Imagine a plane is sitting on a massive conveyor belt, as wide and as 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?
by 
tigueron
ANSWERS: 9
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NO,,the plane is not moving,,only the wheels.
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no the engine would not be running
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then the plane would move backwards and probably crash into something.
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I don't know whether I have interprted your question correctly, and I am not an aeronautical engineer (I work on far more complex machines ;-)) so this is not gospel. If the plane is moving at fast enough speed from the treadmill, the lift generated from the air currents flowing over and under the wing will be enough to create enough lift to allow the plane to take off. The lift is created because of the shape of the wing, forcing air over the top to move faster that the air underneath, causing upthrust. However since the engine is not on, as soon as the plane leaves the conveyor belt, the driving force is lost and so the plane will fall. However if your question means that the plane is not actually moving forwards because of the treadmill runing in the opposite direction, i.e. it's engines are on but the plane is not moving forward due to the treadmill then the airflow over the wings will be negligible, the same as if it was standing still on a runway. So it could not take off.
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It will stay in the same place
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Of course it will fly, you see it makes no difference how fast the wheels are turning it only matters how fast the plane is moving, to build enough thrust. The wheels will be simply turning faster. Once the engines fire the plane is forced forward, the conveyor belt would not restrict forward motion .
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No, if the plane is driving forward and kept in the same place. It needs a lot of wind under the wings to take off.
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If the plane moves 5 mph ahead, the wheels are moving 5 mph ahead, along with the plane. According to the problem, the conveyor would then start to move 5 mph in the opposite direction, producing 10 mph worth of spin in the wheels, as the plane travels 5 mph ahead. If the plane slows to a stop then the conveyor slows to a stop. The conveyor only moves when the plane is moving forward, through the air. As defined by the problem, if the plane and wheels aren't getting closer to the end of the runway, the conveyor doesn't move. If the runway is 1 mile long, the conveyor will move exactly 1 mile in reverse, only because the plane has travelled 1 mile forward to the far end of the runway. If the plane starts moving ahead at 200 mph, the conveyor will start moving 200 mph in reverse again, causing the wheels to spin at 400 mph as they move at a speed of 200 mph forward. But the plane still travels through the air, producing lift, and flies normally. The wheels spin freely and loose, however fast they need to spin. The rotation of the wheel will be twice the speed of the wheel.
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Assuming the engine are running, then it does not really matter if the plane is on a conveyor belt or not. The plane is not driven forward by the wheels. It is driving by the engines which are throwing air out behind them. This creates a force that pushes the plane forward. Also, with respect to flight, the ground speed is unimportant to whether the plane will fly or not. What is important is the airspeed. So, the engines would drive the plane forward regardless of which way the ground underneath it was moving. There might be a small amount of frictions from the wheels slowing the rate of acceleration. However, I doubt that that would be enough to prevent the plane from taking of unless the runway were only just barely long enough for the plane under normal circumstances.
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