Actually, perfect rolling generates zero frictional force opposing the thrust of the jets.

The group paid $27 INCLUDING the $2 in his pocket... and got $1 each back.

Nothing happened to the $1 but bad math.

Again, friction forces don't really enter into it. You WANT high friction, but whatever friction you have is going to apply equally to the wheels and the treadmill.

The operative variable is resistance to the treadmill spinning freely.

No, they paid $27 ($25 + $2 = $27).

He gave each back $1 (x3) = $30 total.

Nothing to see here.

You realize the friction in question is in the wheel bearings, not the tires, right? Besides, those are made of MagicHefium, so no worries there.

I'm not sure you are adding up your forces correctly. The force of the jets is moving the plane forward. The wheel is only spinning because of its frictional contact to the pavement. However, that is partly from the downward force of the weight of the jet along with a component of the forward force. However, the whole force isn't transferred to the wheels, so the treadmill can't counteract all of it.

$30 - $2 (kept) - $3 returned = $25 (meal price).

The original question is flawed (presumably by design).

The friction I am talking about is the friction between the wheels and the ground/treadmill. This is the coefficient of friction.

For dragging you want low. For rolling you want high.

I think orange and I have fundamental differences in how we each view this scenario, so keep that in mind as you are discussing this with us.

This.

Yes, it is. The wheels MUST keep up with the rest of the plane or the plane rotates forward and plunges nose first into the ground.

For the wheels to keep up, they MUST roll or slide along the ground (unless you have a hopping plane). Once you generate enough speed to produce lift, you can then, well, "lift" them off the ground.

Force of jets - rolling resistance = large positive number

(large positive number) / (mass of jet) = acceleration

Lets say after 1 second, the jet is moving at 1 mph.

Jet speed 1 mph and gaining. Wheel speed 1 mph. Treadmill speed = 0.

Now start your treadmill. Run it at 100 mph.

Jet speed 1 mph and gaining. Wheel speed 101 mph. Treadmill speed = 100 mph.

Double the speed of the tread mill, same thing. Meanwhile, the jet just keeps on picking up speed relative to the ground.

The tread mill is just making the jet wheel free spin. The force of the engines cannot practically be overcome by spinning the wheels faster. Just like you can't break the rope by spinning the treadmill faster under the shopping cart. You just can't generate the force.

I guess you're still using a motor to spin your treadmill?

I think we figured that out long ago, when cdcox pointed out the ambiguity I applauded.

You view the hypothetical as inviolable, the way you read the wording the airplane CANNOT be allowed to move forward or the conveyor is failing in it's [ambiguously] stated mission. If a plane can't move forward it can't take off. And if it takes wheels with Herculean rolling resistance sufficient to counteract the thrust of 4 jumbo jet engines so be it.

However, hypotheticals generally assume [unless stated otherwise] negligible or no friction [rolling resistance]. And in that case the interactions of the wheels and the conveyor are akin to those of molecules flowing under a flying craft or in the water or ice under skids or pontoons on a thusly equipped craft, and they are irrelevant in the dominant force of forward thrust by the engines.

Let's not. The jet NEVER MOVES. The treadmill begins spinning at the precise same instant that the wheels start to turn.