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Newton's third law problem.

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electrodacus:

--- Quote from: Nominal Animal on November 22, 2022, 06:42:56 am ---
This is not a "locked gearbox", because the geared wheel can move horizontally.

The racks and chain are not necessary for correct operation, they just provide lots of friction.  The same works even with thread and smooth wheels, as long as you have sufficient friction that nothing slips.

--- End quote ---

It is a locked gear and I already did the experiment see video https://odysee.com/@dacustemp:8/gear-slow30p2:9
And here is the slow motion and zoomed bit unfortunately is upside down but around second 9 you can see the energy stored is released https://odysee.com/@dacustemp:8/120fps24:9

Nominal Animal:
No, electrodacus.  You're letting your preconceptions override your search for the facts.

This is the complete model of the situation:


Let t be the surface velocity of the treadmill, positive right.
Let c be the velocity of the center of the gears, positive left.
Let R be the radius of the treadmill gear (blueish), and r the ground gear (pale yellow-orange).
Finally, let φ be the angular velocity of the gears.

For the ground gear to not slip, we need φ=c/r.
For the treadmill gear to not slip, we need φ=(c+t)/R.

Combining the two rules, we have an equation that holds whenever the gears do not slip: c/r=(c+t)/R.  Solving this for c yields c=t*r/(R-r).

The only impossible situation is when the two gears are the exact same size.  This is the locked-up gearbox case, where non-slip motion is not possible.

In the case where r<R, c will be positive, and the center of the gears will move in the opposite direction compared to the surface of the treadmill.

Circlotron observed the situation when R<r, about R≃0.867r.  Then, c=t*(-7.5).  Because c is negative, it travels in the same direction the surface of the treadmill travels (or equivalently the wire is pulled).  Because the magnitude of the ratio is so large, the forces are such that you need spool to have excellent traction (stiction, static friction) to ground: a heavy soldering wire spool is an excellent test case.
Then, when you pull the wire towards yourself, the spool will also rotate towards yourself but much faster.  When you pull the wire 20mm, the spool will travel 20mm×7.5 ≃ 150mm, just as Circlotron described.  (I wonder if circlotron agrees that the diameter of amount of solder in their spool was about 0.867 of the outer diameter of the spool?  In any case, if you happen to have a heavy spool yourself, you can easily check the math here.)

Although I called t and c and φ velocities, the math stands exactly the same if you consider them displacements instead.  That is, when the treadmill surface moves right by t (left if negative), the angle of the axis of the gears changes by φ, and the spool/axis of the gears moves left by c (right if negative).

There is no energy storage needed.  You can start from a standstill, move the treadmill surface by a fixed amount, and measure how far the spool/axis of the gears moved.  If the spool/gears were heavy enough with enough friction/traction/stiction, so that there was no slippage, the above formulae will hold.

There is no strangeness related to energy conservation either.  If you do the heavy almost-full spool test, you'll find that it is quite hard to pull the wire.  In other words, it is the treadmill that provides all the energy here, at every instant in time.  It will all be spent in the friction/traction/stiction, if you do the test from standstill to standstill.  All pure mechanics, no slapstick, no aether, no fancy theories.  Plain ol' classical mechanics here.

Sizes and ratios do matter in practice, though.  For example, if your heavy spool is 99% full (meaning, the diameter or radius of the wire in it is 99% of the diameter or radius of its outer edges), the ratio is 1/(0.99-1) = -100.  This means that every millimeter you manage to pull the wire, the spool will travel 100 mm.  It is unlikely that there is enough friction to see this happen; instead, the spool will slip.  So, to see the phenomena better, use a spool with somewhat less wire.

I so wish BigClive would try this.  He's got good cameras, nice bench setup, and suitable spools at the top of his shelves.  Or maybe Dave would?
Me and cameras don't mix too well.  It does look funky, and is a perfect example of how our intuition can lead us astray, which is the reason I answered to this thread in the first place.

IanB:

--- Quote from: Nominal Animal on November 22, 2022, 08:36:35 pm ---I so wish BigClive would try this.  He's got good cameras, nice bench setup, and suitable spools at the top of his shelves.  Or maybe Dave would?

