Originally Posted by Kestrel
The problem only states that the conveyor belt moves backward at a velocity equal to the plane's forward velocity, that's it. The thrust from the engines (to first order) is unaffected by the plane's forward velocity: the engine's always push the plane forward.
The question is whether the conveyor belt will provide enough force to cause the plane to counteract the forward thrust from the engines. If it can, the plane won't move, if it can't the plane moves forward. So, think of this. If I hung the plane from the ceiling using string and roll the wheels by hand. This is essentially what the conveyor belt is doing, it is rolling the plane's wheels. So you might get the plane to sway a little bit, but because the wheel can spin freely, your rolling of the plane's wheels does just that, and doesn't move the plane. The other thing this shows is that the RPM the wheels spin has absolutely no bearing on how fast the plane is moving. So, the conveyor belt exerts little to no force on the plane, and the thrust from the engine allows the plane to accelerates forward.
Umm you are over analyzing man. I know what the question is. You are assuming that the belt can't while when I read it, it is saying it will.
A plane is standing on 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 opposite direction).
Insteads of using speed like you're doing use distance. as soon as the plane moves 1inch the belt will return the plane to it's original position. The belt system will continue to do so no matter how fast the plane tries to accelerate.
That is what the question is saying no?