Kinematics is physics, even though some call it geometry of motion. It is the appropriate level of complexity for analysing mechanisms like these.
You do not model forces until you need to consider things like friction and acceleration. Using only a subset of forces to try and describe a mechanism is an error. OP's evocation of Newton's laws of motion is a straw man, because A) they are not relevant for the analysis of the mechanism behaviour at this level of complexity (ignoring friction and losses, assuming perfect traction, steady state operation with no acceleration), and B) OP has picked an arbitrary subset of forces that do not describe the system at the level of complexity where those laws would apply, i.e. their "model" does not sufficiently describe the systems at hand.
For an example of an analysis where a complete set of forces would be used, would be to assume the entire system at rest at initial time \$t = 0\$, and then integrate the equations of motion to find out whether the vehicle would accelerate or slip, when some specific (usually constant) force is applied to the paper or blue surface. Both static and dynamic forces would need to be modeled, both linear and angular, as well as linear and angular momentums. Again, picking an incomplete subset that happens to support your pet theory isn't physics or science, it is just an error.
Have not seen this particular one before but is basically the same setup as mine even the hardware is the same.
What you see there is stick slip hysteresis and energy storage. The front wheel slips else it will not work and by not work I mean wheels will not rotate and vehicle will move in the direction of applied force.
But it is working exactly the same as the geometrical model below. Where is the stick slip hysteresis and energy storage here, since the geometrical model has neither of those, yet it still moves as shown?
This post is a great example of why physics questions that are poorly posed are almost unanswerable
Torque isn't like any other force; it's an emergent property of flexible materials. You can't apply torque to objects with zero stiffness, and no solid objects exist with infinite stiffness that you can physically apply a torque to: https://scholarship.haverford.edu/cgi/viewcontent.cgi?article=1494&context=physics_facpubs
Towards the end of the video you posted, it's pretty clear that you've forced the smaller wheels of your roadster to spin (by very quickly applying force on the paper) before the rest of the system can react and stabilize -- before the front wheels can feel enough force from the rubber band to overcome their stiction and enough force to noticeably modify their rotational inertia.
The rubber band has elasticity; you can stretch it before it can react the same way that the surface of a musical drum has elasticity. If the drum wasn't elastic, your drumstick would shatter the second it touched it. In other words, there's a phase difference between forces applied at one part of an elastic object and forces/movement resultant on the other parts. All movement is a wave of some kind, after all.
Try repeating your experiment with a steel or chain belt and try to show us the same response. The front wheel will slip almost immediately because the steel is much less elastic than the rubber band.
This post is a great example of why physics questions that are poorly posed are almost unanswerable
Torque isn't like any other force; it's an emergent property of flexible materials. You can't apply torque to objects with zero stiffness, and no solid objects exist with infinite stiffness that you can physically apply a torque to: https://scholarship.haverford.edu/cgi/viewcontent.cgi?article=1494&context=physics_facpubs
Towards the end of the video you posted, it's pretty clear that you've forced the smaller wheels of your roadster to spin (by very quickly applying force on the paper) before the rest of the system can react and stabilize -- before the front wheels can feel enough force from the rubber band to overcome their stiction and enough force to noticeably modify their rotational inertia.
The rubber band has elasticity; you can stretch it before it can react the same way that the surface of a musical drum has elasticity. If the drum wasn't elastic, your drumstick would shatter the second it touched it. In other words, there's a phase difference between forces applied at one part of an elastic object and forces/movement resultant on the other parts. All movement is a wave of some kind, after all.
Try repeating your experiment with a steel or chain belt and try to show us the same response. The front wheel will slip almost immediately because the steel is much less elastic than the rubber band.
This sort of vehicle can only move in the opposite direction of the forced applied due to a combination of energy storage and stick slip hysteresis as the trigger for the charge/discharge cycles.
What happens exactly can be seen fairly clearly in this slow motion video https://odysee.com/@dacustemp:8/wheel-cart-energy-storage-slow:8
You can see it starts with an increasing F2 = F1 as the belt is stretched (elastic energy storage).
When F2 = F1 is large enough that the input wheel can slip (it is easier to slip than output wheel as it is already in motion). And the moment wheel starts to slip the force needed to slip is much lower that the force needed to unstick the wheel in the first place so this allows the potential elastic energy to be converted in to vehicle kinetic energy.
Since there is friction the vehicle will slow down so to maintain an average speed this cycle of charge discharge needs to happen multiple times per second and much faster than our slow brain can see.
What I did in this other video you likely seen (first 15 seconds) https://odysee.com/@dacustemp:8/stick-slip-removed-from-front-wheels:0 is reduce grip at output wheels suficient so that they will be the first to slip instead of the input wheels and in this case at initial acceleration the belt is still streched as F2=F1 increase but they will not be able to increase that much before the output wheels slip and the stored enenrgy is not discharged the belt remains at that constant streached level while speed remains constnat with the vehicle being draged as the mechanism as it is is just a locked gearbox.
