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# Re: Bar magnets

John (see below) confirmed Hugh's prediction. I did the same.
The prediction was implicit in Bob's and JohnD's messages
yesterday. Let me add more details (after the first six which

1) Spring constant k=30 N/m, spring natural length 1.4 meters.
2) Mass of the suspended sphere A was 0.5 kg, its charge was
+5*10^-5 C. In the absence of the second sphere B the initial
location of A was x=0, y=+1 meters.
3) The second sphere B was kept at a fixed position (x=0, y=-1m).
The mass of B was 0.5 kg, its charge was -5*10^-5 C.
4) Strong damping was imposed by setting air resistance at
"high" and by imposing 50 kg/m^2.
5) The electrostatic forces were turned on without turning off
gravity.
6) As soon as the RUN button is pressed the sphere A starts
moving toward the sphere B, performs several oscillations
and remains at rest at y=0.506 meters.

Hugh suggested (see below) that I start increasing the charge
on B till the critical separation distance, for my spring, is
reached. Here are the results:

7) I increased the Q on B to 6*10^-5 C and observed the
new stable equilibrium at y=0.322 m

8) Another increase of Q on B (to 7*10^-5 C) resulted in
slow elongation toward the equilibrium which was followed
by rapid precipitation of sphere A toward sphere B.

9) Sorry, Hugh, I forgot to reduce the damping.

John Mallinckrodt wrote:

Ludwik,

I have created an IP simulation that seems to show all the
behaviors you have described and put it on my IP web site at

<http://www.csupomona.edu/~ajm/myweb/index.ip.html>

As I would expect, weak springs show the instability more clearly
than stiff springs. When the free dipole is raised toward the
lower end of the hanging dipole, the spring stretches to a new
equilibrium position. If the separation becomes too small, the
equilibrium becomes unstable and the upper dipole moves rapidly
downward until it contacts the lower dipole. After that happens,
lowering the free dipole again stretches the spring even more and,
eventually, the upper dipole is pulled back up. A hysteresis loop
is created in a plot of spring stretch as a function of lower
dipole position.

Anyway, check it out if you like.

John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm

On Sun, 18 Feb 2001, Ludwik Kowalski wrote:

I replaced the attractive magnetic poles by electrified pith balls
(sphere A and sphere B) and performed an Interactive Physics
simulation (see the details below). The result is that the two
pith balls had no trouble of finding the equilibrium position;
they did not jump to each other suddenly, as my bar magnets
did.

Does it mean that Interactive Physics is not good for this kind
of simulation or that the experiment was not good enough to
prevent small sidewise and vertical oscillations?

Here are the details (there is nothing special about them)

1) Spring constant k=30 N/m, spring natural length 1.4 meters.
2) Mass of the suspended sphere A was 0.5 kg, its charge was
+5*10^-5 C. In the absence of the second sphere B the initial
location of A was x=0, y=+1 meters.
3) The second sphere B was kept at a fixed position (x=0, y=-1m).
The mass of B was 0.5 kg, its charge was -5*10^-5 C.
4) Strong damping was imposed by setting air resistance at
"high" and by imposing 50 kg/m^2.
5) The electrostatic forces were turned on without turning off
gravity.
6) As soon as the RUN button is pressed the sphere A starts
moving toward the sphere B, performs several oscillations
and remains at rest at y=0.506 meters.
Ludwik Kowalski

Try reducing the damping force and see if you can get the instability
to appear. You may also have inadvertently picked a region where the
interaction of the linear and inverse square forces are not unstable,
which, it seems to me, is where the absolute value of the slope of
the inverse square curve is less than the k of the spring. In that
range the change in electric force will be smaller for a given change
in distance than the change in spring force. When the distance gets
small enough, then the slope of the inverse square gets larger than
that of the spring force and a small change in distance will lead to
a smaller change in spring force than increase in electrostaic force,
and the instability should appear. If you increase the charge on the
two spheres (easier than changing the distances, in IP), you should
be able to create the situation where the slope of the inverse square
is greater than that of the spring force.

Hugh