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Force multiplier
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cbutlera:

--- Quote from: electrodacus on February 12, 2023, 01:21:02 am ---
--- Quote from: cbutlera on February 12, 2023, 01:08:21 am ---
That may or may not be true, depending on the circumstances.  The tension meter is one body with several forces acting upon it.  Newton’s third law applies to "the mutual actions of two bodies upon each other". It has no relevance to the forces acting on any one body.  You cannot use Newton’s third law to conclude that the forces applied by the rope on either side of the tension meter are the same. 

Remember, the tension meter has a mass, and the rope has a mass per unit length.  The rope and tension meter may or may not be accelerating.  You cannot assume that they are not accelerating.


Well I know that it is possible, because mechanical analysis shows that it is possible, and as I mentioned in another message, as a child I once had a toy that worked exactly that way.  So I have seen experimental evidence too.

--- End quote ---

That drawing is a bit bad as the string is not perfectly horizontal so yes the gravity will play a role in case you consider string has mass since the the connection at the wall that is higher will see a larger force due to gravity acting on the string.

If you replace the newton meter with mechanism in case (a) so spool the string on the wheels and also keep the string perfectly horizontal so there is no gravity involvement then nothing will move.
The reason nothing move is because you eliminate the ability to slip at both wheels.
...

--- End quote ---

That has nothing to do with it.  Please read what I wrote above again.

You are trying to answer the question, will the tension meter (or some gearbox in its place) move?  If it is starting from rest, and if it is going to move, it will have to accelerate.  So the question becomes will it accelerate?  If it does accelerate, the net force acting upon it will not be zero.  So you cannot assume that the net force acting on it is zero, and then conclude from that that it cannot accelerate.  That is circular reasoning.

You didn't reply with any further Newton's third law force-pairs in the book resting on a table example, beyond the two that you mentioned previously.  I can tell you if you really can't do it, but it would be much better if you could identify them for yourself.
electrodacus:

--- Quote from: Nominal Animal on February 12, 2023, 01:48:07 am ---Before I look at your question, please specify what your astrological sign is?

--- End quote ---
:)


--- Quote from: Nominal Animal on February 12, 2023, 01:48:07 am ---It does not matter, because it applies to your setup.  \$G \gt 0\$ for a direct belt, \$G \lt 0\$ for a twisted belt.

It even applies to chain and gear gearboxes, with \$G\$ being the input:output turn ratio.

I must say, electrodacus gives a completely new meaning to the term dodgy.
I bet if they were to spout their theories outside in the rain, they'd manage to not get wet; they dodge so much.

--- End quote ---

In my setup a 2:1 gear ratio means for each full rotation of the input wheel (right) output wheel will make half of a rotation.
Both wheels in my setup have the same diameter the sprockets have different diameters.

A direct or twisted belt will make no difference in the gear ratio only the direction the wheel rotate.
All gear ratios and belt configurations result in a locked gear except for the 1:1 gear ratio with and twisted belt.

So no matter the gear ratio with direct belt the vehicle can not move without wheel slip.
The gear ratio is relevant when input wheel slips as at that point the energy stored in the belt powers the vehicle F3 = F4 but offset due to gear ratio thus it can move the vehicle oposited to F1 direction.


So ignoring forces in case (a) and looking just a kinematics (so like pushing the vehicle body relative to ground and having a freewheeling treadmill )
For a 2:1 gear ratio you have

X = 1m relative to ground
Y = 2m distance the input treadmill surface moved relative to ground.

In your example it seems you considered the input wheel diameter half of the output wheel diameter and that is not what it happens in case (a) with both wheels having the same diameter so input wheel needs to make 2 full rotations while the output wheel just makes one.
 
electrodacus:

--- Quote from: cbutlera on February 12, 2023, 01:51:24 am ---That has nothing to do with it.  Please read what I wrote above again.

You are trying to answer the question, will the tension meter (or some gearbox in its place) move?  If it is starting from rest, and if it is going to move, it will have to accelerate.  So the question becomes will it accelerate?  If it does accelerate, the net force acting upon it will not be zero.  So you cannot assume that the net force acting on it is zero, and then conclude from that that it cannot accelerate.  That is circular reasoning.

You didn't reply with any further Newton's third law force-pairs in the book resting on a table example, beyond the two that you mentioned previously.  I can tell you if you really can't do it, but it would be much better if you could identify them for yourself.