So eliminating the stick slip hysteresis from the input wheel removes the ability of the vehicle to take advantage of the stored energy thus it can no longer charge and discharge that to move in the opposite direction of the applied force.
If I were to replace the soft belt with a stiffer belt then displacement for same force will be lower meaning less energy will be stored before input wheel slips and that means the cycles of charge discharge will need to be faster (more cycles per second for same constant speed).
If the belt is to stiff then amount of energy may be to low and not be able to cover the frictional loss and to have extra to convert to kinetic energy so vehicle will no longer be able to move in the opposite direction so it will be dragged or maybe stay in place while the paper is dragged under the input wheels.
So now the treadmill is unpowered free to move and you push the vehicle body to the right. Of course since you apply a force to the right to the vehicle body the vehicle body will move in that direction.
But it has basically nothing to do with the original problem where the only applied force is to the left (not to the right) and it is applied at the input wheel.
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Did you miss the Newton's 3'rd law ? It is present in all non accelerating frames and of course when whe are in an accelerating frame the 2'nd law also applies.
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Do you want to learn that it does indeed have something to do with the original problem, or must you hide under your safety blanket?
Now, imagine the right wheel is not connected with a belt (and, sorry, I used 'horizontal belt' previously when I should has used 'treadmill' to save confusion). The wheel is locked rigid. You, the HoG or whatever push the vehicle to the right and that causes the treadmill to move to the right. I presume you are perfectly OK with that since it's pretty basic. So..
Let's say the vehicle moves to the right (via whatever strange force) at 2m/s. With a locked right wheel the treadmill will move to the right at 2m/s. Yes? Good. Clearly, any clockwise rotation of the right wheel will reduce the speed of the treadmill. We can thus have three distinct situations:
1. The connection between the wheels is 1:1 (that is, the left wheel drives the right wheel at the same speed). In this case, the vehicle moves right at 2m/s, the right wheel rotates at the same speed the vehicle is travelling and the treadmill is stationary.
2. The connection is 2:1 (that is, the left wheel drives the right wheel at half the speed). In this case the vehicle moves right at 2m/s and the treadmill moves right at 1m/s (since the right wheel is rotating slower than is necessary to keep up with the vehicle speed).
3. The connection is 1:2 (that is, the left wheel drives the right wheel at twice the speed). In this case the vehicle moves right at 2m/s and the treadmill moves left a 1m/s (since the right wheel is rotating faster than is necessary to keep pace with the vehicle speed).
Do you agree with those? If not, which of 1..3 do you think is wrong? I can assure you that this will resolve your original problem if you stick with it.
From your responses to my own postings and those of a number of others, it seems that you do understand the arguments that we are making. However, in every case you throw a spanner in the works by bringing up your version of Newton’s third law.
Try a very simple experiment. Extend the forefingers of you left and right hands, then press the tips of those two fingers together. You will notice that the forces you can feel at your two fingertips are equal and opposite and there is no way of performing this experiment where that would not be the case.
You may regard this experiment as pointless, and that it just demonstrates a law of physics which is intuitive and completely obvious. So obvious in fact that there would be no point in giving it a name. But it does have a name, it is Newton’s third law of motion. A key characteristic of this law is that the two forces involved always act on different objects, in this case the tips of your left and right forefingers.
The setup in diagram (a) as well as the real setup in my video has only two points of contact (no HoG involved or anything else touching the vehicle body) and in this conditions you can not have a functional gearbox as that will require 3 points of contact.
With only two points of contact F2 can only be equal and opposite to F1 in non accelerating reference frames so when vehicle is not moving or when it is moving at constant speed. In accelerating reference frames to this newton's 3'rd law F2 = F1 you add the Newton's 2'nd law m*a.
The requirement for 3 points of contact is not correct, so this argument can be rejected.
With a kinematic structure neither forces nor Newton's laws are relevant to the analysis. Do you need forces or acceleration to analyze the movement of the gears in a clock? So this argument can also be rejected.
In summary, you have no arguments, therefore there is nothing to debate.
The best thing is for us to leave you to your own thoughts and let the thread rest. We do not need to care what you believe, it is not our problem, and it ceases to be entertaining after a while.
Why do you keep creating these threads anyway? This is what, the third thread now?
It is on you to prove that as there is no functional gearbox that can do force multiplication with just two points of contact.
I offered video evidence that things work the way I say they work and you want to contradict a real experiment with kinematics only "the study of motion of a system of bodies without directly considering the forces or potential fields affecting the motion"
The best thing is for us to leave you to your own thoughts and let the thread rest. We do not need to care what you believe, it is not our problem, and it ceases to be entertaining after a while.
It's not on me at all. You started the thread and are asking the questions. Neither I nor anyone else has any obligation to help you.
You can believe whatever you wish. Since everyone else in this thread can make an apparatus that does what the diagrams show it will do, and you alone cannot do so, that is your problem and not our problem.
