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Originally Posted by PARAGON
The logic simply eludes you.
You are making an assumption to come to your conclusion. An assumption that is not offered by the question.
tracks the plane's speed
plane's speed relative to what? Relative to the conveyor? Airspeed, relative to the surrounding air?
The plane's speed relative to anything but the air is irrelevant to lift. The conveyor system can track whatever it wants and move the conveyor at any speed forward or backward. It wouldn't matter because the plane freewheels over its surface and propels itself by pushing static air.
If it's airspeed, the very point at which the plane breaks the hold (There is no hold - nothing attaches the plane to the conveyor) and theoretically begins to move, the conveyor would be moving it backwards (How? nothing attaches the plane to the conveyor) and the wheels would never rotate and the plane would remain stationary. (The wheels would roll but their rotation is irrelevant - they don't move or drive the plane) The plane is not being held stationary by any physical force, it's being held by the question. (False, the question does not create a scenario of zero velocity.) You have to assume that the plane starts to move and rotate the tires for the plane to gain airspeed. (Not so. the wheels are irrelevant except as a friction reducer between the plane and runway ... the same outcome would hold if it were a seaplane on pontoons over an ocean current, or on skis over a moving ice floe. Besides, if the conveyor followed the plane, the wheels wouldn't move either, but the plane would nonetheless move forward through the air, creating lift.) Well the question limits this assumption because one can make an assumption that allows for a different answer, therefore the question is flawed in that it allows for a yes and an no answer. (The assumption you say I "have to assume" is based on a false premise - the premise that the motion of a conveyor belt under a freewheeling air-powered vehicle can affect its linear motion)
If you can't see the simplicity of logic. I can't help further. (Right back at you, brother  )
You have to go and make it "fit" into |
One more analogy and I'm done ...
Imagine a moving sidewalk like those at the airport. If you walk in the direction of the movement, you travel at double your walking speed relative to the windows next to you. If you walk in the opposite direction, you remain stationary relative to the windows.
Why? Because the source of your motion is your feet pushing on the on the walkway thanks to friction.
Now, put on a pair of roller skates. I'll walk next to the moving sidewalk and pull you onto it with a rope. No matter what direction we take on the sidewalk, you will travel at the speed I'm walking. If we travel with the sidewalk, your wheels won't roll, because I'm walking as fast as the sidewalk. If we travel against it, the wheels will roll twice as fast as if I was pulling you over the carpet.
Why? Because the source of your motion is no longer your own feet "attached" to the conveyor through friction ... it comes from my feet exerting force on the stationary floor next to you while you freewheel on your skates.
Or if you like, I'll tie the rope to the wall and you can haul yourself up the rope towards me. The source of your motion is no longer me, it's you ... exerting force on the rope connected to the stationary wall. The moving sidewalk can speed up, slow down or stop, but it doesn't matter. Your motion relative to the windows next to you depends on your arms pulling the static medium of the rope tied to the wall while your skates freewheel below you.
Likewise, an airplane exerts its force directly on the static air around it ... not on the ground. The conveyor under the wheels can do what it wants (regardless of the sensors or relative speed) because the plane's engines are acting on the air while the tires freewheel below it. The plane's motion relative to the air around it depends on its engines pushing the wing through the static air, thus creating airflow and lift.
Consequently, the plane absolutely can take off within the parameters of this question as stated.
Have a nice day and thanks for the brainteaser. This was great!
