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Newton's third law problem.
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electrodacus:

--- Quote from: IanB on November 25, 2022, 03:58:00 am ---This is faulty reasoning. The movement of the cart has nothing to do with the size of F2 and F1. They don't affect the analysis.

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That is your mathematical approach only. The cart can not move if all forces acting on it are equal and opposite.
In the math model you do not care about physics just geometry so you select an arbitrary distance that you want to move the vehicle and then plot the movement of all parts but in real world there is nothing that can move the vehicle if there is no energy storage and stick slip hysteresis.
IanB:

--- Quote from: electrodacus on November 25, 2022, 04:07:45 am ---The gearbox body is not connected to anything so it is free to rotate with the input shaft if there is enough friction in the front wheel bearing.
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Don't be absurd. The gearbox is fixed to the cart, so it can't rotate unless the cart rotates, which clearly the cart doesn't.


--- Quote from: IanB on November 25, 2022, 03:56:00 am ---So F1 is the equal and opposite force in this setup and so they will always be equal unless energy storage and stick slip hysteresis or some similar trigger for charge discharge exist.

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F1 acting on the wheel has an equal and opposite force F1' acting on the belt the wheel is in contact with. F2 can be anything different from F1, depending on the design of the system, and F2 definitely doesn't have to be equal and opposite to F1.
electrodacus:

--- Quote from: IanB on November 25, 2022, 04:19:40 am ---
Don't be absurd. The gearbox is fixed to the cart, so it can't rotate unless the cart rotates, which clearly the cart doesn't.


F1 acting on the wheel has an equal and opposite force F1' acting on the belt the wheel is in contact with. F2 can be anything different from F1, depending on the design of the system, and F2 definitely doesn't have to be equal and opposite to F1.

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The cart body just happens to be the same with the gearbox body.

There will be no F2 without F1 and if slip is not allowed and there is no energy storage then F2 will be equal and opposite of F1.

This device can be called a cart or a gearbox it just depends on the definition you want to give but there is nothing more than just a gearbox.
It has the input connected to treadmill the output to ground and the body not connected to anything.
IanB:

--- Quote from: electrodacus on November 25, 2022, 04:29:16 am ---The cart body just happens to be the same with the gearbox body.
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And since the cart doesn't fly through the air doing somersaults, we can agree that the cart/gearbox doesn't rotate, right?


--- Quote ---There will be no F2 without F1 and if slip is not allowed and there is no energy storage then F2 will be equal and opposite of F1.
--- End quote ---

There is no law of physics that says this.


--- Quote ---This device can be called a cart or a gearbox it just depends on the definition you want to give but there is nothing more than just a gearbox.
It has the input connected to treadmill the output to ground and the body not connected to anything.

--- End quote ---

Just like car's gearbox then? It has the input connected to the engine, the output to the road, and the body not connected to anything? And yet, somehow, the gearbox in a car works.
electrodacus:

--- Quote from: IanB on November 25, 2022, 04:42:10 am ---And since the cart doesn't fly through the air doing somersaults, we can agree that the cart/gearbox doesn't rotate, right?

--- End quote ---

It could fly if the friction is high enough or the acceleration rate of the treadmill is large enough.
The point is the body is floating.


--- Quote from: IanB on November 25, 2022, 04:42:10 am ---There is no law of physics that says this.

--- End quote ---

It is for this particular gearbox configuration as it is locked basically no different from a rock


--- Quote from: IanB on November 25, 2022, 04:42:10 am ---Just like car's gearbox then? It has the input connected to the engine, the output to the road, and the body not connected to anything? And yet, somehow, the gearbox in a car works.

--- End quote ---

The car gearbox body is connected to the motor stator or engine body.
It is like the treadmill body was connected to this vehicle body instead of the ground.
 
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