Re: [Phys-L] Perpetual Motion Machine

[John Denker <jsd@av8n.com>]

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On 03/25/2015 04:42 AM, Peter Schoch wrote:
> https://www.youtube.com/watch?v=7KqOwJKWIAw
>
> and wants me to explain how this is NOT a perpetual motion machine.
>
> I think I can explain the chain one fairly well.  I'm having trouble with
> the liquid motion one, explaining it in terms of freshman physics.

Well, in terms of freshman physics, or high-school physics,
you can analyze the thing in terms of /energy/.  Going back 
to Day One of modern science, to the interrupted pendulum, 
more than a hundred years before there was a well developed 
concept of energy in general, Galileo knew that gravitational
energy is a /potential/ ... dependent on height, not on how
you got there.  This will get you the right answer.

Another lesson at all levels from third grade on up:
    *Draw the diagram.*

If it's an electrical circuit, draw the circuit diagram.
If it's a special relativity problem, draw the spacetime
diagram.  Et cetera.  This is standard advice:
  https://www.av8n.com/physics/problem-solving-checklist.htm#advice-diagram
It never ceases to amaze me how beginners try to solve
the problem in their head, in situations where world-class
experts would draw the diagram.

Here's the diagram for the wheel:
   https://www.av8n.com/physics/img48/overbalanced-wheel.png

When you draw the diagram, it's so obvious that the thing
is balanced (not overbalanced) that I had to go back and
re-watch the video to remind myself which way it was
supposed to turn.  Seriously, I had guessed wrong, and
I had labeled the points in reverse alphabetical order
the first time.  I had to go back and relabel them.

In lurid detail:  The energy going from (a) to (g) is
the same, mo matter whether you go CW (ahg) or CCW
(abcdefg).   So the full cycle from (a) back to (a)
is zero energy, no matter whether the cycle goes CW
or CCW.

As another way of saying the same thing:  The  inner
path (gha) is a semicircle, a nice symmetrical semicircle
CCW from 6:00 to 12:00.  The outer path (bcdef) is also a
semicircle, but it does not go from 12:00 to 6:00; it is 
more like 10:30 to 4:30.  You gain energy going from (b)
to (e) ... but you give it all back going from (e) to (f).

This is characteristic of all perpetual motion machines:
There is generally some little detail that is easy to 
overlook or misunderstand.  If you overlook it, you get 
perpetual motion.  If you include it, everything cancels 
out as it should.  (Often the guy who is trying to sell
you a perpetual motion machine will mis-describe one of
the details, making it easier to misunderstand.)

Now that we have analyzed it in terms of energy, we
can also analyze it in terms of force.  If you just
compare supposedly-corresponding points
  -- (a) versus (b)
  -- (c) versus (h)
  -- (d) versus (g)
then sure, there is a net torque in the CCW direction.

However (!) that leaves out point (e) and especially 
the critical points between (e) and (f).  There is a
backwards (CW) torque everywhere along the (ef)
segment.  If you overlook this, you get the wrong
answer.

Summary of key points:
  *) Draw the diagram already.
      https://www.av8n.com/physics/problem-solving-checklist.htm#advice-diagram
  *) Check the work.
      https://www.av8n.com/physics/problem-solving-checklist.htm#advice-show-checks
      https://www.av8n.com/physics/problem-solving-checklist.htm#sec-checking
  *) It is characteristic of perpetual motion machines
   that there is some little detail that is easy to
   overlook or misunderstand.  When analyzing an alleged 
   perpetual motion machine, very often it comes down to 
   a hunt for the wayward detail.

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