Newton's third law problem.

[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.

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.

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]

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.

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.

[Nominal Animal]

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.

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

You may need some kind of energy storage to be able to accelerate, but I do not think it is necessary for steady-state operation.
(I'd need to model the entire system, including friction and momentum and losses, to be able to examine the system phase space, and determine whether acceleration is possible without energy storage or not.)

Also: aw crappola, I topsy-turvied myself with the gearing ratio.   I thought inverse to what I wrote.  It is a typical error for me, too.  Dammit.
Teaches me right for not testing it with a model first.  Apologies.

If we ignore losses, it makes no sense to look at the forces involved.  The mechanics of the situation suffice.

If we use \$v_t\$ for the speed of the surface of the treadmill (going in the opposite direction), \$v_d\$ for the speed for (the surface of) the driven wheel on the treadmill, and \$v_c\$ for the speed of the car itself (and therefore also (the surface of) the driving wheels), the machine requires
$$\left\lbrace \begin{aligned}
v_d &= v_t + v_c \\
v_c &= \lambda v_d \\
\end{aligned} \right.$$
where \$\lambda\$ is the gearing ratio, i.e. number of turns of the driving wheels per each turn of the driven wheel, assuming their diameters is the same.
The lower equation describes the locked gearbox.
The upper equation describes that the driven wheel must have a surface speed that is the sum of the treadmill surface and "car" speeds, or something has to give (slip).

Combining the two, and solving for \$v_c\$, we have, in the steady state ignoring any losses,
$$v_c = v_t \frac{\lambda}{1 - \lambda}$$
so there is a steady state for \$0 \le \lambda \lt 1\$ only.

In your example, \$\lambda \gt 1\$, and there is no steady state.

However, do check what happens if you reverse the gearing.  For example, with \$\lambda = 0.6\$ (driving wheel surface speed 3/5 of that of the driven wheel, or if their diameters are the same, the driving wheel turning 3 times in the time the driven wheel turns 5 times), the solution is \$v_c = 1.5 v_t\$, i.e. the car runs at 1.5 times the treadmill speed.

When \$\lambda = 0.5\$, \$v_c = v_t\$.  When \$\lambda = 0.2\$, \$v_c = 0.25 v_t\$.

I do believe that losses can be adequately modeled by reducing the gearing ratio.  If the actual ratio is \$\lambda\$, then the model \$\lambda^\prime = (1 - \epsilon)\lambda\$, where \$\epsilon\$ represent the overall losses in the system, should match physical results.

A real world vehicle does probably need energy storage for acceleration and to avoid tiny losses causing a catastrophic failure, and an adjustable gearing \$0 \lt \lambda \lt 1\$, so it can optimize the gear ratio to the current car velocity \$v_c\$.  Achieving any ratio \$\lambda \gt 0.5\$ is sufficient to travel faster than the treadmill.

In case anyone is wondering where the necessary energy is coming from, the answer is obvious: from the treadmill.  When the "car" is placed on the treadmill, the larger \$\lambda\$ is, the more energy is needed to keep the treadmill moving at a given velocity \$v_t\$.

[PlainName]

Seems that is a bit of a boring subject

More likely it's already been done to death in previous threads and no-one has the energy (ha ha) to go through all that again.

or not sure why there are no comments

Probably because we know full well that whatever explanations, theories, laws of physics, etc. are posted, nothing will drag you from your insistence that it is all about energy storage (and, as a corollary, the movement against the power source cannot happen).

[Nominal Animal]

A simplified example is a pair of wheels with almost as large a pulley in between, with a thread rotated on the pulley.  What happens when you pull the thread?

If you start examination at the zero-movement state, you'll find that the angle at which the thread exits the spool, with respect to gravity down, largely determines whether it starts moving or not.  If you pull the thread exactly level, the forces do not leverage the wheel to turn so that it would travel opposite to the direction the thread is being pulled to.  If you pull the thread slightly upwards or downwards from level, the forces are no longer balanced, resulting a small torque on the wheel, so it'll start traveling opposite to the direction the thread is being pulled to.  If you pull the thread nearly vertical, the torque is maximized, and it is easiest to get the wheel to travel (away from where you are pulling the thread).

