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Force multiplier
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electrodacus:

--- 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.

If you disagree I'm ready to spend some time finding the toy vehicle and do a short video demonstrating that.
Of course I can make changes to case (a) and allow motion but the particular case (a) is discussed. How it works is relevant else you may not be able to do a correct prediction.
electrodacus:

--- Quote from: jonovid on February 12, 2023, 01:11:56 am ---my father had one for lifting engines out of cars.
endless chain block

--- End quote ---

Yes it has 3 points not just 2 so of course it can do force multiplication.
jonovid:

--- Quote from: electrodacus on February 12, 2023, 01:23:12 am ---
--- Quote from: jonovid on February 12, 2023, 01:11:56 am ---my father had one for lifting engines out of cars.
endless chain block

--- End quote ---

Yes it has 3 points not just 2 so of course it can do force multiplication.

--- End quote ---
life your self in a cage  = 2 points
electrodacus:

--- Quote from: jonovid on February 12, 2023, 01:35:19 am ---life your self in a cage  = 2 points

--- End quote ---

Points of contact on which forces can be applied.
You can not do force multiplication with only two points as in that case the forces can only be equal ignoring any acceleration force.
If you have 3 points then you can use the 3'rd point as a leverage in order to be able to do force multiplication.
Nominal Animal:

--- Quote from: electrodacus on February 11, 2023, 10:15:50 pm ---
--- Quote from: Nominal Animal on February 11, 2023, 09:04:40 pm ---
--- Quote from: electrodacus on February 11, 2023, 04:11:33 pm ---I will not say that 2:1 is anywhere close to 1:1. I will understand if it was 1.1:1 but not 2:1
--- End quote ---
That is because you do not understand the kinematics here.  Review the math in my reply #92.  In your vehicle, the wheels are the same size, \$r = R\$.  Per your definition, gear ratio \$G = 1/\lambda\$.  Using \$x\$ for the vehicle speed right, and \$y\$ for the treadmill surface speed left, kinematics analysis shows that
$$x = y \frac{\lambda R}{r - \lambda R} = \frac{y}{G - 1} \quad \iff \quad \frac{x}{y} = \frac{1}{G - 1}$$

Instead of testing these, you rely on your hand-eye coordination and a single video clip as "proof".  That is not science, it is religion.

--- End quote ---

Before I look at your math please specify how are the two wheels connected in your setup ?
--- End quote ---
Before I look at your question, please specify what your astrological sign is?

It does not matter, because it applies to your setup.  \$G\$ is the gear ratio.  \$G \gt 0\$ for a direct belt, \$G \lt 0\$ for a twisted belt.
For belt pulleys, \$G = d_\text{driven} / d_\text{driver} = N_\text{driver} / N_\text{driven}\$, i.e. the ratio of the diameter of the driven wheel to the diameter of the driver wheel, or equivalently the number of rotations of the driver wheel per driven wheel rotation.

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.
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