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Re: [Phys-l] Sharing a problem for students

On Dec 21, 2007, at 3:37 PM, John Mallinckrodt wrote:

Oops! I dashed this off after reading Ludwik's first couple of
points, which made me think he was still laboring under the
misconception that his proposed system was stable. I see now that he
has performed the experiment and seen the expected result.

And this message, John, came as was ready to hit the reply button. Most of why I wrote is not necessary but let me paste it anyway.

Thanks John,
1) I am probably missing something. My message above, to which you are responding, did describe a simulation similar to what you are suggesting.

2) Let us go to a simple case of static stable equilibrium. I am thinking about an equal-arms balance. The center of mass of the suspended frame is below the point of suspension. The weight indicator is vertical when two weights are equal. Put an extra weight, dW, on one of the plates and the indicator shifts accordingly. Here many equilibrium positions are possible, one for each dW. In the ideal case this is an example of a "stable system." Suppose we begin with dW=0; this is one equilibrium position. We disturb the system, by adding a dW, and a new tilt of the indicator is established, perhaps after some oscillations. Here the term "stable" is used to say that the original orientation is recovered when the disturbance is removed.

I was not aware that the term "dynamic equilibrium," implies that the same is true for a planet orbiting the sun. That is why I removed it. In the first sentence of your reply (see above) you are saying that my electrical "system is highly unstable." The same is true for our solar system. Is this what you have in mind? If so then I agree. To avoid possible confusion I will start using the term "durable," instead of "stable" or "dynamically stable." But I suspect you have something different in mind. Perhaps you think that, unlike a solar system, my electric system will not be durable. If so then please explain. Keep in mind that my model ignores gravitational forces and emission of electromagnetic waves.






John

On Dec 21, 2007, at 12:29 PM, John Mallinckrodt wrote:

Ludwik,

It should be quite apparent that your system is highly unstable. But
because you have an IP simulation, it is completely trivial to do the
experiment and to gain considerable insight about the dynamics in the
process. Have you really not done it yet? (As a Mac user, I've been
abandoned by IP and sorely miss being able to use it.)

Simply perturb the initial conditions of your system in some
arbitrary and arbitrarily minute way: i.e. change any position or
velocity component from the perfectly symmetric situation you
describe to one that is ALMOST but not quite perfectly symmetric.
Then let it run. What you will see is that the negatively charged
central body will approach one or the other of the positively charged
bodies, reducing the net force on the OTHER positively charged body,
whereupon it will "escape" leaving the other two drifting off, bound
in a two body Kepler orbit.

John

On Dec 21, 2007, at 11:38 AM, Ludwik Kowalski wrote:

On Dec 21, 2007, at 11:37 AM, Bob Sciamanda wrote:

If you do a search (Google, Wikipedia, etc) you will find "dynamic
equilibrium" usefully defined
only for chemical and biological interactions. In Mechanics a
somewhat related set of useful concepts is stable vs unstable
equilibrium.

Note that in mechanics we say that an object at rest under the
action
of a set of forces which sum to zero is in a state of static
equilibrium. This same object could be said to be in a state of
dynamic equilibrium when viewed from a different frame, in which the
object is in motion. This distinction does not add much and
AFAICT is
not used.

Thanks Bob,
1) I changed the verbal description slightly at

http://pages.csam.montclair.edu/~kowalski/cf/339students.html

(see the ending of point 5).

2) Is there any reason to think that my electrical orbiting system
(three equal masses) will be less durable that a binary star or a
solar
system? Unfortunately, the Interactive Physics does not allow to
simulate in 3 dimensions.

3) Is my virtual displacements argument, and Figure 2, sufficiently
convincing that the initial plane of the orbit will not change (in
our
laboratory frame)?

4) Using the IP simulation, I did what I wanted to do yesterday, but
did not know how. The suggested idea was to create a short time
disturbance and to show that original trajectories of rotating
particles are not restored after the disturbed parameter is restored.
This should have been obvious but a simulation was worth creating.
The
disturbed parameter was the mass of one positive particle. It was
changed from 1.0 kg to 1.1 kg for the duration of 0.01 seconds.
What
do you think happened? Close your eyes, produce the answer and then
read the next paragraph.

The particle whose mass was disturbed started moving away from the
other two particles. These two particles started spiraling toward
each
other. They ended orbiting elliptically around each other (like a
binary star, I suppose). The trajectory of the third particle was
becoming a straight line. Naturally, I could have disturbed any other
parameter, for example, the speed of one particle, the location of
the
negative particle, etc. The term "dynamic equilibrium" was not
appropriate because it implied that the original trajectories
would be
restored (after restoring what was disturbed). The IP could be an
effective teaching tool.
_______________________________________________________
Ludwik Kowalski, a retired physicist
5 Horizon Road, apt. 2702, Fort Lee, NJ, 07024, USA
Also an amateur journalist at http://csam.montclair.edu/~kowalski/cf/

_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l

John Mallinckrodt
Acting Editor, American Journal of Physics
Professor of Physics, Cal Poly Pomona

_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l


_______________________________________________________
Ludwik Kowalski, a retired physicist
5 Horizon Road, apt. 2702, Fort Lee, NJ, 07024, USA
Also an amateur journalist at http://csam.montclair.edu/~kowalski/cf/