Entroper said:
@drkohler, the plane will move forward, not just roll forward. Remember, the plane's engines, whether they're jet or prop, are thrusting against the air, not the treadmill. Your comparison with the car is invalid, because the car's method of propulsion is by its wheels pushing against the treadmill. |
Well the problem is worded in a way that assumes the plane does _not_ move forward....
Maybe the car thing was more confusing the matter than resolving it. We must take care of the reference frame we look at (and let's say our reference is somebody standing still at the conveyor belt) where the plane is initially:
Assume the plane engines do not work but the conveyor belt runs backward at speed x. What happens? Of course, the plane will be moving backwards at speed -x of the conveyor belt (assuming friction holds the plane on the belt). Its wings are also moving backwards with speed -x in relation to us and the still air surrounding us, therefore creating downward momentum (and increased friction) since the plane moves backwards so the wings 'point in the wrong direction'.
Now assume the plane's engines run and it rolls forward exactly with the speed +x of the conveyor belt, on the moving belt. Its relative velocity to an observer standing next to the belt is now -x (from the belt) + +x (from the plane), so -x +x = 0, the plane is stationary to an observer - and therefore stationary in relation to the air surrounding the observer.
However, the working engines themselves now move air backwards in reference to the wings at a velocity z (z is high enough to achieve a forward roll movement with speed +x). It now depends on where the air comes from and where it goes to. If we somehow glue an engine to the wheels, the air sucked into the engine and expelled behind it 'never sees the wings' - therefore it does not create any vertical momentum (assuming the engine is glued horizontally onto the wheels, otherwise we have built a rocket, not a plane). If the air flow from the engine is along the wings (as is the case with a propeller engine), it creates upward momentum on the wings and the plane will, in fact, lift off the belt when it surpasses lift-off speed.
That's my take and I stick to it 
