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Edit: These musings of a drunk man are irrelevant to the question.
Much like the question of what happens if an irresistible force meets an immovable object - the answer is that you can't have a universe that allows both to exist. Thus the question is a philosophical one, not a physics one.
If someone can explain in terms of forces and Newtonian physics what actually happens to the plane and the thrust when you match the wheel speed with the conveyor speed, then I'll be happy. Dismissing it as 'a paradox' is avoiding the answer.
Also chips are "Plant-based" no matter how you cook them.
But at the end of the day, the wheels are going faster than the treadmill, which the question states cannot happen. Despite whatever forces are at play. So yeah, it'll take off, but you haven't read the question.
I don't think it can be described in those terms, because the setup doesn't allow for Newtonian physics to function. But I will try.
1. Plane's engines fire.
2. Pilot increases thrust just enough to break the stixion (sp?)in the wheel system.
3. At this point the thrust from the engines should move the plane forward, so the wheels start to roll.
4. The conveyor instantly matches the speed of the wheels, so the plane doesn't move.
5. The thrust from the engines should still move the plane forwards, so the wheels start to roll faster.
6. Goto 4.
7. The conveyor therefore instantly reaches relativistic speeds trying to achieve 4, which requires infinite force and energy (impossible) otherwise the plane and thus wheels would move faster than the conveyor, which isn't allowed.
8. The conveyor and wheels turn into plasma, destroying the whole setup.
That's the problem - the conveyor is impossible, and this becomes apparent if you put a plane or wheeled rocket or jetcar or propellor-driven car or a trolley you push from alongside onto it. If you put something with driven wheels on it'd all seem fine.
Therefore in a conundrum where the belt matches the plane's speed, the plane moves forward and takes off.
In a conundrum where the belt is supposed to match the wheel's speed, the plane still moves forward and takes off - because - there is only one throttle setting at which the plane's thrust matches the friction of the wheels - and that results in the plane remaining stationary, regardless of belt speed. If the pilot increases the throttles, the plane moves forward (thus temporarily breaking the rule) and the belt operator increases the speed of the belt to match, but the whee..... SHIT SHIT SHIT SHIT SHIT !!!!!! I almost had it !!!
Also chips are "Plant-based" no matter how you cook them.
Sort-of yes.
Either the belt never moves, which is impossible if the engines fire, or it instantly accelerates to infinite speed, which is just downright impossible, or it doesn't match the speed of the wheels, which isn't allowed by the question.
Thus the belt isn't possible. The question isn't possible. That's why your attempts to analyse it from a Newtonian-physics point of view hasn't worked. It's not that the physics is wrong, it's that the setup of the scenario is wrong.
What do I get as a prize ?
Also chips are "Plant-based" no matter how you cook them.
Another experiment you can do at home.
Take a matchbox car tie a string to it with a weight at the end.
Let the weight hang over the table.
Place the car on a mat. Leave the mat stationary the car will move. Now pull on the mat forward (opposite direction to the travel of the rotation of the wheels) The car will still drag its way forward but the wheels will most likely slip.
Pull the mat backwards and the car will still travel forward.
How can the conveyor slow the aircraft down? It can only influence the rotation of the wheels.
I thought we had agreed that this has to be s frictionless scenario otherwise it all falls apart (there is no conveyor belt that can support the weight if a jet in a point loading). Therefore the movement of the conveyor can impart no equal reaction in the aircraft.
So the conveyor stating up only has the inertia of the wheels rotation to overcome it cannot move the aircraft and hence the wheels spin faster, though they still only move at the same speed as the aircraft.
This is why none of you are musicians.
Yes, no conveyor can slow the plane down. However, the question states that the conveyor matches the speed of the wheels, but in the opposite direction.Thus the setup of the scenario precludes the plane's wheels, and thus the plane, from moving.
However, this is clearly impossible. The scenario is impossible because it prevents the plane from moving via a method which could not, in the real world, prevent the plane from moving.
Paradox.
Opposite direction of what?
Nomad
Nobody loves me but my mother... and she could be jivin' too...