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Newton's third law problem.

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electrodacus:
I have the diagram below.
The vehicle has only two points of contact.
Front wheel the one of right sits on a treadmill witch can apply a force F1 to that wheel
Back wheel the one of the left is on the ground (red box is connected to ground) same as treadmill body witch is also connected to ground.

The question:
a) What will happen in a theoretical case? where there is no wheel slip and no components can deform in any way elastic or plastic including the belt.
b) What happens in a real setup? where both slip and deformation exist and can not be get rid of.



Edit:
Seems that is a bit of a boring subject or not sure why there are no comments but to help things out I will add a video with what happens in a real setup

https://odysee.com/@dacustemp:8/wheel-cart-energy-storage-slow:8

What you see in the video is a slowed down video of a toy vehicle with the same design as in the diagram.
The front wheels are on a moving paper simulating the treadmill and the back wheels are on the ground.
What happens in the video is as follow (my interpretation so if you disagree please explain).

When treadmill starts to move the vehicle remains stationary while the front wheel rotates charging the build in energy storage (stretching the rubber belt).
The force F1=F2  increases until force is high enough for the front wheel to slip and at that exact moment the energy stored in the belt is used to rotate the back wheel and move the vehicle from left to right so in the opposite direction from treadmill surface.
Once the stored energy is used up the cycle repeats and this happens many times per second so much so that in most cases is not possible to realize what happens without watching a slowed down video.

So the reason why this locked gearbox vehicle can move opposite to the treadmill direction (the only thing powering the system) is a combination of energy storage and stick slip histeresis.

Nominal Animal:
To properly model this situation, you need to account for momentum (both linear and angular), and therefore the masses of the components also.  Having a springy belt makes it quite difficult to model; a thin tiny-mass thread or wire would be better –– modelled in real life by making the wheel masses much larger, and using e.g. a toothed belt.

One could model the springy belt using a torsion spring conforming to Hooke's law, F=-kϕ, where ϕ is the angular difference between the two wheels, but it is not at all obvious it matches how a springy elastic belt behaves.

Stiction (static friction) and dynamic friction are key here, and depend on the materials used, and definitely affect exactly what will happen.  Oscillating motion at the static-dynamic friction boundary is annoyingly difficult to model, because tiny changes drastically alter the behaviour of the system; in real world, you get chaotic effects, in the simulation, rounding errors and such can cause unphysical oscillations or oscillation dampening.

While I can create a simulation model for you, it's a lot of work; and I don't really see the point here.
If the stiction on the two surfaces is sufficiently great –– say, toothed wheels and matching rack-like surface on both –– then the device will move right (opposite direction to the top surface of the treadmill).
 _ _ _ _ _

A better model would be to have two parallel racks, with a chain drive between, with top surfaces level.  Create a three-wheeled "car", running on top, that has a center sprocket as the front wheel, and two pinion wheels at the back, with front and back connected using a gearbox so pinions rotate faster than the sprocket.  (You only need one pinion wheel, but with two it will stay upright and not try to skew.)

You can do this easily if you have suitable Technics Lego sets (specifically, some gears, racks, and chain).  I might...  :-[
The "car" will always move opposite to the top surface of the chain.  But what does this prove?  Do you need a video to prove this?
You can also use Lego Digital Designer (Windows 7) or Bricklink Studio (Windows, Mac) to design the models digitally first, but AFAIK they do not model technics in operation, only statically.


--- Quote from: electrodacus on November 17, 2022, 11:16:10 pm ---So the reason why this locked gearbox vehicle can move opposite to the treadmill direction (the only thing powering the system) is a combination of energy storage and stick slip histeresis.
--- End quote ---
No, I don't think so.

Yes, the vehicle can definitely move opposite to the treadmill direction, but you do not actually need energy storage to achieve this; all you need is sufficient friction between the wheels and the treadmill and the static surface.

electrodacus:

--- Quote from: Nominal Animal on November 20, 2022, 11:09:04 am ---Yes, the vehicle can definitely move opposite to the treadmill direction, but you do not actually need energy storage to achieve this; all you need is sufficient friction between the wheels and the treadmill and the static surface.

--- End quote ---

Thanks for taking the time to replay. It seems this is not an exciting subject.

If you take a theoretical case where the mass of the vehicle is zero and you exclude any energy storage (no elastic deformation or gravitational energy storage as it will happen with a louse chain).
What then will be the mechanism allowing the vehicle to move opposite to the treadmill direction?

The only reason I see for F2 to exist is as the pair of F1 thus equal and opposite.

I can show the same behaviour with gears as you can just not get rid of elastic deformation or gravitational energy storage (if some parts lift up) in real world  but what I can do is reduce the friction at the back wheels so that the back wheels slip before the front and then this is what happens https://odysee.com/@dacustemp:8/stick-slip-removed-from-front-wheels:0

As I expected eliminating the slip at front wheel will result in vehicle being dragged (as it is a locked gearbox) in the direction that force is applied by the treadmill.

AndyBeez:
My reading, with no elasticity, the 'car' should advance at 1/2 the speed of the treadmill - due to the gearing ratio. Otherwise, it will stutter as energy pumps and dumps in the band. As Nominal Animal states, energy transfer is chaotic.

Another way to think of your problem is, what would happen if you replaced a metal bicycle chain with a band made from bungie rope? How hard would you have to pedal to overcome the elasticity in the bungie rope before the back wheel turns - and would the pedals feel like they were made from jelly? This would make an impossible bike to ride :)

bdunham7:
Yikes!  You're back!

As explained clearly to you earlier, this is not a Newtonian physics problem, it is basic Archimedes-era problem.  Your knowledge here is not hundreds of years behind, but rather a few thousand.  You simply need to understand the force multiplication possible with levers and then go one step further and use that to understand torque multiplication by pulleys and gears.   A big hint--gears and pulleys in the static case are the same as levers.

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