How does the conveyer belt (acting through the virtually frictionless wheel bearings) cancel out the immense thrust of the engines on the rest of the world.
Force from conveyer belt (regardless of speed) acting on plane is close to zero.
Force from engines acting on air behind plane = huge
huge - close to zero = huge, and therefore the plane accerates relative to the ground beneath the belt.
Sure, but in that case it isn't even a question worth asking. Of course a plane moving forward at more than take-off speed will take off. The "Straight Dope" link includes a few comments on the other (more interesting) variation though.
Lift of a plane is generated by the wing angle against the moving air and air speed difference above and below the wings. Mostly notably the wing angle. If the lift of those is bigger than the force downwards (gravity), it gets up. Simple as that.
It doesn't matter how many engines, wheels, conveyers etc you have. So it is down to the air/wind speed. That's why aircraft carriers turn towards the wind when they launch aircraft (to increase lift and shorten the takeoff distance). Some light aircraft can (theoretically at least) fly backwards relative to ground if the wind is hard.
What does it matter WHAT drives the plane?
Imagine this:
The plane is at a standstill, on a treadmill which doesn't move.
The plane starts its engine, so it starts to move. The plane will go forward, which makes the wheels rotate, and the treadmill matches the speed the wheels have. Thus the plane is still at a standstill.
The plane tries to accelerate more, the forward movement of the plane makes the wheels turn faster, again, the treadmill matches this speed.
So it keeps standing still
And if the plane is standing still, it doesn't generate lift, so it won't take off.
Don't you realise, that the force moving the plane does not come from the wheels which ultimately means that it doesn't matter how fast the belt is going, the plane will allways take off.
The easiest way to explain it is with what Jack said, the planes engines act although someone is pushing the plane. The wheels are not linked up to any sort of engine so they roll freely, so long as the wheels can withstand double the speed of a normal takeoff then the plane will allways take off as normal.
As said before, the wheels are a insignifect factor in the force giving the plane speed, they are only there to reduce the friction.
EDIT - Of course the real issue is that chances are the bearings wouldn't survive double take-off speed - iirc take-off speed for the planes I would class as "normal" is 200 MPH - assuming that it would still take 170 MPH to take off, the wheels would be going at 400 MPH - while I imagine this wouldn't be an issue for the ultra-strong aeroplane tyres (which are designed to go from 0-200 MPH in a fraction of a second, and to freeze totally), that could pose an issue for the wheel bearings.
I think the whole introduction was flawed. Or at least not properly defined what exactly it ment.
From the intro it could have been understood the plane is kept still relative to the ground (somehow), but actually it just matches the wheel rotation speed (I guess).
Lift is generated by air speed relative to the plane, so even if the plane stationary relative to GROUND, there can still be lift if there is 'wind'. Besides some planes do not even have an engine - sail planes. So certainly if there wouldn't be wind (relative to ground) and the plane is not moving (relative to ground) for what ever reason, it cannot get up (unless the engine is so powerful it can lift the plane alone).
It doesn't mention what sort of plane, but model planes have often very much power compared to it's mass and its engine can often lift it up from almost standstill. If it is a plane with tail gear (not nose gear), the engine is pointing slighlty upwards, so the engine generates lift even without air speed. At an extreme think Harrier or Osprey - neither needs any other lift than the one from the engine
About tyres: Yes, I think the most stress comes from the fact that they have to accelerate from 0 to the landing speed in a fraction of a second. Especially large passenger aicraft tyres have to take the acceleration, relatively high speed (heavy planes have often high stall and landing speed), heavy mass and high temperature and pressure changes. I don't know if the landing gear rooms are pressurised or heated in space shuttle but I would assume tyres take one heck of a beating anyway.
Apparently a "good pilot" will get around 750 takeoff/landing "cycles" from a Tyre, although iirc they don't replace them at that point they just "resurface" them. Always wondered why they don't spin them up first, as pictures like the one i've attached (taken by me in Germany) really don't look good for the tyre.
The riddle posted in the first post is NOT clear enough to formulate a definite answer.
"This conveyer has a control system that tracks the planes speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction)."
The ending of this line states that the conveyor will be moving at the same speed the plane is, but relative to what?
It does not define if the plane's speed is measured from the conveyor, or from a relative point on the "ground" (the observer).
Way to over complicate things. Assume that it's in laymans' terms, and as such the speed is relative to the world at large (absolute speed if you will).
It's perfectly clear if you read it for what it is - a little puzzle.
I know it's not but it has to have air speed or else no lift thats why flaps help them to take off the air resistance builds up due to the speed forcing the plane into the air.
The "Straight Dope" link includes a few comments on the other (more interesting) variation though.
