As long as the plane is moving at the same speed as the treadmill, then the huge turbine engine might as well be an engine attached to the wheels of the plane. Where do you get the idea of "whether the planes wheels are touching the ground or not"? The wheels are going to start on the ground and they are going to stay on the ground. Without air moving over the airplane, lift will not be generated. Without lift, the plane is going to stay on the ground.
So, theoretically, the plane could start to fly if it was able to overcome -9.81m/s^2 of vertical force (ie. gravity) and sustain it long enough so that the plane would no longer be restricted to a velocity of 0 m/s while on the treadmill AND still be creating the forward propulsion so that it will travel forward. The only planes capable of creating vertical and horizontal force at the same cost billions of dollars and are used by the military.
Please try again.
A plane DOES fly as soon as the accerlative force upward exceeds gravity, lol. All planes exert both a upward and downward force, did you read about bernoulli's principle. Air flowing across the wings, ala the planes horizontial force creates a upward lift "vertical force". Anyway that's off subject, think about this and PLEASE tell me where my thinking is flawed. Actually do the thought experiment. Imagine the forces at work on the plane.
car moves because the wheels spin. They spin around, push against the ground and the car moves forward. If you put a car on a treadmill going the same speed in the opposite direction the car will not move forward. The treadmill pushes one way the wheels push another and the car stands still. That should be fairly apparent and intuitive.
Now let's add 1 thing to that car, lets make it like the batmobile. The force that now moves the car isn't the wheels. We have strapped a rocket to the back. The rocket propels air backwards, which pushes the car forwards. Even if the wheels were not moving at all the car would still move, assuming the rocket could overcome the friction of the wheels grinding on the ground. Now when we put the rocket powered car on a treadmill the wheels forces are still cancelled out. The wheels wont' push the car forward, but the force of the air being expelled by the rocket WILL move the car forward. This is how a plane moves. The wheels arent' what physically drives a plane down the runway, it's the force of the fans displacing air. So despite the fact that the treadmill cancels out the wheels propulsion, the plane will stil go forward. The treadmill speed is irrelavent, unless the thing can spin so fast that the the frictional forces on the wheels can counter the tremendous force of the air being displaced by the engines.
As long as the plane can move forward there is air under the wings moving, hence we get lift....
Overall what you need to realize is that the wheels spinning in a byproduct of the moving plane, not the reason the plane moves, hence the treadmill can counter the wheels all it wants, the plane will still go forward.
The force that causes a wheeled object to move forward on a treadmill is FRICTION. In a frictionless world a person on a treadmill would simply stand in place as the belt moved beneath him. Wheels would remain motionless, etc. The force of friction applies a horizontal force to the wheels as they rotate. A car runs on this priciple. The wheels spin and push against the ground with a force. If the wheels are moving clockwise then this force would be negative. The wheels push backwards. However, the ground pushes back, propelling the car forward. When you hit gravel, the gravel cannot push back hard enough without getting repelled, hence no friction, no movement, just rocks flying backwards, the opposite way you want the vehicle to go. What forces are involved when a car is on a treadmill if the car isnt' moving. No motion means NO NET FORCE. The car isn't moving becuase whatever force is pushing it forwards, is being counteracted by a force pushing it backwards. If we put the car on a treadmill with spinning wheels and no motion we have 2 forces at play. Treadmill vs wheels, wheels vs treadmill. Now tell me what happens when we strap a rocket to the back of that car. Adding another means of movement. We have the plane's fan pushing against air and air pushing against the plane, does the treadmill's movement counter that.. Math can quickly give you an answer...
PS. If what your saying is true then I have great news. All we need to do to stop a plane is put it on a runway that moves backwards.... We could stop the plane as quickly as we liked! After all, we deploy wheels they hit the runway moving backwards at whatever speed the plane is approaching at and BOOM instant landing. The wheels would be spinning at a speed proportional to the speed of the plane, simply match it and according to your theories, we are golden. Something tells me however that since NOTHING is being done to address the non rotational movement forces, we'd find the plane still goes forward. For that matter, how does a plane continue to move once its' wheels leave the ground. IF the wheels force vs the ground is what moves the plane?(according to you it can stop a plane, so obviously it IS the net force, not simply a biproduct of the ACTUAL force....)
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