I ran across this brain teaser a while ago and I thought I'd post it.
If you built a 100 foot wide, mile long runway that was a conveyor belt that would exactly counter the effect of the wheels on an airplane would the airplane still take off.
How to solve this?
One question to ask is; does it matter if the plane has wheels? Of course not, there are seaplane that use pontoons to take off from the water, and planes can also be fitted with skis for taking off on snow. We could take the physicist take on that matter and set the plane on a frictionless plane instead. So really the wheels are not all that important to the problem.
Plane fly because of the flow of air over the wings that provide lift and the trust of the engines, the drag of the aircraft itself and the force of gravity.
So back to the problem, when the pilot spools up the engines, the plane pushes itself forward, the wheels will move forward slightly, the conveyor with have to move forward slightly to counteract the roll of the wheels, that will still move the plane forward. All the plane wants to do is to move forward so it can have airflow over the wings and that is happening even if the wheels are not moving.
So the plane should take off normally.
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Typically when a problem says something like "exactly counter the effect of the wheels" the first thing to consider what the effect of the wheels is.
So what is the effect of the wheels? To eliminate as much of the friction between plane and runway as possible, allowing the plane to travel forward through the air and by that method gain airspeed for takeoff.
If the conveyor belt exactly matches the speed of the wheels, the plane does not travel forward through the air, so it does not take off. (Unless the conveyor belt creates some sort of wind tunnel effect!)
So, in summary, it is rather important not to assume we're already on a frictionless plane, since that *is* the function of the wheels.
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