The plane will not take off people, I can’t believe people are debating this.
Why you ask? The airspeed relative to the wings of the airplane will be zero. For example when this happens in flight, your plane stalls and you fall from the air. You are not going to get off the ground no matter how much thrust those engines put out unless the airspeed over the wings changes.
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The conveyor belt can not prevent the plane from moving. Your error occurs due to assuming that it can because of the wording of the question. The plane would take off.
IEEEEEEEEEEEEEEEEEEE…. Sure, ok lets look at the orginal question:
“Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway. The conveyer belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?”
The plan will not move, no matter how fast it accelerates, because it’s velocity relative to the ground will be zero. No velocity, no lift, no take off.