Quote:
"Does the force due to friction increase with speed?". If yes, then there's a belt speed at which the thrust is balanced-out, and the plane doesn't take off. If no, the plane takes off.



I donīt think thatīs true. Once the engines apply thrust to the air, the plane will move forward. And once the plane has moved forward at all, the belt has been defeated as the wheels haved turned faster.

That is unless the belt can go from a standstill to infinity miles per hour instantaneously.