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Originally Posted by PARAGON
That's not true. Newton's law of motion states that the rocket or plane wants to stay still. As power is applied, as soon as it wants to start to roll, the conveyor moves, sending the motion back to a zero point.
That's where the conundrum lies with this version of the question. The plane can really never get up to any speed because it can't get past zero simply due to the limitations of the question IF you make certain assumptions OR it will take off IF you make other assumptions.
If the speed of the plane will always be instantaneously matched, the forward movement of the plane will never increase relative to it's surroundings.
If the plane starts to move at x MPH and instaneously the belt moves it -X MPH, the body of the plane remains still and actually does not move from a math standpoint.
But, assuming it's not a fictional question and the plane can move past this fictional "barrier of movement" then, as the plane increases it's speed, the plane is moving through the air and the belt is moving beneath and theoretically moving the wheels twice as fast.
That's why there were apparently different versions of the question. The one here was too vague and allowed for the No answer to be argued. The ones Bluehummer posted, that said speed relative to the wheels, changes the whole argument and allows the "body" of the plane to move without respect to the wheels.
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Thank you for the coherent explanation. The only flaw in your evaluation lies in your application of the 3rd law of motion. "For every action there is an equal and opposite reaction".
A car on the conveyor would behave exactly as you describe, since its forward motion is dependent on the force its wheels apply to the conveyor surface. The wheels turn, exerting rearward force on the conveyor belt. The conveyor rolls, absorbing the force and negating forward motion relative to the ground next to the conveyor and the air around it. In other words, although the car moves forward relative to the conveyor, it remains stationary relative to the ground and air.
However, an airplane doesn't have drive wheels. Its forward motion depends the force of the props applied directly to the air. The props turn, exerting force on the air. As air is pushed rearward, the props are pushed in the opposite direction and the plane moves forward through the air, rolling over the conveyor's surface. Meanwhile the conveyor tries to spin, as if to counteract the forward motion of the plane, but the plane's wheels roll freely over it at higher and higher speeds. As the props push air rearward, the wings slice through the static air around the plane until the airflow over the wings produces enough lift for takeoff.
Nothing can stop the plane from taking off unless the tires blow out. Then, the extra friction between the landing gear and the conveyor could crash the plane or slow it down enough to prevent takeoff velocity.