Linear momentum conservation puzzle

The (say) left side does work and increases the energy on the right hand side. Left side gets lighter, right side gets heavier. Precisely how the work is done (eg by pure torsion) is a red herring.

 

Log in or Sign up to hide all adverts.

The common shaft as a red herring. I like that. The common shaft is a means for coincidence, not for continuity.

 

Log in or Sign up to hide all adverts.

It was made clear in #1 the concern is COM of the entire MGS (motor-generator set) system considered as a whole but otherwise isolated. Inclusive of the batteries used in specific scenario in #1. Of course if axial forces exist, no-one expects they will be uniformly distributed throughout all parts of the MGS. But momentum of the whole is unconcerned about exact location of (any) impulse.

It is, but at least you gave it a shot.

Originally, I planned for about a day before revealing the answer, but my how time flies. Giving it some more time, just to see if anyone can figure it out.

 

Log in or Sign up to hide all adverts.

According to the following sources, dynamotor and MGS (Motor-generator set) are not synonymous in design; only in overall function:
http://www.dictionary.com/browse/dynamotor
http://www.thefreedictionary.com/dynamotor
https://en.wikipedia.org/wiki/Motor–generator (3rd para).
All 3 there suggests no axial separation in dynamotor case. Link to MGS article in #1 was for a reason; to make clear there is a distinct axial separation between source and load along a common shaft.

Pretty much everything - going off on an irrelevant tangent as usual, Dan. Maybe go back to #1 and think about it carefully.

 

It would be clearer to have stated precisely "the centre of mass shifts", but that is the only interpretation of above that makes sense. Or you actually meant something else?

 

What does that even mean? You made a number of wildly inaccurate conjectures earlier on, and now this enigmatic statement.

 

Does the center of mass of a light bulb shift when you turn it on and energy starts radiating away in all directions? Same basic issue, with or without energy-mass equivalence. The mechanical equivalent of heat works the same way. A poorly designed center of mass problem that is no problem at all, really. Anyone can partition a system incorrectly and get odd results.

Thermodynamics is chock full of non-problems like those.

 

You think so, Dan? So state your position clearly: The net centre of mass shifts or not? Yes, or no? Give a clear explanation as to why your straight yes or no answer applies to the scenario in #1.

 

Why not partition the system along the lines of JUST the battery, so that center of mass actually does move? Measure the specific gravity of electrodes and electrolytes inside of the battery as it charges or discharges. No net movement of electrons occur, but ions actually move. They move quite a lot. If it is a lead acid battery, some of them end up as a heavy sludge at the bottom of the lead plates, and that definitely moves the center of mass (of just the battery), but moving electrons through wires results in no net movement or transport of the center of mass of the battery or the system at all, other than the energy losses that are radiated away due to friction, acoustic vibrations, or Ohmic heating of windings or wires from the system.

What detail(s) have I missed here?

 

You think so, Dan? Keep forgetting or ignoring or discounting that we are dealing with an isolated system? In an isolated system, fire a bullet from a gun fixed at one end, to a target at the other end, and the net shift in COM is exactly zero, Dan. And you think that moving battery sludge is somehow relevant? I don't.

OK to first bit there, but as to radiating.....already forgotten the added bit in #18?:

"Mass decreases at one location and increases by the same amount at another (as a gedanken experiment, ideally lossless energy conversion & transfer is assumed). Without a counteracting linear impulse, directed along the shaft axis, the centre of mass has shifted."

Wasn't really necessary to add that bit inside parentheses; it's expected to be understood irrelevancies like ohmic losses and friction are ignored. Unfortunately, even having added it, some folks will persist in side-tracking into such mundane matters. Sigh.

About everything actually relevant imo. Once again - will there be a net shift in COM of the isolated system? Yes or no? Try giving a detailed, coherent justification for either answer.

 

Only if the bullet eventually stops, Q-reeus. What if the gun (or artillery) is fired in empty space, and it continues to infinity (I know, it can't possibly)?

If your protestations are aimed at convincing me that center of mass is not a useful concept to begin with, you are preaching to a member of the choir.

Yet Einstein used COM arguments to derive E=mc^2 before an audience of Newtonian physicists who evidently thought the idea of COM was valid.

 

Let me think. Did I mention bullet was fired into a target? Why yes, I did! Should I have needed to add that said target stops said bullet? Wouldn't have reasonably thought so. But then what's reason got to do with the reason for our (unnecessarily) extended chat?

I was trying to make you disregard COM? Really??!! How awful of me! Just can't quite see where or how I managed to do that though.

Too right Dan! Let this one go. Please. Any further into the mental maze and there may be no way back out. On a positive note - always interesting to anticipate the novelty in a Dan response.

 

Thats pretty trivial (not the OP question), COM of an isolated system in absence of external force is either at rest or moves in straight line at constant speed.

 

If I make a small change in your mechanical system, say somewhat uneven shaft, then rotation would cause change of center of mass in cyclic manner. That would be independent of both batteries change.

If I take the basic thrust of your question on and around batteries, then we will have to get into MG set electrical circuit. The flux and electromagnetic forces in the air gap viz a viz rotor shaft torque, must either create a net force or help in maintaining the COM.

 

You mean say a bowing shaft giving an eccentric offset? So the whole thing vibrates? How could that change net COM? Not just on a time average but at any instant whatsoever?

You will need to both clarify and justify reason for imo delving into unnecessary peripheral issues.

 

No vibration, say a cut in shaft for key, this certainly would change the COM on rotation without causing vibrations.

The issue of forces in air gap, and electromagnetism, is not trivial here. The change in feeding battery current/voltage on strength loss would certainly cause change in forces in air gap. On the other hand charging saturation would, if cut off circuit is not in place, create its own complications.

There are too many open parameters, generally people are shooting in all directions, give some spoiler.

 

The Lagrangian dynamics of a spinning body acted on by a gravitational field yields both precession and nutation (not just vibration), both perturbations of COM. This would occur independent of any electric or magnetic field interaction(s).

Lots of worthwhile physics in this problem. Moment of inertia too.

 

Same difference. Creating an eccentric rotating mass. It will cause vibration of the whole but will not cause any change in COM of the whole isolated system. Fail.

All such matters are of no concern to issue of OP. Sorry you can't see that.

Yes, people are indeed shooting in all directions. Including you.
My only spoiler is to remind of that stated back in #1. Unless an axial impulse (more explicitly, an impulse profile) exists in the common shaft, the system experiences a net shift in COM - towards the charged-up battery. Or whatever other energy storage (or dissipation) arrangement that might have been chosen.
Same question to answer as always; is there such an axial impulse? If so, how exactly does it arise?

 

A simple mechanical equivalent of heat problem? Sure.

 

Some thought bubbles are worth the effort of bursting with a sharp pin. Not when they are aimless. But then who am I to judge others inner thought processes.