(The same applies to acceleration: it will only accelerate as you pull harder, if the thread is not exactly level.  The minimum angle for a constant velocity depends on the losses, and the minimum angle for acceleration depends on losses and rotational inertia.)

This is why omitting any forces, and only looking at some, will often lead to unphysical results.  Would you have considered the effect of the thread angle?  It is not obvious until you examine all of the forces acting here, not to me at least.

When the pulley is exactly the size of the wheel, you cannot get it to move (in the opposite direction of where you pull the thread).
When the pulley is larger than the wheel, the angle of the thread no longer matters, and it is easy to get the wheel to move (in the opposite direction of where you pull the thread).

Here, the treadmill is a continuous thread, and the pulley/wheel size ratio represents the gearing between the driven and driving wheels of the "car". 

[electrodacus]

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

On a bicycle the rider provides the force and against ground and it is connected to bicycle frame so there is no analogy that can be made with this vehicle that is powered from outside by the treadmill and the vehicle frame is floating.
The elasticity of the belt only exaggerate what will happen with any mechanism including a bicycle chain.

This is a locked gearbox since F1 = F2
Please show how F2 can be larger than F1. As F1 can not exist without the equal and opposite F2 in this particular example.

[electrodacus]

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.

There can not be a force multiplication in this particular problem as the vehicle has only two points of contact.
Think about this way:
A rope tied to a tree and you pull the rope. Is there any chance that rope can get shorter and pull you towards the tree using your own power ?
Cut the rope in two and add anything you like that has no internal energy source and that can pull you towards the tree while you pull away from it.
It is the same problem here not sure why so many people fail to see this even with the clear video evidence showing exactly what I'm describing.

[electrodacus]

A real world vehicle does probably need energy storage for acceleration and to avoid tiny losses causing a catastrophic failure, and an adjustable gearing \$0 \lt \lambda \lt 1\$, so it can optimize the gear ratio to the current car velocity \$v_c\$.  Achieving any ratio \$\lambda \gt 0.5\$ is sufficient to travel faster than the treadmill.

In case anyone is wondering where the necessary energy is coming from, the answer is obvious: from the treadmill.  When the "car" is placed on the treadmill, the larger \$\lambda\$ is, the more energy is needed to keep the treadmill moving at a given velocity \$v_t\$.

The claim I make and it is proved by the video's I shwed is that no vehicle including this one can move from left to right without both energy storage and stick slip systeresis.
I showed what happens when you have both energy storage and stick slip hysteresis https://odysee.com/@dacustemp:8/wheel-cart-energy-storage-slow:8
And also showed what happens if you remove the ability of the front wheel to slip https://odysee.com/@dacustemp:8/stick-slip-removed-from-front-wheels:0

Against all evidence and theoretical explanation of how it works people think is not true.

The friction of the back wheel slip in second video is significantly higher than the internal friction of the rotating parts of the vehicle. And is clear vehicle is dragged as that type of gearbox for this particular application is locked.
I think I will need to make a drawing showing the lever type equivalent of this vehicle as that may be more easy to understand.
You need to twist the belt (infinite symbol shape) in order for this mechanism to not be locked so changing the gear ratio will not help with anything.

[bdunham7]

There can not be a force multiplication in this particular problem as the vehicle has only two points of contact.

That's just silly.  But perhaps think about motion amplification or reduction instead of forces if that helps.  If you want to use a basic lever analysis, your 'third point of contact' is the net force against or motion of the body of the vehicle itself.  And that might require Newtonian mechanics if you let it progress beyond the static case, but you have to understand Archimedes first. 

As far as the video, it clearly shows just the opposite of what you say it does.  Your interpretation of the video appears to be an optical delusion.

[electrodacus]

Probably because we know full well that whatever explanations, theories, laws of physics, etc. are posted, nothing will drag you from your insistence that it is all about energy storage (and, as a corollary, the movement against the power source cannot happen).

