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No. In the thought experiment, the conveyor is moving forward relative to the ground at the same speed as the plane, in order to keep the wheels stationary.
The plane is propelled forward by the engine thrust alone, how it is supported is completely irrelevant.
"Take these three items, some WD-40, a vise grip, and a roll of duct tape. Any man worth his salt can fix almost any problem with this stuff alone." - Walt Kowalski
"Only two things are infinite - the universe, and human stupidity. And I'm not sure about the universe." - Albert Einstein
Like a bent version of Zeno's paradox, it leaves reality way behind by making the word 'exactly' a logical constraint.
Think about what the wheels are doing, powered or unpowered. If the conveyer is going 1000mph then, for the plane to move forward at 1mph, the wheels MUST be going at 1001mph (or the rpm equivalent). The question states that the two must be equal. The plane cannot move forwards. It is tethered to the conveyor.
Regardless of the wheel/conveyor situation, the plane's engines will pull it through the air. Assuming the plane is not tethered to anything, this means it would move forwards.
when that happens, either it falls off the front of the conveyor, or the conveyor is conceived in such a way that it can move parallel to the ground, or the conveyor is so long that the plane would travel along it.
The fact of whether or not the wheels rotate is entirely independent from the speed of the air passing over the wings, and the speed of the engines. This is the in the example and also in real life - they rotate on a real plane during takeoff because the plane is moving along the runway, not that other way around.
Thanks for the education @Maynehead !
Another theoretical factor is that the wheels would not turn at all without any forward movement provided by the jet and forward movement had already been shown to be "impossible" since the wheels cannot turn relative to the ground.
The jets would fire, the wheels would not move, the conveyor wouldn't move. Or, the wheels would instantly turn at infinite rpm and so would the conveyor. It is, indeed, a paradox.
For a body to lift away from the earth's surface there needs to be a component of force in the upwards direction that exceeds the downwards force (i.e. exceeds the mass of the body multiplied by the earth's gravity).
If there's no lift from the wings (because there's no forward motion and no wind) then the jet engine would at least have to be angled with respect to the horizonal and a produce a sufficiently large component of force in the upwards direction to overcome the mass times gravity (as would be the case for a rocket).
Being that thrust is a much higher force than drag, it should be able to take off, but to get forward motion the wheels still need to be going faster than the conveyor in the opposite direction. Since the question states they always go at the same speed the plane can not achieve forward motion under this condition.
I think it's a bit of a trick question, the conveyor would have to be going extremely fast to increase drag enough to match the thrust of the plane. In a real world scenario (not that a plane on a conveyor belt is very real whatever way you look at it) thrust would overcome the drag of the wheels on the belt, unless the belt went at an implausibly fast speed.
If the wheels were tougher or not finite the movement of air from the engines (the air in the experiment is stationary) would push the plane off the belt and away.
Think of the air as being like water and a wheeled boat being half submerged with its prop pushing it forward against the conveyer.
Ahem...
https://blog.xkcd.com/2008/09/09/the-goddamn-airplane-on-the-goddamn-treadmill/
2) Even if a system were to exist which DID generate drag, that drag would and could be overcome by extra thrust. Look at a seaplane taking off, there's tons of drag yet it is able to overcome this and take off (and land successfully) on water in not-ideally-smooth conditions.
Which is because there is no discussion if you understand how planes work.
I'm almost sure it's been practically demonstrated with a light plane and a flatbed lorry simulating the 'conveyor', anyway. The plane takes off.
"Take these three items, some WD-40, a vise grip, and a roll of duct tape. Any man worth his salt can fix almost any problem with this stuff alone." - Walt Kowalski
"Only two things are infinite - the universe, and human stupidity. And I'm not sure about the universe." - Albert Einstein
Funny how accurate it is:
"So, people who go with interpretation #3 notice immediately that the plane cannot move and keep trying to condescendingly explain to the #2 crowd that nothing they say changes the basic facts of the problem. The #2 crowd is busy explaining to the #3 crowd that planes aren’t driven by their wheels."
Dude, I've been with you from the start. We are #3 crowd.However, as I mentioned, this is more of a thought experiment than a practical one, and assuming the wording in the question is taken at face value, the plane cannot take off, as a speed differential between that of the wheels and the inverse of the belt cannot be achieved.
By the way, I haven't read any of the internet blurb, but as soon as I thought it through thoroughly this was the only logical conclusion.
Supportact said: [my style is] probably more an accumulation of limitations and bad habits than a 'style'.