Saturday, March 21, 2009

The Airplane/Treadmill Problem


It's time for a physics/logic problem. This problem has been circulating for a while, and there have been a couple of interesting arguments and an ocean of stupid ones.
Imagine a 747 is sitting on a conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?

The problem is actually sort of bogus. Figuring out exactly what's bogus about it and how to explain it is the real challenge. There are several ways to solve the problem just by saying "physics doesn't work that way", but since they're technical explanations and they're not satisfying answers, I'll go ahead and rule real-world physics out: the wheels are massless and frictionless, and all physics discovered after the year 1900 is off-limits.

I have my own thoughts on how to "solve" the riddle, but I'll give you a chance to look it over and ponder it for a while before I post my "solution".

2 comments:

Eustace Bright said...

Since lift is not generated by the turning of the wheels but by the ratio of lift, which is the creation of relatively higher pressure under the wings compared to above the wings by the passing of air over the specially-curved structure of the wings) to drag, then unless you somehow have all the air in the room magically attached to the conveyor belt I'm saying that bird just sits there.

piahwef said...

...unless you somehow have all the air in the room magically attached to the conveyor belt...
Actually, in some scenarios the air might move in the direction of the belt, but in my scenario (with no friction or anything like it), I don't think you can say for sure whether the air would move enough for liftoff or not.

BTW, I will explain my take on a couple different scenarios (some with more correct physics) along with my "solution", so there's no need to adhere strictly to my description. They pretty much just make the difference between one "cop-out" solution and an ever-so-slightly less "cop-out" solution =).