HAY /sci/, logic problem!

There is a giant, 10 mile long stetch of runway with a 747 on the middle of it. The runway, however, is specially designed to move, much in the same way that a treadmill will move, in the opposite direction of the plane. Secondly, the treadmill is attached to a computer which will match the acceleration of the plane exactly and constantly, in the opposite direction.

What is the result of this experiment? Does the plane ever take off?

>>40
the plane is broken?

>>31
>>32
so now the question is whether the treadmill takes into account the additional thrust provided by the jet engines. Assuming it does, the plane still won't take off

lol poor trolling

http://www.michaelbuffington.com/articles/2006/02/09/conveyor-belts-airplanes-skateboards

OK, let's take this step by step. Motion in this frame is relative to the ground.

1) plane is at rest on treadmill
2) plane engines start, creating a forward force on the plane's body.
3) plane begins to move forward, and its wheels begin to turn
4) the computer responds by spinning the treadmill backwards at the same speed the plane is moving forward.
6) the motion of the treadmill causes the wheels on the plane to spin faster than they already were (twice as fast, in fact)
5) the engines are still causing a forward force on the motion of the plane, which accelerates it
6) the computer responds by accelerating the treadmill backwards, to match the acceleration of the plane
7) the wheels are spinning even faster now.
8) GOTO 5

The crucial point is that the motion of the treadmill, though it causes the wheels to turn, is not transmitted to the body of the plane, which accelerates due to the action of its engines.

∴ the plane is in motion relative to the ground, so it is in motion relative to the air around it, so lift is generated by the wings, so it eventually takes off.

>>45
Thread over.

as the plane's wheels move faster, the treadmill moves faster, and that just keeps going on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on (so nothing ever happens with the wings or body so nothing happens) and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and then it explodes because its going so god damn fast

On paper: the plane will take off
Real life: Unknown, depends on how fast the wheels will be spinning when the 747 pushes off. If the computer matches the acceleration of the airplane then the treadmill will keep going faster and faster in proportion to the velocity of the plane, up to unreal levels for even a small change in position of the plane. Airline wheels are not meant to stand up to that kind of abuse, they would burn out and snap before the airspeed needed for liftoff was acquired.
Actually though, its far more likely that a huge complex treadmill will breakdown more easily than a simple airplane wheel, so my hypothesis is the plane will take off, as the runway will jam before the wheels and the backward counterforce will be eliminated.
It all depends on what breaks first.

>>45
6) the motion of the treadmill causes the wheels on the plane to spin faster than they already were (twice as fast, in fact)
lol wut how
the conveyor belt responds to the plane's speed, not the other way around, so the conveyor belt does not cause anything to turn. Rather the wheels turn the conveyor belt.

Jet engines will not do anything extra, as the force must be translated through the wheels, which are obviously resting on the ground.

You seem to believe that the plane is somehow not able to move backwards, should it be slower than the treadmill

>>49
The treadmill starts moving in response to the airplane doing so, but the treadmill only succeeds in moving the plane's wheels faster.

>>50
no the plane moves the treadmill faster

I went to the airport, they have no fucking treadmill

>>51
You have no idea what you're talking about.

The accumulated stupidity of this thread is threatening the stability of the planet.  Please stop.

The computer matches the acceleration. F=MA, therefore the computer will turn the treadmill fast enough so the wheels of the aircraft provide enough resistance to resist the thrust of the jet engines.

The wheels will have to maintain enough acceleration to provide this resistance. It will spin faster and faster and this will result in the rubber of the tyres and axil of the wheels and the treadmill melting causing them to fall apart. Most likely the treamill will fall apart first.

>>55
"the computer will turn the treadmill fast enough so the wheels of the aircraft provide enough resistance to resist the thrust of the jet engines."

NO. The horizontal velocity of the portion of the treadmill under the plane moves in the exact same velocity as the plane, but in the opposite direction. This DOES NOT STOP THE PLANE YOU FUCKING RETARDS.

THE PLANE EXPLODES

>>56
The explanation is ambigious. Does it mean the treadmill itself of the belt part of the treadmill?

If were were to assume it means the treadmill then I am right. If we were to assume it means the belt, then the wheels will spin twice as fast, but the aircraft will accelerate.

ambiguous*

Yeah, it depends on how you define the speed. If the speed of the plane is relative to the ground or air, well the treadmill doesn't move relative to either so the plane will move (although i dunno if it will take off). If the speed is measured relative to the belt on the treadmill, then the plane won't go anywhere.

A 747 will have some kind of GPS tracking device, so it's probably the former definition. However if you measured speed by a speedometer similar to a car (speed of wheels turning) then it would be the latter example.

Nevertheless friction plays a part. A plane moving at x groundspeed will receive friction in its wheels at twice the speed. Also the faster the plane goes, friction will be reduced because some of the air going under its wings will lift it up. Will it fly? lol i dunno

>>58
Why would it be a TREADMILL if the ENTIRE THING was going to move backwards? Read between the lines you dimwit.

>>61
yes its not common sense but if you look at the question it doesn't make sense either
the treadmill is attached to a computer which will match the acceleration of the plane exactly and constantly, in the opposite direction
a treadmill cannot match the acceleration of plane exactly and constantly if the plane is moving off it

>>62 again
i mean the treadmill can't match the plane exactly because a treadmill only moves around in cirlces.

>>62
Oh my god, you're failing so hard.
Listen:
The plane moves forward with velocity v(t) (along the tread) at time t. The computer controls the treadmill so that the velocity of the portion of the tread under the plane at time t is -v(t). The tread is finite and you'd run into problems at/near the end of the tread, but that doens't matter since if the plane is moving it would take off long before then.

Furthermore, even if it was actually the whole treadmill - and not just the belt - moving backwards, the plane would still take off for exactly the same reason. More generally, the movement of the ground doesn't matter (except as an engineering problem because of possible high heat from friction and such) unless the vehicle accelerates by using an engine to rotate its wheels, as a car does. If it uses a jet engine or a propeller, the wheels will simply move faster to account for the movement of the ground.

>>64 again
"the wheels will simply move faster" should read "the wheels will simply rotate faster".

>>64
i agree that the plane would still move forward if it overcame the friction, but i was just pointing out the badly worded problem
i'm not >>58 btw

>>45 here. I'm assuming that this problem is theoretical, so we can take the conditions as ideal; i.e. the treadmill is as long as we need it to be, the wheels can rotate without friction, etc.

For a physical case, yes friction, size, structural integrity and all that come into play (and are dominant), but they are practical complications and not relevant to the issue at hand.

The plane can move relative to the ground and the air around it, so it can take off.

>>67
Truth, alright let's leave the thread now, everyone.

>>68
An excellent plan.