Tim West asked what was the OP's question. Here is the exact question, copied from the OP:
The question, as written, describes an impossible scenario, but we can only attempt to answer what we are asked.
I wasn't aware of the videos, but having now seen them, I now understand what the OP was trying to ask. The video of the car on the belt clearly shows what happens: the belt is moving at a constant speed, the car is moving forward along the belt and must therefore be going faster than the belt (due to thrust from anywhere but the wheels) and the wheels are moving faster than the belt and the car. When translated into a plane on a belt, the question should have been:
"With take-off thrust set, a plane will take off at 100 kts. The plane is sat on a conveyor belt which will automatically accelerate to a belt speed of 100 kts at the same rate as the aircaft will do, when the pilot selects take-off thrust. Will the plane take off?"
Answer: Yes. The belt will reach 100 kts, while at the same time the plane will reach 100 kts through the air due to the free wheeling tyres, which will be rotating at 200 kts. This is coarsely demonstrated by the video of the biplane on a tarpaulin. Unfortunately, we were not asked this question.
Megawatt, softus, et al. RTFQ.
An aircraft is standing on a very long runway that can move (a conveyor belt). The aircraft moves in one direction, while the conveyor belt moves in the opposite direction. This conveyor belt has a control system that tracks the aircraft's wheels speed and tunes the speed of the conveyor belt to be exactly the same as the wheels, but in the opposite direction. There is no wind. The pilot begins to add thrust to the engines...
Will the plane ever take off?
The question, as written, describes an impossible scenario, but we can only attempt to answer what we are asked.
I wasn't aware of the videos, but having now seen them, I now understand what the OP was trying to ask. The video of the car on the belt clearly shows what happens: the belt is moving at a constant speed, the car is moving forward along the belt and must therefore be going faster than the belt (due to thrust from anywhere but the wheels) and the wheels are moving faster than the belt and the car. When translated into a plane on a belt, the question should have been:
"With take-off thrust set, a plane will take off at 100 kts. The plane is sat on a conveyor belt which will automatically accelerate to a belt speed of 100 kts at the same rate as the aircaft will do, when the pilot selects take-off thrust. Will the plane take off?"
Answer: Yes. The belt will reach 100 kts, while at the same time the plane will reach 100 kts through the air due to the free wheeling tyres, which will be rotating at 200 kts. This is coarsely demonstrated by the video of the biplane on a tarpaulin. Unfortunately, we were not asked this question.
Megawatt, softus, et al. RTFQ.