There is a giant, 10 mile long stetch of runway with a 747 on the middle of it. The runway, however, is specially designed to move, much in the same way that a treadmill will move, in the opposite direction of the plane. Secondly, the treadmill is attached to a computer which will match the acceleration of the plane exactly and constantly, in the opposite direction.
What is the result of this experiment? Does the plane ever take off?
Name:
Anonymous2006-11-03 16:04
OK, let's take this step by step. Motion in this frame is relative to the ground.
1) plane is at rest on treadmill
2) plane engines start, creating a forward force on the plane's body.
3) plane begins to move forward, and its wheels begin to turn
4) the computer responds by spinning the treadmill backwards at the same speed the plane is moving forward.
6) the motion of the treadmill causes the wheels on the plane to spin faster than they already were (twice as fast, in fact)
5) the engines are still causing a forward force on the motion of the plane, which accelerates it
6) the computer responds by accelerating the treadmill backwards, to match the acceleration of the plane
7) the wheels are spinning even faster now.
8) GOTO 5
The crucial point is that the motion of the treadmill, though it causes the wheels to turn, is not transmitted to the body of the plane, which accelerates due to the action of its engines.
∴ the plane is in motion relative to the ground, so it is in motion relative to the air around it, so lift is generated by the wings, so it eventually takes off.