The wheel is free spinning, absent a negligent kinetic friction coefficient, the plane's forward motion just makes the wheels spin faster.

The 747 would take off. It's the airspeed of the airplane not the groundspeed. Mythbusters did this one

Its okay to admit defeat.

If it were a plausible scenario, the wheels and treadmill would each spin fast enough that the force from the friction in the wheel bearings would equal the force from the engines. Obviously this is not realistic, but this is what would happen if the treadmill exactly matched the speed of the wheels.

Unless there's wind, the airspeed is the same as the groundspeed.

The conveyor belt is not driven by any motor. It is simply free floating. As the wheels rotate, the belt rotates under them. All the energy is used pushing the belt. The plane isn't going anywhere.

If you've ever had an emissions test, you have seen this in practice.

The plane won't get airborne because with no forward motion, you have no air across the wings, hence no lift.

i apologize, looking back i dont know how i believed it

i really need to think things through before i post
going to try to work on that

Okay:

a) It's not the same scenario, as the mechanics of flight for a bird and a plane are very different, birds do not require air velocity over their wings to generate an upwards force.

b) There is no mechanism in this scenario that causes the rollerskates to have no velocity.

Reversible mixing.

I saw this for the first time a few years ago and was amazed. Click on the video tab.

http://www.stevespanglerscience.com/...e-laminar-flow

unless the plane's brakes are on it doesn't matter what force is applied to them

Ever seen an emissions test with a plane on a treadmill? Didn't think so.

No, but you see your car on a "treadmill" and it doesn't go anywhere - no matter that the speedometer says 60 mph.

It's a stupid question, and in the real world, such a treadmill would not exist, and the answer would be that it couldn't keep up with the plane, and the plane would take off. But, in a world where such a treadmill could exist, the plane would not move, and thus would not take off.

Orange, the difference here is that you are thinking of a car, which uses the wheels pushing off the ground to gain velocity and travel forward.

A plane on the otherhand, its wheels are not connected to anything other than barrings and they spin freely.

The plane doesn't use the ground to move forward, it uses the air.

Sorry, all of it's energy is going to be directed to the treadmill, eliminating the plane's forward motion. Its energy from the engine pushes it forward. The friction between its wheels and the treadmill holds it back. All of that energy is transferred to the treadmill through the friction.

If the system is imperfect, you get some sort of wreck (the wheels come off, the treadmill breaks, etc.) but we're talking about a system that is functioning properly.

For the plane to move forward, the wheels have to move. If the wheels move, the treadmill moves under them and the plane goes nowhere.