General > General Technical Chat
Force multiplier
electrodacus:
--- Quote from: cbutlera on February 10, 2023, 07:07:10 pm ---I think that I may be making some progress here, but rather than this specific example, I’m trying to understand the analytical method that you are advocating. For me that is much more useful. I have made a list of the key points that I have picked up from what you have written. Am I on the right track here? If you do see any errors, could you correct the text as necessary.
1) Intuition plays a key role in classical mechanics.
--- End quote ---
I do not know if I will agree with that. There is not much if anything that was not studied in classical mechanics. Sometimes "intuition" seems to be wrong.
For example using kinematics only and not considering forces will not provide the correct answer.
To me it seems that people always imagine that the force is applied between vehicle body and input wheel not as it is the case between the input wheel and the ground.
The only time the force is applied between the vehicle body and output wheel is when stored energy is discharged in that case the vehicle is powered from inside and not form the exterior.
--- Quote from: cbutlera on February 10, 2023, 07:07:10 pm ---2) Before making any calculations, it is vital that the analyst chooses the correct frame of reference in which to perform those calculations. This can only be done through intuition, built up from years of experience. Inexperienced analysts can easily get this step wrong and choose the wrong frame of reference. In which case any conclusions that they draw from subsequent mathematical analysis will be invalid.
--- End quote ---
Again not sure we have the same definition for intuition.
Result will be the same independent of the reference frame chosen.
--- Quote from: cbutlera on February 10, 2023, 07:07:10 pm ---3) There are two classes of frames of reference, which are the accelerating and non-accelerating frames of reference.
--- End quote ---
For this particular example you can only have acceleration if either input or output wheels slip so unless that happens there will be no acceleration.
The applied force F1 needs to be large enough for slip to happen else if that is less nothing will happen other than belt will be stretched the input wheel will rotate correspondingly with the amount of stretch but vehicle body will not move relative to ground.
If output wheel (left one) slips first then vehicle will be accelerated to the left and F1 the applied force will be F1 = F2 + m*a so sum of 3'rd and 2'nd law.
If input wheel slips (right one) (this is what happens if you have the same type of wheels and and material since the input wheel already rotates and it will slip more easy) the you have F2 = F1 + m*a and F2 can be larger due to belt applying a force inside the vehicle between the vehicle body and output wheel and this force is possible because of stored energy.
As you see from this equations the gear ratio is not involved unless you look at the amount of stored energy as that will depend on the gear ratio.
--- Quote from: cbutlera on February 10, 2023, 07:07:10 pm ---4) In an accelerating frame of reference, objects within that frame obey Newton’s second law of motion.
--- End quote ---
As I mentioned 2'nd law is involved only if you allow wheel slip. And the direction the vehicle is accelerated depends on which wheel slips.
If the vehicle worked the way you think it works there will be no wheel slip but that is not the case in any experimental test where vehicle moves.
--- Quote from: cbutlera on February 10, 2023, 07:07:10 pm ---5) In a non-accelerating frame of reference, Newton’s second law is not relevant, because nothing is accelerating. In this case, Newton’s third law will apply to every object in that system, so every object in the system will be subject to a net zero balance of forces. In the case of two forces acting on an object they must necessarily be equal and opposite. This is what Newton meant by stating "To every action, there is always opposed an equal reaction”.
--- End quote ---
That is not quite true. It is true that net forces for this particular problem is zero in an non accelerating reference frame.
But if you have a proper (working) gearbox that means 3 points of contact so vehicle body connected to ground. Then the applied F1 will be between vehicle body and input wheel and the F2 will be between vehicle body and output wheel and at 2:1 gear ratio the F2 = 2*F1 and that will be the case in an non accelerating frame of reference.
If not convinced by this think about a balance with fulcrum the third point offset as in image below.
Nothing will need to move for the input force to be smaller than output force and Newton's 3'rd law works here as two separate loops with F1 input force having a pair at the fulcrum and the other pair F2 output also relative to fulcrum.
But example a has no 3'rd point the fulcrum equivalent so with that missing input and output force can only be equal.
--- Quote from: cbutlera on February 10, 2023, 07:07:10 pm ---6) Some mechanical systems can alternate between being in accelerating and non-accelerating frames of reference. The analyst needs to take great care here to allocate the correct frame of reference to each moment in time. Inexperienced and even many experienced analysts can get this wrong, and is one of the most difficult skills to master.
--- End quote ---
Yes that is the case here when vehicle moves to the right against the applied force as the vehicle will accelerate in burst many times per second so fast that it looks like smooth motion to the slow human brain.
Maybe it is a difficult skill but as soon as you see a device moving in the opposite direction of applied force you will know that some other energy source is present like in this case a small energy storage device.
Because you know from experience and Newton's 3'rd law that for every action there is an equal and opposite reaction so you can not have an unpowered item like this vehicle pushing with higher force F2 against the applied F1 as that will also violate the energy conservation.
