The original question stated that the treadmill rotates exactly proportional to the speed of the wheels. It doesn't matter that airplanes get their forward motion from thrust, the treadmill's still going to turn. Again, no forward motion, no fly. Now, if the wings made their own relative wind, like a real aircraft (helicopter), then we'd have flight.
The real question is, where do my socks go when I do laundry?
The original question stated that the treadmill rotates exactly proportional to the speed of the wheels. It doesn't matter that airplanes get their forward motion from thrust, the treadmill's still going to turn. Again, no forward motion, no fly. Now, if the wings made their own relative wind, like a real aircraft (helicopter), then we'd have flight.
The real question is, where do my socks go when I do laundry?
The question does not say the speeds are proportional. If it did, I think nearly everyone would have said yes it will fly. What it did say was that the treadmill moves backward at the SAME speed as the tires. But that is impossible once the plane begins to move. (If the plane is moving forward, the wheels will, by definition, be spinning forward faster than the treadmill moves backward - ignoring skidding.)
To the pilot, you missed the comment I just relayed. It isn't addressed in your commentary. And though I believe your answer is right, it is not the right answer to this question. It turns out there is no right answer to this question because the question is improperly drafted so that it presents an immediate infinite scenario (wheels and treadmill quickly accelerate to infinite speed as the treadmill hopelessly tries to keep up).
Now are there people out there that think that by retracting the cable into the winch, and therefore pulling the bike forward (much like a propeller or jet engine would do in the case of aviation) that the bike would still not move forward???
Yes it will move the bike forward, but the wheels of the bike would have had to been spinning faster than the treadmill to make it move forward.
It doesn't matter that the engines aren't directly related to how fast the wheels turn. The fact is, as stated in the orginial question, the plane will not make any forward movement.
As a plane accelerates on a stationary surface (runway) what happens to the wheels at the pilot gives it more throttle? They spin faster. Now think of the conveyor as the runway. Say at 3/4 throttle the wheels travel 10m/s. Now stick that plane on the conveyor that is traveling at 10m/s. The plane wont be moving anywhere. Now accelerate to 20m/s... the conveyor will match that same speed causing the plane not to still not be moving.
These recent arguments are what I kept banging my head upon (1105, thank you for the encouragement - I felt like I had to be missing something and that I was the only one not seeing things in that perspective). It seemed to matter-not what was propelling the plane because ANY forward motion (no matter the source) had to go through the wheels - and the motion of the wheels was being met equally in the opposite direction via the treadmill. This was with me being only hung up on the wheels.
The points brought up by Mike (quite eloquently and logically, IMHO) and others interested me because while I still envisioned the vessel not moving absolutely in the X-direction (see paragraph above), it didnt seem unreasonable at all (this viewpoint had to be made by folks smarter than I because it takes into account so many other factors. Remember, I'm simpleminded). I figured I must be simply missing the proverbial boat (I get most concepts, but there have been some that I simply had to accept by convention because I couldn't wrap my mind around something).
I'm still hinky on it - I see all sides and still like my original stance because it simply makes sense to me (and likely only me). And in a way, I think everyones' right - by all of their various perspectives and definitions. Oh, and the original question is invalid.