>>11312814Alrightey
The plane is an object on top of the treadmill, but it has a very small coefficient of friction since it has wheels, you can think of it like a box sitting on top of some marbles doesn't take a lot of force to move it around.
Now then, since the wheels are a part of the plane we can safely say that the speed of the wheels = the speed of the plane.
With those parts explained lets see what happens. A force (the turbines) starts pushing the airplane, a friction force will start pushing into the opposite direction of the turbine force since friction always resists change, but since we can be pretty sure that the friction force is smaller than the turbine force we can see that there is a net force into the direction of the turbine force, and therefore acceleration.
Now here comes the tricky bit, the treadmill will start accelerating at the very exact same rate into the opposite question but here's the thing, friction force does not depend on speed, friction is coefficient of friction times force and since neither of those change when we change speed we can see that speed doesn't matter, ie. the speed the treadmill does not matter, even if it were rolling at light speed the friction force would still be the same, not that it will ever get to light speed since the take off weight of a 747 is around 120 mph
To make it short, the plane will accelerate at normal and take off as normal.