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Try a very simple experiment. Extend the forefingers of you left and right hands, then press the tips of those two fingers together. You will notice that the forces you can feel at your two fingertips are equal and opposite and there is no way of performing this experiment where that would not be the case.
You may regard this experiment as pointless, and that it just demonstrates a law of physics which is intuitive and completely obvious. So obvious in fact that there would be no point in giving it a name. But it does have a name, it is Newton’s third law of motion. A key characteristic of this law is that the two forces involved always act on different objects, in this case the tips of your left and right forefingers.
Now you imagine the same experiment but the finger from right hand is under the right wheel and the finger from your left hand is under the left wheel.
Try to bring the hands together and you will understand why it is a locked gearbox and can be treated as a single object.
Your right hand will try to move to the left and you left had to the right and so the right wheel will try to move clockwise and the left wheel counter clockwise.
Due to the way the belt connects the two wheels it will be impossible for the wheels to spin in different directions thus what I call a "locked gearbox"
So unless you allow for one of the wheels to spin on your finger you can not move the hands closer and all you can do is apply a force that will be as you mentioned Newton's 3'rd law of motion.
I can think of little further to add to what I wrote in my previous message. You didn't disagree with anything, you just threw in a distraction.
You yourself have claimed to identify the understanding of Newton's third law as the fundamental difference between us. A belt driven trolley is hardly the clearest and simplest example with which to examine that difference.
Here is a definition of Newton's third law that I regard as correct.
"To every action, there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts."
The left wheel of your trolley is a different object to the right wheel, the stationary block and the treadmill belt are also different objects. So your F1 and F2 cannot be viewed as the mutual actions of two bodies upon each other, and are therefore not the subject of Newton's third law as defined above.
If you have a definition of Newton's third law that makes your F1 and F2 a Newton's third law force pair, then please write it down.
You can als imagine having this in your hands right hand applies F1 and the left hand will apply the equal and opposite force F2 else there will be no F1 so Newton's 3'rd law pair.
You can als imagine having this in your hands right hand applies F1 and the left hand will apply the equal and opposite force F2 else there will be no F1 so Newton's 3'rd law pair.
Once again you are assuming something that isn't true. If you hold that object in your hands and try to apply opposing forces F1 and F2 then the object will simply move and rearrange itself to cancel out the forces, so that no force remains. It will be like trying to apply a force to an object that moves out of the way when you touch it. In reality there are no forces on that system, all forces are zero.
Please explain what part moves when you apply F1 = F2 ? There is no net force and F2 can not be anything other than equal and opposite to F1
The body when F5 = F6 acts is solid so there is nothing to rearrange and the F3 = F4 act on a material that can not deform.
So there is no movement.
How can the assembly be rigid when it has hinges and moving parts? You don't need to imagine this when you can easily make it with cardboard, paper fasteners and string. If you push on the two legs they will get closer together.
It will act as a rigid object even if it has hinges.
I feel that you need to build this to test since you think there will be some movement when that is not the case.
Do you want to learn that it does indeed have something to do with the original problem, or must you hide under your safety blanket?
Now, imagine the right wheel is not connected with a belt (and, sorry, I used 'horizontal belt' previously when I should has used 'treadmill' to save confusion). The wheel is locked rigid. You, the HoG or whatever push the vehicle to the right and that causes the treadmill to move to the right. I presume you are perfectly OK with that since it's pretty basic. So..
Let's say the vehicle moves to the right (via whatever strange force) at 2m/s. With a locked right wheel the treadmill will move to the right at 2m/s. Yes? Good. Clearly, any clockwise rotation of the right wheel will reduce the speed of the treadmill. We can thus have three distinct situations:
1. The connection between the wheels is 1:1 (that is, the left wheel drives the right wheel at the same speed). In this case, the vehicle moves right at 2m/s, the right wheel rotates at the same speed the vehicle is travelling and the treadmill is stationary.
2. The connection is 2:1 (that is, the left wheel drives the right wheel at half the speed). In this case the vehicle moves right at 2m/s and the treadmill moves right at 1m/s (since the right wheel is rotating slower than is necessary to keep up with the vehicle speed).
3. The connection is 1:2 (that is, the left wheel drives the right wheel at twice the speed). In this case the vehicle moves right at 2m/s and the treadmill moves left a 1m/s (since the right wheel is rotating faster than is necessary to keep pace with the vehicle speed).
Do you agree with those? If not, which of 1..3 do you think is wrong? I can assure you that this will resolve your original problem if you stick with it.
As I mentioned in your imaginary setup the vehicle has 3 points of contact and that god will need to be real as a force will need to act against the vehicle body and not an imaginary one as you think.
If a real force acts against the vehicle body then due to 3 separate forces acting on the different vehicle parts the vehicle will work as you mentioned.
I already provided an example but in my example the vehicle body was rigidly connected to ground and in that case the mechanism acts as a functional gearbox and the red box can be moved by the treadmill and force acting on the box provided by left wheel can be 2x larger than the input force at the right wheel provided by the treadmill.