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plane standing on a runway that can move (conveyer).plane move in one direction, but conveyer move in the opposite direction. This conveyer has control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in opposite direction).
The question:
plane takes off?

No. Please lay off the drugs.
Yika's right. The plane has no air moving under the wings, and therefore cannot generate any lift.
See Bernoulli's theroem, co-efficient of lift etc.
( I trained as an aeronautical engineer - but my job now is on an altogether different plane)
Posted by: mr. eriddle me this gullibies
Gullibies, eh? Are they anything like huckabees? 
I think its Gullifacts told to a person before he sleeps. Gullible Lullabies. Gulliebies. :)
Paul Robeson sang something like..
So lula, lula lula, gullibye bye."
I still think he had the most wonderful velvet voice.
Posted By: PaulustriousSee Bernoulli's theroem, co-efficient of lift etc.
( I trained as an aeronautical engineer - but my job now is on an altogether different plane)
Will the puns ever end?
Sorry, Paul. I'm just playin'
...On words.
Yes the plane will take off of course. The wheel of an airplane does not make it go any faster or slower. It is the thrust from the propellor or jet that gives the forward force.
So as the prop or jet propels the plane forward at speed X, the belt moves at speed X in the opposite direction and just spin the wheels faster. There is a slight reduction in speed due to wheel friction but wheels are designed to have very low friction so it does not matter. If anything, the ground-effect from the moving belt would increase the lift and allow the plane to take off a little sooner.
Imagine the problem another way: what if the conveyer belt was slippery and the plane was on sleds?
The ground effect would actually pull the plane down.
A little experiment. Take a piece of paper, rest your hands on your desk with the piece of paper resting on the back of your hands. Blow sharply underneath the paper. (ie between your thumbs) Instead of rising as you would expect it, the centre will sink down.
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