Here's a question that's been bothering me for a little while now. I'll try to phrase it as concisely as possible with limited knowledge of the specific terminology:

You may be familiar with the copper tube experiment wherein a magnet is dropped down the length of a copper pipe - it's velocity due to gravity is slowed as a result of magnetic eddies which form in the copper tube because of the electricity induced by the movement of the magnet through the copper pipe. These eddies in the pipe retart the movement of the magnet by opposing its magnetic field, potentially capturing the magnet altogether - levitating it within the tube. (please feel free to explain this better)

As a result of this, the momentum of the magnet is transferred to the copper tube- which doesn't move anywhere, given that it's affixed to the table.

This experiment is always performed on earth for obvious reasons.

However, if the copper tube was free floating in space and the forward momentum of the magnet was imparted by another method, such as a soleniod, as the magnet passes through the copper tube, how much of that force is transfered to the copper tube? does any of that force go into creating the magnetic eddies in the tube? (i.e. does the momentum of the magent generate the electricity?)

Here's the thing that bothers me (and PLEASE don't think i'm a free energy guy! I believe VERY much in conservation) - if work (magnetic friction or otherwise) is performed as a result of the magnet's passing through the tube, and the resulting force imparted to the system of 'magnet and copper tube' is less than the original force the magnet entered the system with, is there is a net loss of momentum? And, if NO WORK is done, yet electric energy is created as a result of the interaction, where does it come from?

I read something recently in a post about magnetic fields and their potential for work. does this come into play?

What i'm trying to work through is how energy is conserved in a senario like this. Can anyone break it down fully?

thanks!

Originally posted by unbill
potentially capturing the magnet altogether - levitating it within the tube.
This can't happen. As soon as the magnet stops moving, so do the eddy currents, and the opposing force on the magnet goes to zero.
how much of that force is transfered to the copper tube? does any of that force go into creating the magnetic eddies in the tube? (i.e. does the momentum of the magent generate the electricity?)
The copper tube will be pushed away by the moving magnet. At some point the velocity lost by the magnet will match the velocity gained by the tube, and the tube (with the magnet inside) will move away from the solenoid at a constant velocity. It's just a particular example of an inelastic collision.
if work (magnetic friction or otherwise) is performed as a result of the magnet's passing through the tube, and the resulting force imparted to the system of 'magnet and copper tube' is less than the original force the magnet entered the system with, is there is a net loss of momentum? And, if NO WORK is done, yet electric energy is created as a result of the interaction, where does it come from?
The energy that was initially the kinetic energy of the magnet is transferred partially to the tube. Momentum is conserved. Energy is conserved. Almost all of the incoming magnet's kinetic energy is split between the tube and the magnet; a little is lost to heat in the eddy currents in the tube by the tube's electrical resistance.
I read something recently in a post about magnetic fields and their potential for work. does this come into play?
A static magnetic field does no work; it acts at right angles to the velocity of a test charge, and thus is capable only of changing the direction of velocity, not the magnitude. A changing magnetic field creates a changing electric field, which can certainly do work.

- Warren

Thanks for replying Warren, I've enjoyed your replies to previous posts!

To refine my question in response to your reply..

This is what i expected from this system- heat generated by the eddies. When you track the process back, where does the energy come from that ends up as heat? Can it be traced back to the momentum of the magnet?

In other words F = F' - (a little bit of heat) ? When all is considered?

Originally posted by unbill
Thanks for replying Warren, I've enjoyed your replies to previous posts!
Anytime.
When you track the process back, where does the energy come from that ends up as heat? Can it be traced back to the momentum of the magnet?
Yep.
In other words F = F' - (a little bit of heat) ? When all is considered?
Well... the symbol F is usually reserved for force -- and forces are not conserved....... in normal language, a conservative force leads to conserved energy. The energy of the magnet-tube system is conserved.

I sense that maybe your difficulty is that you don't understand that friction is NOT a conservative force.

Let's take a pendulum. When you let the mass go, gravity does work on it, trading potential for kinetic energy. At the bottom of its swing, the work due to gravity goes to zero. As it swings back up, gravity begins to do work again, slowing the mass down, trading kinetic for potential energy. Gravity is a conserative force, because there is a definite potential energy. In the absence of friction, the pendulum will swing forever, having the same energy all the time.

Let's take another system -- sliding a book across a table. If you slide a book across a table, the table does work on the book by slowing it down. There is no way to get the table to do any more work on the book and get it going again -- because the kinetic energy of the book is turned into heat, not into some potential. Friction is NOT a fundamental force, however -- it's a sum of millions of microscopic electromagnetic interactions. The four fundamental forces ARE conservative.

- Warren

I guess another question would be, what is the relationship of electrical resistance to friction? And to exted that further, normally we think of friction in terms of kinetic energy (often resulting in heat) and electrical resistance in terms of electromagnetic phenomenon (also resulting in heat), the copper tube experiment, flywheels, etc, mix these together to either retard movement or store energy.

In these systems energy is concerved byt the momentum is not- if only as a result of the heat generated via friction/electric resistance. True? Am I missing something?

