The speed of the airplane is absolutely not externally set. What is the limit to real speeds? I'll say S(100).

The red part is where I disagree with you. That's like saying that the rotating speed of a shopping cart wheel has no effect on the speed of the shopping cart.

http://upload.wikimedia.org/wikipedi...Resistance.PNG

http://en.wikipedia.org/wiki/Rolling_resistance

So you are telling me that if you lock up the wheels on a shopping cart so they cannot rotate, you cannot make the cart move forward just as fast?

Also a shopping cart has no way to propel itself, unlike a plane.

the conveyor has no ability to counteract the momentum produced by the engines because of the broken link caused by the wheels. because of this, a conveyor of any speed will only cause the wheels to spin faster, while the plane is unaffected

Externally set by the thrust of the jet.
Put it this way, you're standing over a hockey puck sitting on an infinite frictionless conveyor. The conveyor can sense if the puck starts to move in one direction and spin the frictionless surface in the opposite direction. You flick the puck with your finger, what happens?


[and yes, I'm familar with your 'rolling resistance stronger than 4 jet engines gambit' but you know and admit it's BS]. Frictionless/negligible is a very safe assumption.

Well, you can have the wheels skidding across the floor. The issue of whether or not the wheels are skidding on the treadmill is not addressed in the problem, but I have been assuming that they are not. The shopping cart is being pushed by someone rather than being propelled by its wheels, which is somewhat analogous to a jet engine.

Try this MagicHef.

Take a pen and a roll of tape, or a toilet paper roll.

Put the roll over the pencil. Do not spin the roll.

Move the pencil from your left to right. Thats your static speed.

Now bring the pencil back to the left, spin the roll. Thats your rotating speed.

Now do both at the same time. The rotating speed doesn't affect the static speed because there is an outside force moving it (your arm).

This is the same w/ the rotating speed of the wheels. While they are spinning, there is an outside force (the jets or propellers) pushing the plane forward.

Thats the difference between static and rotating speeds (combined with an outside force), and whether or not they affect the plane moving.

Of course, I'm no expert.

No, frictionless is not a safe assumption, and I freely admit that the whole problem is BS. But, if there were a system that met the criteria of the question (which there isn't, and could never be) the plane would not take off.

My plane disintegrated. Is that your argument?

I'm going to take a 400,000 lb 747 and apply 200,000 lbs of thrust to it. What speed do you want to run your conveyor belt at to keep it from taking off?

Do the same with the toilet paper roll being pressed against the ground enough to keep it from slipping. The rotating speed and linear speed are linked quite concretely.

Whatever speed it takes.

But now you are using the ground to push off of to move forward, the plane doesn't use the ground to push off of to move forward, so the rotating speed in this case isn't linked to the linear speed, especially because you are asking what if the linear speed is 0.

If the linear speed is 0, then the rotating speed can be x, y, z, or whatever other number you want to throw out there.

I have no idea what you really mean. The plane's momentum is 0.

p = mv

The plane has no velocity. We start up the engines, energy drives the plane forward. It tries to move forward but it is in contact with the ground. The contact points are the wheels. Friction at the points of contact (i.e. where the rubber meets the road) resists any forward motion of the plane, basically pushing back. Since the contact points can't move forward the wheels spin so a new bit of wheel now contacts a new bit of road.

On the conveyor belt, the "road" also spins like the wheels. The new bit of road is in the same place as the first bit of road. There are now new contact points between new bits of wheel and new bits of road, but the position of these points relative to the surrounding ground is the same as the original position. The plane has not moved relative to the surrounding ground - and more importantly air. The plane's velocity remains 0. The plane's momentum remains 0. The energy that was spent spun the wheels and the conveyor belt.

Rinse and repeat.

No, I'm only using the ground to press down on, much like the weight of the plane is pressing the wheels down on the treadmill. The linear speed does not have to be zero, you can change the linear speed of the pen and you will see the rotating speed change accordingly.