Re: toroidal perpetual motion machine

[John Denker <jsd@MONMOUTH.COM>]

At 10:30 PM 6/28/00 -0700, Leigh Palmer wrote:
> What's the problem here? I sure don't see one. Has viscosity been
> suspended as a mechanism for dissipative work? I can see the tube
> oscillating if the system is underdamped, but surely the very
> small amplitude oscillations will die out due to viscous force.
> If viscous force is zero then I expect that, ideally, the system
> will oscillate freely forever.

The problem here is that a seemingly-reasonable analysis predicts not
oscillation, but steady force and steady velocity in the same
direction.  If anybody has an analysis that predicts oscillation, then
 a) it is a solution to the problem, and
 b) it must contain explain away the unbalanced forces in the original
analysis.  Your mission, should you decide to accept it, is to provide a
physical explanation of the revised force budget.

An unbalanced force has been identified;  a vague general expectation that
it must be balanced isn't a solution;  it is at best a restatement of the task.

If we can't balance the identified forces, we have a perpetual motion
machine of the first kind, i.e. it has an energy output with no energy
input.  It could drive a load if you attach a load.

Viscosity was explicitly considered (not suspended) in the statement of the
problem.  No finite amount of viscosity suffices to resolve the dilemma.

(In contrast, oscillation requires a force that changes sign each
half-cycle.  In an undamped oscillation, the force is out of phase with the
velocity, so there's no average energy flow.  For a damped oscillation, the
energy flow is in the obvious direction: dissipation of whatever energy
existed in the initial condition.)

==========================

Here is a kitchen experiment you can do.

1) Put some water in an ordinary bowl.  A white bowl is nice.  The 30-cm
"serving bowl" size is nice.

2) Sprinkle some fine-ground pepper on the water.  It will rest on/in the
surface layer, allowing you to visualize its motion.

3) Let things sit for a minute or two, so the initial eddies die out.

4) While you are waiting, take a bar of soap and rinse it under the tap, to
make sure its surface isn't dry and hard.

5) Touch one corner of the soap-bar to the water surface.  Observe what
happens.

=================

 *) Where does the force come from?
 *) Where does the energy come from, to give the pepper particles their
initial velocity, and to sustain their velocity against viscosity?
 *) What could this possibly have to do with the inner-tube perpetual
motion machine?