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So, if you run the conveyor and leave the plane's engines at idle or off, the plane will not move? you're kidding...
Sorry, you are neglecting the difference between dynamic and static friction. In the case you just posed, the airplane will accelerate backwards due to static friction. Once the static friction is overcome, the wheels will begin spinning and the lower dynamic friction will apply. Once that happens, the plane will cease accelerating backwards, but still be traveling backwards.
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The friction in the bearings is still negligible as far as my claim goes, and I continue to use the assumption of a frictionless bearing.
Wait, so you're assuming frictionless bearings now? In that case then yes, moving the conveyor underneath the plane will simply cause the wheels to roll and the plane will not move.
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I am simply talking about the rolling resistance of an inflated rubber tire. If we were talking about a train, you'd be correct. However, the difference between the equations and assumptions for steel on steel and rubber on concrete are too different to compare in a problem like this.
By assuming frictionless bearings, you are removing the temperature increase due to that friction, which is the dominant variable in figuring the coefficient of rolling resistance. Yet you do not eliminate the pressure effect on rolling resistance, which is the lesser variable.
This is an invalid set of assumptions. You can not assume the dominant variable is negligible while figuring in the effects of a lesser variable.