--- End quote ---

case (a) is nothing more than a gearbox with floating body.
Due to the way the belt is connected in case (a) and the place the forces act on it, it is a locked gearbox thus there will be no acceleration if wheels are not allowed to slip and if you use a string then they can not slip thus it will not move.
The net force will be zero and there will be no acceleration.
If we use a twisted belt instead then there will be acceleration so during acceleration period F1 = F2 + m*a so both Newton's 3'rd law and 2'nd law are involved.

I'm not really interested in the twisted belt or variant just the the direct belt connection of case (a).
That mechanism can not accelerate unless slip is allowed and the use of strings will eliminate any slip thus nothing will accelerate unless you consider the small rotation of the wheel while the belt is stretched but that will be all.
Only when that case (a) is on a surface and it can slip it will be able to move.

As mentioned if you disagree I can do a video as I still have that toy car somewhere.
cbutlera:

--- Quote from: electrodacus on February 12, 2023, 02:33:24 am ---
--- Quote from: cbutlera on February 12, 2023, 01:51:24 am ---That has nothing to do with it.  Please read what I wrote above again.

You are trying to answer the question, will the tension meter (or some gearbox in its place) move?  If it is starting from rest, and if it is going to move, it will have to accelerate.  So the question becomes will it accelerate?  If it does accelerate, the net force acting upon it will not be zero.  So you cannot assume that the net force acting on it is zero, and then conclude from that that it cannot accelerate.  That is circular reasoning.

You didn't reply with any further Newton's third law force-pairs in the book resting on a table example, beyond the two that you mentioned previously.  I can tell you if you really can't do it, but it would be much better if you could identify them for yourself.

--- End quote ---

case (a) is nothing more than a gearbox with floating body.
Due to the way the belt is connected in case (a) and the place the forces act on it, it is a locked gearbox thus there will be no acceleration if wheels are not allowed to slip and if you use a string then they can not slip thus it will not move.
The net force will be zero and there will be no acceleration.
If we use a twisted belt instead then there will be acceleration so during acceleration period F1 = F2 + m*a so both Newton's 3'rd law and 2'nd law are involved.

I'm not really interested in the twisted belt or variant just the the direct belt connection of case (a).
That mechanism can not accelerate unless slip is allowed and the use of strings will eliminate any slip thus nothing will accelerate unless you consider the small rotation of the wheel while the belt is stretched but that will be all.
Only when that case (a) is on a surface and it can slip it will be able to move.

As mentioned if you disagree I can do a video as I still have that toy car somewhere.

--- End quote ---

There is no Newton's law of the locked gearbox. There is no Newton's law of the slipping wheels.  You just keep quoting your own made-up laws of mechanics as if they represent some kind of proof.

Again, you haven't replied with any further Newton's third law force-pairs from the book resting on a table example.  So I can only assume from that that you don't know, and yet you claim to be an expert on that subject.  I'll give you a clue, gravity is involved.  Now can you list any more of the force-pairs?
electrodacus:

--- Quote from: cbutlera on February 12, 2023, 02:53:30 am ---
There is no Newton's law of the locked gearbox. There is no Newton's law of the slipping wheels.  You just keep quoting your own made-up laws of mechanics as if they represent some kind of proof.

Again, you haven't replied with any further Newton's third law force-pairs from the book resting on a table example.  So I can only assume from that that you don't know, and yet you claim to be an expert on that subject.  I'll give you a clue, gravity is involved.  Now can you list any more of the force-pairs?

--- End quote ---

Seems like you are changing the subject but fine.
A locked gearbox is no different from a solid object so if you apply a force at one end and the other end is constrained like say tied to a wall then net force can only be zero.

I don't even care if someone even heard of Newton as long as it can predict what happens in cases (a) to (c)

The answers I here from people that answered here is gearbox so force multiplication or just completely ignoring forces and using kinematics only.

If that was to be true a 1:1 gear ratio will still have the wheels rotate and that is just not the case. So invalidating your claims can be as simple as showing that gearbox will not move.
But a kinematics only model will predict that wheels rotate at same speed since is like applying a force to the vehicle body relative to ground with a freewheel treadmill.
So none of your theories can predict what happens when you perform the test as it needs to make correct prediction independent of gear ratio.
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