I gave this example earlier but do you think you can add any mechanism (not powered) that can pull you towards the tree while you pull away from the tree ?
Or to be more equivalent pusing a solid pipe against a huge wall and the pipe using your energy to push you away from the wall?

[electrodacus]

That's just silly.  But perhaps think about motion amplification or reduction instead of forces if that helps.  If you want to use a basic lever analysis, your 'third point of contact' is the net force against or motion of the body of the vehicle itself.  And that might require Newtonian mechanics if you let it progress beyond the static case, but you have to understand Archimedes first. 

As far as the video, it clearly shows just the opposite of what you say it does.  Your interpretation of the video appears to be an optical delusion.

Motion amplification ? What will that even mean ?
Are you saying power output of the back wheel can be higher than power input on the front wheel ? Since it sounds like that.

What video and please explain what you see if you do not agree with my explanation of what happens.
I clearly see a vehicle that is not moving relative to the ground and a front wheel that moves while belt is stretched so force increases and so is power that it is stored (stretched belt is stored energy).
Then when force is large enough the front wheel slips allowing the back wheel to push the vehicle using the energy stored earlier in the belt and when that belt is discharged the cycle repeats.

[SiliconWizard]

Wasn't this already shown in one of the threads on people being completely wrong about electricity?

[electrodacus]

A simplified example is a pair of wheels with almost as large a pulley in between, with a thread rotated on the pulley.  What happens when you pull the thread?

If you start examination at the zero-movement state, you'll find that the angle at which the thread exits the spool, with respect to gravity down, largely determines whether it starts moving or not.  If you pull the thread exactly level, the forces do not leverage the wheel to turn so that it would travel opposite to the direction the thread is being pulled to.  If you pull the thread slightly upwards or downwards from level, the forces are no longer balanced, resulting a small torque on the wheel, so it'll start traveling opposite to the direction the thread is being pulled to.  If you pull the thread nearly vertical, the torque is maximized, and it is easiest to get the wheel to travel (away from where you are pulling the thread).

(The same applies to acceleration: it will only accelerate as you pull harder, if the thread is not exactly level.  The minimum angle for a constant velocity depends on the losses, and the minimum angle for acceleration depends on losses and rotational inertia.)

This is why omitting any forces, and only looking at some, will often lead to unphysical results.  Would you have considered the effect of the thread angle?  It is not obvious until you examine all of the forces acting here, not to me at least.

When the pulley is exactly the size of the wheel, you cannot get it to move (in the opposite direction of where you pull the thread).
When the pulley is larger than the wheel, the angle of the thread no longer matters, and it is easy to get the wheel to move (in the opposite direction of where you pull the thread).

Here, the treadmill is a continuous thread, and the pulley/wheel size ratio represents the gearing between the driven and driving wheels of the "car".

I know the tread problem is the same and same stick slip hysteresis and energy storage is involved.
But I think the belt vehicle is an easier example to understand and see the effects.  Especially with a long stretchy belt and slowed down video.
The charge discharge frequency can be quite high for most mechanisms and will be impossible to see without slow motion video.

But I should make a drawing where all forces will be placed (currently the forces acting on vehicle body are not drawn) and I will make it just as a lever system to maybe be even clearer that F2 can not be different from F1 as F1 is the reason F2 exists and vice versa.

[bdunham7]

Motion amplification ? What will that even mean ?

If you have a lever with a fulcrum and the ends of the lever have different distances to the fulcrum, then a small motion on the short end becomes a large motion on the long end and vice versa.  Like I said, Archimedes.

Are you saying power output of the back wheel can be higher than power input on the front wheel ? Since it sounds like that.

I didn't say that.  You appear to be 2000+ years short of even understanding the term 'power'.

What video and please explain what you see if you do not agree with my explanation of what happens.
I clearly see a vehicle that is not moving relative to the ground and a front wheel that moves while belt is stretched so force increases and so is power that it is stored (stretched belt is stored energy).
Then when force is large enough the front wheel slips allowing the back wheel to push the vehicle using the energy stored earlier in the belt and when that belt is discharged the cycle repeats.

