stopping" will then propagate along the rope until finally the pulley
also stops moving. (note 1)
I conclude that the "mechanical energy" I inject into the system can flow
along a rope. If I investigate further, I find that the velocity of
propagation is the same as the speed of sound in that rope-medium. I
conclude that sound and "mechanical energy" are the same thing, and the
flow of "mechanical energy" through a solid material is the same as the
propagation of low frequency sound through that material.
Next I replace the rope with a long rod, and attach the rod to the rim of
the pulley. Now I can PUSH the far end of the rod as well as pull it, and
both motions can do work upon the pulley. Or, I can periodically push and
pull the rod, and the pulley wiggles. In each case, the velocity of
propagation of "mechanical energy" along the rod is the same: it is the
speed of sound. If I push and pull at a decreasing frequency, the
velocity of propagation remains the same. And finally, if I simply push
constantly, why shouldn't I imagine that "mechanical energy" is still
flowing along the rod at the speed of sound? Is there any reason that the
propagation velocity would be different for "DC" than for low-frequency
"AC?" I can't think of one.
I suspect that we are all befuddled by mechanical systems in constant
motion where the flow of mechanical energy is "seamless" and gives no hint
that it is flowing at all. Either that, or we use object of infinite
rigidity in our thought experiments, and this lets us miss the flowing
motion of mechanical energy because the propagation velocity becomes
infinitely fast. Better to perform work in pulses so the "mechanical
energy" can be seen to have a distinct location, and to propagate through
the system at a measurable velocity.
Isn't there a demo where a row of "collision carts" are connected by
springs, and when the cart on the end is pushed, a wave propagates along
the chain? This is a demonstration of sound in a solid. But also it's
not a demonstration at all, it's an device where low frequency sound
(i.e. mechanical energy) is propagating so slowly that its motion can be
directly perceived.
note 1
I'm ignoring the whole issue of wave-reflections by assuming that the
rope, pulley, and the driven load are matched in mechanical impedance.
My pulses of "mechanical energy" are absorbed by the load and do not
reflect.
((((((((((((((((((((( ( ( ( ( (O) ) ) ) ) )))))))))))))))))))))
William J. Beaty SCIENCE HOBBYIST website
billb@eskimo.com http://www.amasci.com
EE/programmer/sci-exhibits science projects, tesla, weird science
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