--- End quote ---

There's really no point.

You know that thing children do, when they are playing a game and about to lose, they find some way of cheating so they can try to avoid the outcome? Electrodacus is playing that game here. There is no evidence you can provide, no experiment anyone can perform that will persuade him, because he will just come up with some kind of nonsensical word salad to dispute the result.

Notice how he never does any analysis himself, never shows any equations, but always tries to make other people do the work? It's a game for him, trying to make people jump to his command, and then getting satisfaction from the "power" that gives him. As I said above, this has all the signs of sociopathic behavior. It is really best not to enable it.

electrodacus:

--- Quote from: Nominal Animal on November 22, 2022, 08:36:35 pm ---No, electrodacus.  You're letting your preconceptions override your search for the facts.

This is the complete model of the situation:

Let t be the surface velocity of the treadmill, positive right.
Let c be the velocity of the center of the gears, positive left.
Let R be the radius of the treadmill gear (blueish), and r the ground gear (pale yellow-orange).
Finally, let φ be the angular velocity of the gears.

--- End quote ---

I did not quote everything just to keep it readable but I read all your repay in details.

I mentioned before but while this mechanism looks simpler is more complex than the one with the belt.

When R=r the gear is locked as you already mentioned.
When R>r the gear is still locked as nothing was changed just the size of the gears.

You can have a working gear box with a gear ratio of 1:1 so the gear ratio is not what makes a gearbox locked or unlocked.

Set the speed of the player at 0.25x and pay close attention to what happens https://odysee.com/@dacustemp:8/gear-slow30p2:9

It is irrelevant witch of the two surfaces move the system will work the same way.

The reason it works has to do with the shape of the tooths on most gear as they allow the gear assembly to lift up when you apply a force.
So energy storage in this case is gravitational the wheel is lifted when charging then falls back when discharged.
If you make custom gear's with the shape of the tooth so that it will not allow this lifting of the gear you can eliminate the energy storage and you will no longer be able to move it.
With typical gears as the ones in my video the horizontal applied forces allow the gear to lift up and thus store potential gravitational energy.
If you push a triangle against an upside down triangle horizontally the triangles will slip against each other and lift up. So charge the shape of the tooth's to eliminate this and you will see that it no longer works.

Nominal Animal:

--- Quote from: IanB on November 22, 2022, 09:06:16 pm ---
--- Quote from: Nominal Animal on November 22, 2022, 08:36:35 pm ---I so wish BigClive would try this.  He's got good cameras, nice bench setup, and suitable spools at the top of his shelves.  Or maybe Dave would?

--- End quote ---

There's really no point.
--- End quote ---
You misunderstand.  I meant that as a short video, it would be interesting, exactly because with sufficient weight and thus friction, the spool does behave unintuitively.  Moreso because we can't "see" how hard one must tug on the wire to get it to move; it looks unintuitive.

Like the trick with rails that become wider as they go up, and how a suitable double cone seems to roll uphill along such rails.  Or how you can accidentally power an IC via an I/O pin.


--- Quote from: IanB on November 22, 2022, 09:06:16 pm ---Electrodacus is playing that game here. There is no evidence you can provide, no experiment anyone can perform that will persuade him, because he will just come up with some kind of nonsensical word salad to dispute the result.
--- End quote ---
True; I've lost all hope of being able to help electrodacus here.

Yet, there is still a possibility that someone else reading this thread –– say, arriving here via a web search –– might start thinking about whether they just assume things because they're intuitive, and learn to question their intuition, and maybe even how to find out for themselves.  If that happens, all my effort has not been in vain..  My last couple of posts have been trying to round the topic up in case that does happen.

If I were still believing I might be able to help electrodacus see, I would have added another figure that contains the force vectors.  The key vectors would obviously be the two torques around the gear axis, because once one realizes their importance on how this system works, everything else including friction/stiction/traction becomes obvious and straightforward.  But no, I haven't drawn such an image, and will not.  Anyone truly interested in the subject can use any (classical) mechanics 101 book, and draw this themselves, and work it all out.  Or indeed grab some Technic Lego, and build working models, and compare their behaviour to what I described.

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