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Originally Posted by Wisha Haddan H3
A plane is standing on a runway that can move (like a giant conveyor
belt). This conveyor has a control system that tracks the plane's
speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction) instantly.
Will the plane be able to take off?
The question is not flawed. It also never states the plane never breaks from zero speed. It is clear, direct and perfectly logical. Here's why. The conveyor can match the plane's forward velocity in the opposite direction because it is not connected to the airplane in any way, neither by physical attachments nor by forces. Since the airplane rolls on wheels, it can move forward at 100 knots while the conveyor moves backward at 100 knots. The relative speed between the two is 200 knots, and there is no contradiction in either logic or physics. Or the conveyor can move forward with the plane so the relative speed between them is 0 knots. Either way, the plane is moving at 100 knots relative to the air it is pushing through.
There is a logical flaw but it lies in your assumption that the relative speed between the plane and the conveyor determines the relative speed between the plane and the static air around it.
A ground-based conveyor cannot hold back a freewheeling vehicle that uses air for its locomotion. If the scenario involved an airplane in a wind tunnel, a submarine in a water current, a car on a conveyor or any vehicle where the medium of propulsion could be reversed, you would be absolutely correct. But that's not the case here.
The conveyor is a ground-based reversal, but the air around the airplane hasn't been touched. It remains static and the props can pull the airplane through it, causing airflow, lift and takeoff. This is the correct solution to the riddle.
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To me what makes this question interesting isn't just the physics. It's our human approach to the problem. Human experience is ground-based. We see birds and airplanes fly, but we cannot. Whether we walk, drive, skate or bicycle, we depend on forces pushing against the ground for locomotion. So our instinctive approach to this problem is also ground-based.
When we imagine ourselves on a conveyor, we realize that unless we walk on it, it will carry us along. We also realize that if the conveyor matches our walking speed, our position relative to the ground and air next to us will remain the same.
Our experience tells us that if we put an airplane on the conveyor, it will also be carried along, and if it tries to move forward it will also remain in the same place relative to the ground and air next to it. We also know that lift requires airflow, and if the plane's position is stationary relative to the air, there can be no lift and it cannot take off.
We assume all this from our ground-based experience ... but the reality is counter-intuitive.
First, there's the question of friction on the conveyor. When we stand on a treadmill, our feet stick to it through friction and we are pulled along unless we walk. However, the airplane is mounted on wheels that roll freely on it. It does not stick to the conveyor and is not pulled backwards as we would be. Thus, the conveyor cannot hold the airplane back.
Second, there's the question of propulsion. When we walk on a conveyor, our movement results from pushing against the moving conveyor with our feet. However, an airplane doesn't drive on the conveyor using its wheels ... the wheels roll freely over the conveyor, as the props push against the static air above it. Newton's 3rd law allows the plane to move forward, independently of the ground-based conveyor. The wing is drawn through the static air around it and the resulting airflow creates lift, allowing the plane to take off.
Thus, the speed and direction of the conveyor below the plane is irrelevant unless the tires blow.
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