Can the Plane Take-Off?

[ahecht]

Originally Posted by greencactus3

yes.... except one thing.
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).

so. laws of wear and tear and motor output of either engine(plane or conveyor) ignored, but friction not ignored, the conveyor belt spins fast enough that the friction of the wheel bearings keep the plane from accelerating. so if the conveyor really can turn exactly the same speed(but in the opposite direction) of the plane, the plane would not be accelerating. relative to the conveyor belt it may as well be going almost the speed of light but since the conveyor belt is going the opposite way at almst the speed of light, the plane doesnt move....

Ahh, I see where the confusion is here. The problem states that the speed of the conveyor is exactly the same as the speed of the plane. If this is the case, the plane will take off with no problems. However, you are interpreting the problem as saying that the conveyor is moving at exactly the same speed as the surface of the wheels (relative to the plane).

In a car, where the interaction between the wheels and the road provide the forward motion, these two are equal. However, in the case of an airplane, these aren't necessarily the same.

If the conveyor moved as the same speed as the surface of the wheels, the plane would probably not take off because as soon as the plane started moving, the speed of the wheels would always be larger than speed of the conveyor, and you would get the belt up to an infinite speed, and the friction would be providing an infinite force backwards (this is all assuming, of course, that the wheels don't slip at all, which they would far before the force equalled infinity ).

However, since the problem clearly states that the speed of the plane is being matched, Ken (and the others on that side) are correct.