Quote:
"A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction).
The question is:
Will the plane take off or not? Will it be able to run up and take off?"
|
Quote:
Originally Posted by RP Robotics
The plane could take off.
The only way it would not work is if the conveyer belt was not long enough or there was a strong tail wind. but a plane can not take off without a conveyer belt in thos conditions.
|
Here we go again.
The key to this puzzle is the statement in the initial conditions "This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction)."
As soon as the thrust of the engine pushes the plane forward some small distance (thus it has some speed), the conveyer moves at whatever speed necessary to counteract that speed. It can move at any speed!
So, the force on the plane from the belt is limited by the friction of the wheel bearings. Move that belt at a high enough speed (a fraction of lightspeed, for example) and the force transmitted to the aircraft through the freely rolling wheels will be enough to counteract the force of the engine.
By definition, the plane cannot move because the belt is free to move at any speed, and while the rolling wheels don't transmit a lot of force to the airframe, the force is nonzero and therefore you must account for it.
Oh, in a
real, practical world, you are correct: The plane will move before the belt can reach 0.1c. But, that wasn't the puzzle question...
Don