Extrapolate from my answer in #185. As the wheel rotates, the plane's hypothetical forward speed equals circumference/(time/rotation); the conveyor belt's speed must equal this.

The wheels are solidly attached to the plane, so they affect the motion of the plane in the sense that the speed of the plane in relation to the speed of the treadmill will always be equal to the speed of the wheels.

So at some point the wheels are moving faster than the treadmill? And the treadmill must catch up?

And is also identical to a pontoon plane on water, or a ski plane on ice.
The lift comes from the rearward thrust pushing the plane body forward as it 'skates' on the conveyor surface.

If the plane isn't moving forward relative to the ground, then its speed is 0, meaning the treadmill's speed is also 0, but that cannot be the case. The speed of the wheels in the original question was referring to the speed in which they were spinning.

Am I wrong here?

No. Let's say the wheel starts out with point A in contact with treadmill point X. The next instant wheel point A+1 makes contact with treadmill point X+1. Both are in simultaneous motion, both bits are driven back to position A and X.

The plane's speed has no effect on the treadmill's speed.

The plane is only 'skating' relative to the conveyor surface - which is also 'skating' at equal and opposite speed. Neither water nor ice is a perfect treadmill (certainly not ice which doesn't move at all - ski plane on ice relies on relatively frictionless contact with "the ground").

The plane is NOT moving forward relative to the atmosphere and produces no lift.

Motion is relative, remember?


The "plane" INCLUDES the wheels. The wheels are moving. That's where all the energy is going. Spinning the wheels. The wheels are resisted by friction against the treadmill. The treadmill absorbs that energy and moves in the opposite direction.

What makes the treadmill begin to move?

I think this problem is set up with an impossible tautology, just like my rollerskate, moving sidewalk, and tow rope example. You cannot match the speed of the wheels and the conveyor belt because the speed of the airplane is externally set. I believe the author of the problem has done this intentionally to get people to talk past one another.

I will defend this to the end of time:

Put a jet on a tread mill. Once the jet starts rolling, run the tread mill at any real speed and direction (it hast to be a real speed, but even 500 mph would be okay). The jet will take off.

Theoretically, no, unless someone came up and pushed on the treadmill or something.

Ok, am going to word this differently, again.

The planes wheel's clearly have 2 different speeds. The speed in which the plane is moving forward, which I'm going to label as its static speed, and the speed in which the wheels are spinning, which I'm going to call their rotating speed.

If the question is

Imagine a 747 is sitting on a conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the static speed of the plane (you can substitute the word wheels for plane here because the wheels, as part of the plane have the same static speed of the plane), moving in the opposite direction. Can the plane take off?

then you have a case.

If the question is

Imagine a 747 is sitting on a conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the rotating speed of the wheels, moving in the opposite direction. Can the plane take off?

then, you have no case, because the rotating speed of the wheels has no affect on whether or not the plane can move forward or take off.

LOL
i just read a comment here about the plane crash in the ocean near Brazil. Which one of you posted it? LMAO reerun?

That's perhaps the most succinct way of putting it exactly right.

As the thrust comes from the jets exerting force on the air behind, everything concerning the wheels and conveyor are just variations on what happens to molecules in the atmosphere as the jet flys by, or molecules in a lake or ice slab as a pontoon or ski plane takes off.