[geocentrism] Re: Joshua's Long Day
- From: "Robert Bennett" <robert.bennett@xxxxxxx>
- To: "Geocentrism" <geocentrism@xxxxxxxxxxxxx>
- Date: Fri, 27 Apr 2007 22:28:48 -0400
An interesting problem.
Let the test magnet be small in mass and field and bar shaped, the source
magnet large in mass and mag field.
The force on the large magnet and the change in the total B field will then
be neglected.
The mass and initial speed at infinity are m and v0; there?s no initial
spin.
The impact parameter ip is the perpendicular distance from the near end of
the source magnet to the extended initial path of the test magnet.
When the test magnet is inserted into the main field, there will be a
torque on the test object because of the difference in the forces on its N
and S pole. So the object begins to spin, gaining rotational kinetic
energy. But the torque reverses every half spin, so only the original
torque causes a rotational acceleration.
The net force on the object with each spin is ~ zero, since half the time
it?s attracted to the nearest pole, and other times repelled. The path will
thus vary little from a straight line, its original direction.
If initially aimed at the source magnet, the test magnet will hit it. Else,
the path will miss the source by a distance ip.
When the test object leaves the source field, it will be moving and
spinning. The source has no recoil energy, from the assumptions made above.
We can invoke conservation of energy to say the energy entering the magnetic
field = the energy at exit.
½ m v02 = ½ mv2 + ½ Iw2, where v and w are the final linear and angular
speed, I the moment of inertia of a bar of length d.
Knowing any 2 of the 3 speeds will determine the third.
There?s no escape velocity, but we can ask what if the final speed is ~ 0
and the final energy is all spin energy. ?.
The spin speed is 2sqrt(3) v0/d and the speed at the tip of the bar is
sqrt(3) v0.
In this purely classical analysis if the initial speed of the bar magnet is
< c, the final rotational speed can be > c!
Robert
So I just got a problem that is so complex it needs a High priest of math.
In the sense that gravity causes acceleration because it is a constant, how
does one calculate the acceleration on a unit pole from a magnetic field
that is not constant universally???
No one on google knows.. But experiment shows that the force between
magnets increases rapidly with decreasing distance..
My experiment.. I want to shoot a magnet oriented for poles attracting very
close to but through and at right angles to a powerful magnetic field. If
it is too slow it will get captured.. How do I calculate the escape velocity
for a fly past.??? would there be one?
I mean, a mag field can accelerate a particle up to the speed of light.
I just bet this will cause pages of calculations???
Philip.
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