Not much force there. The plane would not feel much tug on the wheels at all. Not enough to matter.
How much force or resistance do the wheel bearings and tires have when you land a plane. Not enough to stop it. How much do they have when you take off, not enough to hold it back. How much would they have on a conveyor, not enough to hold it back.
The conveyor would not reach anything near "light speed" unless the plane was able to reach lightspeed because the conveyor will only go as fast as the plane can go and the wheels will only go twice as fast as either. Most small planes takeoff with around 70-80 knots of airspeed.
So, the plane sits still on the conveyor. The pilot starts the engine and releases the brakes, the plane starts to roll because the prop is pulling it forward through the air. As it starts to roll forward, the conveyor starts backward. The plane rolls forward at 5 knots of airspeed, the conveyor rolls back at 5, the wheelspeed is 10. This goes on up until the plane reaches 80 knots of airspeed, the conveyor is going 80 knots backwards, the wheels are going 160 knots. These figures assume no headwind.
How hard is this anyway.
Not to complicate it more but if the question was formed to mean that the conveyor matched the wheelspeed of the plane and not the airspeed or groundspeed of the plane, then the conveyor would never move. So I guess it is true that if the conveyor matched the "wheelspeed" of the plane, the plane could not ever move because as soon as it started to roll, some unknown, magical, question generated force would stop it. As a matter of fact, the whole question would be null because if the plane isnt able to move, the conveyor would not move either and it would be nothing more than a plane sitting still on the runway, not moving. This is where the second explanation in the link starts to break down. Why would the conveyor start "tugging" in the first place. Its only job is to match the speed of the plane. If the planes wheels arent rolling, the conveyor isnt moving. If the planes wheels where to ever start rolling, guess what, the whole plane is moving, now we are back to the plane moving and it will take off.
Heres the question as it is stated "as the plane moves the conveyor moves but in the opposite direction.the conveyor has a system that tracks the speed of the plane and matches it exactly in the opposite direction." It clearly states that the conveyor matches the PLANES speed.