The energy conservation is not violated in this case only because energy is stored so treadmill moves say 1cm while vehicle is not moving at all but this 1cm and the F1 was stored as elastic energy in the rubber band then in the next moment this stored energy could be converted in kinetic energy in the opposite direction and if there was no friction with just this initial energy the vehicle can maintain forever the gained kinetic energy but since there is friction the cycle of charge discharge needs to repeat all the time to maintain an average speed. Speed of this vehicle is not constant but it is not possible for humans to detect that without faster more sensitive measurement equipment.
fourfathom:
--- Quote from: electrodacus on February 10, 2023, 11:54:19 pm ---some other energy source is present like in this case a small energy storage device.
--- End quote ---
This is *NOT* an energy source.
electrodacus:
--- Quote from: fourfathom on February 11, 2023, 12:30:52 am ---
--- Quote from: electrodacus on February 10, 2023, 11:54:19 pm ---some other energy source is present like in this case a small energy storage device.
--- End quote ---
This is *NOT* an energy source.
--- End quote ---
It is a charged energy storage device. How will you call that if not an energy source ?
cbutlera:
Thanks for that detailed response, I think I am getting closer to understanding your method of analysis. I was trying to make generalised statements that could be applied to any mechanical system rather than just to this specific example.
--- Quote from: electrodacus on February 10, 2023, 11:54:19 pm ---
--- Quote from: cbutlera on February 10, 2023, 07:07:10 pm ---I think that I may be making some progress here, but rather than this specific example, I’m trying to understand the analytical method that you are advocating. For me that is much more useful. I have made a list of the key points that I have picked up from what you have written. Am I on the right track here? If you do see any errors, could you correct the text as necessary.
1) Intuition plays a key role in classical mechanics.
--- End quote ---
I do not know if I will agree with that. There is not much if anything that was not studied in classical mechanics. Sometimes "intuition" seems to be wrong.
For example using kinematics only and not considering forces will not provide the correct answer.
To me it seems that people always imagine that the force is applied between vehicle body and input wheel not as it is the case between the input wheel and the ground.
The only time the force is applied between the vehicle body and output wheel is when stored energy is discharged in that case the vehicle is powered from inside and not form the exterior.
--- Quote from: cbutlera on February 10, 2023, 07:07:10 pm ---2) Before making any calculations, it is vital that the analyst chooses the correct frame of reference in which to perform those calculations. This can only be done through intuition, built up from years of experience. Inexperienced analysts can easily get this step wrong and choose the wrong frame of reference. In which case any conclusions that they draw from subsequent mathematical analysis will be invalid.
--- End quote ---
Again not sure we have the same definition for intuition.
Result will be the same independent of the reference frame chosen.
--- End quote ---
Perhaps I should have written that it is vital to choose the correct class of reference frame. In other words, for an unspecified mechanical system, not one of the examples we have been considering, is the analyst free to choose an accelerating or a non-accelerating frame of reference in which to perform his analysis. With the same result being obtained either way?
For instance would it be appropriate to analyse an accelerating car using a non-accelerating frame of reference?
--- Quote ---
--- Quote from: cbutlera on February 10, 2023, 07:07:10 pm ---3) There are two classes of frames of reference, which are the accelerating and non-accelerating frames of reference.
--- End quote ---
For this particular example you can only have acceleration if either input or output wheels slip so unless that happens there will be no acceleration.
The applied force F1 needs to be large enough for slip to happen else if that is less nothing will happen other than belt will be stretched the input wheel will rotate correspondingly with the amount of stretch but vehicle body will not move relative to ground.
If output wheel (left one) slips first then vehicle will be accelerated to the left and F1 the applied force will be F1 = F2 + m*a so sum of 3'rd and 2'nd law.
If input wheel slips (right one) (this is what happens if you have the same type of wheels and and material since the input wheel already rotates and it will slip more easy) the you have F2 = F1 + m*a and F2 can be larger due to belt applying a force inside the vehicle between the vehicle body and output wheel and this force is possible because of stored energy.
As you see from this equations the gear ratio is not involved unless you look at the amount of stored energy as that will depend on the gear ratio.
--- Quote from: cbutlera on February 10, 2023, 07:07:10 pm ---4) In an accelerating frame of reference, objects within that frame obey Newton’s second law of motion.
--- End quote ---
As I mentioned 2'nd law is involved only if you allow wheel slip. And the direction the vehicle is accelerated depends on which wheel slips.
If the vehicle worked the way you think it works there will be no wheel slip but that is not the case in any experimental test where vehicle moves.
--- End quote ---
As a general statement, but not with reference to the current examples, is my statement 4) correct in your view?
So using the accelerating car example, would you agree that an accelerating frame of reference must be used, so that Newton’s second law can be applied?
--- Quote ---
--- Quote from: cbutlera on February 10, 2023, 07:07:10 pm ---5) In a non-accelerating frame of reference, Newton’s second law is not relevant, because nothing is accelerating. In this case, Newton’s third law will apply to every object in that system, so every object in the system will be subject to a net zero balance of forces. In the case of two forces acting on an object they must necessarily be equal and opposite. This is what Newton meant by stating "To every action, there is always opposed an equal reaction”.