BTW- thanks in advance for your patience with me on this : )

Let me try to set a scenario that can be measured:

If you have a copper tube (or tube of material capable of having magnetic eddies induced) of Mass=2 moving in a certain direction at a constant speed of K and a magnet (that can fit inside the barrel of the copper tube!) of Mass=1 moving in the opposite direction at the same constant speed of K. For argument's sake, let assume that all of the magnet's kinetic energy is transfered to the system, either through magnetic influences or by some other means of capture (like piece of tape! - which we can ignore for the moment)

Is the resulting velocity of the system (the tube and the magnet) 1/2 of the copper tubes starting velocity and direction, or is it slightly less than 1/2 because some of the kinetic energy of the two elements was 'lost' to magnetic friction?

Also, while some heat is generated in the copper tube's magnetic eddies, are there any similar physical results in the magnet? So that they both dump kinetic energy as heat at the same ratio, thereby cancelling out any net effect.

I know I'm missing a logical step somewhere.

Originally posted by unbill
Is the resulting velocity of the system (the tube and the magnet) 1/2 of the copper tubes starting velocity and direction, or is it slightly less than 1/2 because some of the kinetic energy of the two elements was 'lost' to magnetic friction?
I don't know exactly why you'd expect it to be anything near 1/2 of the tube's initial velocity.

The problem here is that we're dealing with an inelastic collision, but we don't know yet exactly how strong the magnetic friction force will be. It depends heavily on the strength and shape of the magnet, the thickness of the copper walls, the spacing, and many other factors. If you require that I derive an expression for a simple case, I will -- but my textbooks are all at home and it's a very difficult problem I can't do off the top of my head.

Assuming you find out (experimentally, or via the very difficult calculation) how strong the friction force is, you can calculate everything else just as a simple inelastic collision problem, with a given loss of kinetic energy. Here's a good page on the physics of inelastic collisions:

http://hyperphysics.phy-astr.gsu.edu/hbase/col1d.html#c1
Also, while some heat is generated in the copper tube's magnetic eddies, are there any similar physical results in the magnet? So that they both dump kinetic energy as heat at the same ratio, thereby cancelling out any net effect.
If the magnet induces currents in the tube, then those currents induce magnetic fields that induce currents in the magnet. Both would heat up. I don't know in what sense two things heating up can be called a "cancellation," though.

- Warren

thanks for the link, i'll take a look at it.

expecting 1/2 of the initial velocity, was for the sake of argument, given that you could alter wall thickness, and similar factors to achieve that result and simplify the premise.

http://hyperphysics.phy-astr.gsu.edu/hbase/inecol.html#c1

GREAT RESOURCE - muchas gracias.

Originally posted by unbill
http://hyperphysics.phy-astr.gsu.edu/hbase/inecol.html#c1

GREAT RESOURCE - muchas gracias.
It's nothing you'll have trouble finding in a basic university physics text...

- Warren

What happens with the magnet in the tube is that the changing magnetic flux through the sides of the tube due to the magnet's motion induces an electric current in the copper. That current in turn produces an opposing magnetic field, which interacts with the magnet to slow it down.

In terms of energy conservation, kinetic energy of the magnet is turned into electrical potential energy of the electrons making up the current in the tube. When the electrons flow, energy is lost as heat through resistive dissipation. The net effect is that kinetic energy of the magnet is turned into heat.

Originally posted by James R
What happens with the magnet in the tube is that the changing magnetic flux through the sides of the tube due to the magnet's motion induces an electric current in the copper. That current in turn produces an opposing magnetic field, which interacts with the magnet to slow it down.

In terms of energy conservation, kinetic energy of the magnet is turned into electrical potential energy of the electrons making up the current in the tube. When the electrons flow, energy is lost as heat through resistive dissipation. The net effect is that kinetic energy of the magnet is turned into heat.
Umm.. yeah, James, thanks. Perhaps you should read the replies in the thread before posting your own.

- Warren

chroot:

I did read the previous replies. I didn't think things were particularly clear. There was talk about momentum being transferred to the "tube", and "magnetic eddies". I wanted to make it clear that we are talking about electron motion here.

For the tube floating in space, I <i>suspect</i> that the system (both magnet and tube) will begin to rotate about the tube axis, but I'm not sure about that.

why would they rotate about the axis of the tube? a result of the induced currents?

Yep. If the electrons flow one way, conservation of momentum suggests the tube and/or the magnet must rotate the other way.

if the copper tube was actually a stretch of pvc wrapped in copper wire, the path of the electrons would be in one direction - so i can see that, but how regular are magnetic eddies? i pictured them as somewhat random, appearing on the copper tube like spots rather than rings circling the tube.

Maxwell's equations dictate that the electrons must flow around the tube (probably in a helical trajectory).

ah. that is familiar, it happens with some satellites.

so would that effect even be considered as induced 'magnetic eddies' - or do the magnetic eddies feed into the helical movement of elecrtrons?

also, if the tube were constructed of long strips of copper separated by long strips of insulators, eliminating the possibility of the helical movement about the tube, would that localize the magnetic eddies and eliminate the rotation?

<i>so would that effect even be considered as induced 'magnetic eddies' - or do the magnetic eddies feed into the helical movement of elecrtrons?</i>

I don't know what a "magnetic eddy" is. I've been talking about eddy <b>currents</b> made of electrons, which create magnetic fields.

<i>also, if the tube were constructed of long strips of copper separated by long strips of insulators, eliminating the possibility of the helical movement about the tube, would that localize the magnetic eddies and eliminate the rotation?</i>

Yes. It would effectively stop the eddy currents and the magnet passing through the tube would no longer be slowed.