Your video.  I don't see any wheel slippage at all.  I see a bit of jerkiness and stretching of the rubber band, all accentuated by the stop-action of the slow frame rate, but none of what you describe.  Even if the band were entirely inflexible or the equivalent function was implemented with gears, the result would be the same.

[electrodacus]

Wasn't this already shown in one of the threads on people being completely wrong about electricity?

Do not change the subject. This is a problem where everything can be seen and you are still getting things wrong.

[AndyBeez]

Reciprocal: a connecting rod between a piston and a wheel is replaced with a shock absorber. Does the wheel rotate if the shock absorber is 'storing' energy?

[Nominal Animal]

The claim I make and it is proved by the video's I shwed is that no vehicle including this one can move from left to right without both energy storage and stick slip systeresis.

Sure it can.  Just swap the gearing ratio, and replace the rubber band with a non-springy belt.

You need to twist the belt (infinite symbol shape) in order for this mechanism to not be locked so changing the gear ratio will not help with anything.

No, you don't.  Just make the floor-wheel gear or pulley larger than the treadmill gear or pulley, and be amazed.  The bigger the ratio (rear size to front size), the easier it moves.

Please, try it.  I'm not tricking you.  I showed you math that *proves* it works.  The only reason for you to not try it, would be to avoid being proven wrong.  Keep your mind open, friend, and try it.

[electrodacus]

If you have a lever with a fulcrum and the ends of the lever have different distances to the fulcrum, then a small motion on the short end becomes a large motion on the long end and vice versa.  Like I said, Archimedes.

Let me know if you see the image and if you agree with the lever option as analog to that vehicle.

[electrodacus]

Sure it can.  Just swap the gearing ratio, and replace the rubber band with a non-springy belt.

All materials have elastic and plastic deformation in real world so you can not get rid of that.
You can reduce the size of energy storage but that is irrelevant the frequency of charge discharge will increase and it will still work the same way.

No, you don't.  Just make the floor-wheel gear or pulley larger than the treadmill gear or pulley, and be amazed.  The bigger the ratio (rear size to front size), the easier it moves.

Please, try it.  I'm not tricking you.  I showed you math that *proves* it works.  The only reason for you to not try it, would be to avoid being proven wrong.  Keep your mind open, friend, and try it.

See attachment and let me know if you agree with that analogy.

[Nominal Animal]

See attachment and let me know if you agree with that analogy.

I won't tell you, before you actually retry the experiment with swapped gear ratio, and describe your observations here.

It is a very small, simple thing for you to do, after all.  You've already posted videos of two variants above, so how much more effort would a third one be?

Or is it that you did it, and observed exactly what I said you would, and are now annoyed that your model is broken?
I'm not doing this –– responding here –– because I want to break your model, or break anything at all.
I am responding here only because I want you to have a *working model*.
Please understand that.

[electrodacus]

See attachment and let me know if you agree with that analogy.

I won't tell you, before you actually retry the experiment with swapped gear ratio, and describe your observations here.

It is a very small, simple thing for you to do, after all.  You've already posted videos of two variants above, so how much more effort would a third one be?

Or is it that you did it, and observed exactly what I said you would, and are now annoyed that your model is broken?
I'm not doing this –– responding here –– because I want to break your model, or break anything at all.
I am responding here only because I want you to have a *working model*.
Please understand that.

I tested all variants and there is no difference the vehicle works the same way with charging and stick slip hysteresis as there is no other way for the vehicle to work.
Please see that attach diagram and let me know how is not that a locked system that will not be able to move to the right without both energy storage and stick slip hysteresis and to the left without slip.

[IanB]

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.

The vehicle will move to the right, obviously.

Until you can see that, your reasoning is defective, and many things you try to deduce with your defective reasoning will be wrong.

The reason nobody will debate with you is not because it is boring, but because it is pointless. Since you cannot, or will not, understand, there is no point trying to explain anything to you.