Linear momentum conservation puzzle

Yes.

Energy is inputted at one end of the shaft. Energy is taken out from the other end of the shaft. So, there will be an energy gradient throughout the length of the shaft. This will cause the axial force to the shaft.

 

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It is possible that we have torque without a rigid frame to prevent the left and right sides rotating relative to each other. Not an important point though. IF the battery being charged wants to move to keep the centre of mass in the same place THEN (in the absence of a rigid frame) there will be some axial stress in the shaft joining the motor to the generator. Big IF because I'm still not sure what's going on here.

 

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There is no appreciable 'energy gradient' along and within the shaft. I discussed that sort of thing back in #55. Please read it again.

 

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Re the charging battery wanting to move. No, it simply accumulates mass/energy 'on the spot'. You might argue exact placement of feed-wires connecting the battery may induce forces (not the usual magnetic ones between leads), but that would entirely depend on some arbitrary particular placement if so. In short, the shaft is not being pressed on by batteries etc.

 

Torque is applied at one end of the shaft. Due to rigidity of the shaft, this torque will be transferred to the other end of the shaft. So there is some axial energy flow along the shaft.

 

There obviously is power transmission hence energy transfer via the shaft. The difficulty is in characterizing that as a flow of energy along the shaft. Whatever - if you think there is an answer there, you will need to show how exactly it results in an axial force, and provide a quantitative analysis justifying that supposition. Good luck.

 

As a marine engineer, this puzzle interests me. I do work with machinery and drive shafts and therefore not entirely unfamiliar with the basic calculations involved. Maybe I should start with what we can agree on, working from first principles, and see where that leads to?

The amount of Mass to be transferred between the batteries depends on the amount of charge in Volt-Amp-Hours, or Joules of Energy. The amount of Energy transferred in a given time period is Power. The Torque on the shaft is Power/ω in Nm. The Torque, together with polar moment of inertia J, and the shear modulus of elasticity G, will cause a torsional twist along the length L of the shaft of angle Θ. Θ=TL/GJ That in turn causes sheer stress and strain in the shaft, equal to RΘ/L where R is the radius of the shaft.

Summarizing the above, there is shear stress and strain on the shaft and is directly related to the energy being transferred from one battery to the other. That is about as far as I can get to answer your question because I don’t know how to calculate the axial component of the shear stress and strain and I definitely do not know how to check if that axial component acts in such a way to preserve linear momentum and com.

So, show me already!

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But, Q-reeus has generalized the question. He says it does not matter whether it is his original batteries-mg set up or flywheel brake system. I hope whenever he decides to enlighten all, it be a good solution, not some trivial negligible effect.

As far as I can tell you, when you apply a brake on the circumference of the shaft on the other side of the flywheel, there is a possibility of twist which could have a persistent axial force component, not impulse. This force may be absorbed by the brake/bearings.

 

He he. Maddening huh

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. Like I told Fednis48, you are getting slightly warm. In this case in bringing in shear stress. But still several crucial conceptual steps away from cracking it. It has dragged on. OK, throwing out a crucial bone that, given the earlier clues, surely a few here can run with at last to the finish line. Special relativity needs to be brought to bare. One needs to perform a Lorentz transformation. And at that, under a given condition. Let's see if anyone gets it at last.

 

See my response to OceanBreeze.

 

So my guess is right.

See, if the rigidity of the shaft is not enough; the shaft may twist because the torque being applied only on one end. If the shaft twists, there will be some relative radial movement of one shaft end. This implies a radial energy flow. But the rigidity of the shaft is stopping the twist of shaft. This means rigidity of the shaft is stopping the radial energy flow. So energy flow is axial only.

 

No material is perfectly rigid so the shaft twists. SeaBreeze gave calculations on that.

Huh?

A possibly correct conclusion from totally wrong premise. I have thrown out all the clues needed now. Especially since #89. Funny no-one here seems up to the final step. So many accusing me of being 'anti-science' elsewhere, yet when it comes to a modestly hard physics problem, none of my accusers make an effort here. Figures.

 

If the shaft twists, the surface area will be stretched towards the torque end. Its mass density will increase and the COM will shift.

 

Simply not true. Unless appreciable elastic non-linearity is brought in - and the starting assumption is linearity applies - no shift in shaft size or mass distribution occurs. Even with non-linearity, it will just mean an overall change in shaft length - but evenly distributed. Where do you get such an idea as above from?

 

Its amply clear that your bones thrown to not so hungry dogs are not working. So please let's see the full spread. No more fooling around. No one seems to be interested in your bones.

Mind you, your clear solution, should not invoke, I told you so. So it better be good.

 

Alright then.
The only possible connection I can think of with SR is the shaft becomes magnetized and is acting similar to a unipolar generator. Then it will also have DC polarity across it. Whether that will cause it to move according to the energy-mass that is transported across it, is another matter.
Before I waste a lot of time delving into unipolar generators and SR, at least let me know if I am on the right track.

But I agree with The God also, that this has dragged on long enough. Time to enlighten all of us dullards with your luminescent intelligence and esoteric knowledge.

 

You are, or you wouldn't post. The reason many others don't or have stopped is their inability to figure it out, and/or fear of that being exposed. At least you and a few others were up to trying. That's something.

What?

It will be. So you have completely given up trying then?

 

Sorry to say, no.

Nothing esoteric, I can assure you. Just keep hoping someone with a maths/physics background will step out of the shadows and give it an educated stab. Again.

 

I think you got yourself in a self dug ditch. The process of battery discharge to mg set to battery charge is continuous, and process of fly wheel brake system is also continuous. So I cannot understand your axial impulse trick. Whatever axial has to be some kind of continuous torture to the bearings.

 

Think that all you like. I know better, being the paradox presenter. It would be stupid indeed to go out on a limb bluffing.

The torture is in your mind. Once seen, the answer seems 'obvious'. And nothing or very little at best to do with any stabs at the answer so far.