--- End quote ---
That is not quite true. It is true that net forces for this particular problem is zero in an non accelerating reference frame.
But if you have a proper (working) gearbox that means 3 points of contact so vehicle body connected to ground. Then the applied F1 will be between vehicle body and input wheel and the F2 will be between vehicle body and output wheel and at 2:1 gear ratio the F2 = 2*F1 and that will be the case in an non accelerating frame of reference.
If not convinced by this think about a balance with fulcrum the third point offset as in image below.
Nothing will need to move for the input force to be smaller than output force and Newton's 3'rd law works here as two separate loops with F1 input force having a pair at the fulcrum and the other pair F2 output also relative to fulcrum.
But example a has no 3'rd point the fulcrum equivalent so with that missing input and output force can only be equal.
--- End quote ---
I can see that now. Your lever and fulcum example clarifies your understanding of Newton's third law to me quite well.
Would you agree that my statement 5) is always true in a non-accelerating frame of reference? Again, as a general statement about non-accelerating frames of reference, not just with regard to this specific example.
--- Quote ---
--- Quote from: cbutlera on February 10, 2023, 07:07:10 pm ---6) Some mechanical systems can alternate between being in accelerating and non-accelerating frames of reference. The analyst needs to take great care here to allocate the correct frame of reference to each moment in time. Inexperienced and even many experienced analysts can get this wrong, and is one of the most difficult skills to master.
--- End quote ---
Yes that is the case here when vehicle moves to the right against the applied force as the vehicle will accelerate in burst many times per second so fast that it looks like smooth motion to the slow human brain.
Maybe it is a difficult skill but as soon as you see a device moving in the opposite direction of applied force you will know that some other energy source is present like in this case a small energy storage device.
Because you know from experience and Newton's 3'rd law that for every action there is an equal and opposite reaction so you can not have an unpowered item like this vehicle pushing with higher force F2 against the applied F1 as that will also violate the energy conservation.
The energy conservation is not violated in this case only because energy is stored so treadmill moves say 1cm while vehicle is not moving at all but this 1cm and the F1 was stored as elastic energy in the rubber band then in the next moment this stored energy could be converted in kinetic energy in the opposite direction and if there was no friction with just this initial energy the vehicle can maintain forever the gained kinetic energy but since there is friction the cycle of charge discharge needs to repeat all the time to maintain an average speed. Speed of this vehicle is not constant but it is not possible for humans to detect that without faster more sensitive measurement equipment.
--- End quote ---
Nominal Animal:
--- Quote from: electrodacus on February 10, 2023, 04:42:57 pm ---The gear ratio makes no difference on how the vehicle performs.
--- End quote ---
I showed you in reply #97 in clear math that it does. Others have tested it, and agree it does. Yet, you insist on asserting that it does not, without any explanation –– except that your single video with an extremely bad choice of a gear ratio somehow proves to you it doesn't.
That is bullshit. We have shown you a number of vehicles that prove the gear ratio makes a major difference in how the vehicle performs. I've shown the exact math, derived from kinematics, which is the simplest form of mechanical analysis, showing it does. Yet, you insist on claiming it doesn't matter, why? Is it because you know it does matter, and that demolishes your argument, and you're not interested in learning, and are here just to try and "win" some kind of word or trolling game?
Gearing ratio 1:1 is a singular point in the math (leads to division by zero) – the vehicle will not work in the cases we're examining here at all then –, and all ratios close to 1:1 are extremely sensitive to wheel-surface friction, inducing all kinds of flexing in the mechanism (because the induced velocities are large compared to the torque available, leading to parts twisting and flexing), leading to incorrect interpretation of what is happening. Ratios far away provide more torque with smaller steady-state velocities, which does not stress the mechanism as much (so no flexing or twisting even with lightweight plastic parts), and show the movement is smooth.
Is the reason you refuse to admit this, that you know it proves your belief and assertions incorrect, and you just don't want to admit that –– because it would stop this language game you like to play here at EEVblog forums?
I don't care about your games one way or another, but I do care about the fact that other people, especially youngsters lacking the education yet, can find these threads by doing a web search using suitable search terms, and may be swayed by your convincing-sounding writing, even though there is no logic, science, or rational thought behind your language. It's exactly the same mechanism charismatic movements and cult leaders gather following, by manipulating others. And I hate that, because it wastes those peoples' time and honest efforts; those youngsters doing the web searches are really trying to learn, and you're deliberately fucking that up for them. I despise your behaviour here for that reason, just like I despise people who smear human excrement on the walls, even if they do it to a building I myself will never visit.
All my efforts in this thread are not for you, electrodacus, even though I don't consider you an enemy, and only want you too to learn. My efforts have been to minimise the long-term negative efforts your language games here are making to others' efforts to learn. Regardless of what do you here to "win" or bolster your ego, you need to remember we're spending our time and effort in this thread, only to minimize the negative effects of your illogical and irrational babble has on others reading these texts. It is quite sad, really.
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