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I myself overlooked it too but wikipedia actually happens to have a great such list at https://en.wikipedia.org/wiki/Quantum_gravity#Points_of_tension There are other points of tension between quantum mechanics and general relativity. First, classical general relativity breaks down at singularities, and quantum mechanics becomes inconsistent ...
It is all about the distribution of pressure under the contact. For a block of uniform weight the pressure can be assume almost constant under the area and so when traction is broken it will happen all at once all over with a force of $\mu N$ as you stated. But for other geometries, or for elastic parts (like tires, or marbles or billiard balls on felt) the ...
When you say underinflated tires experience more friction, do you mean static friction (i.e., resistance to slipping) or rolling resistance, which is something quite different? Afaik the origin of the friction law is very much phenomenological, and has it's limits of applicability (especially at the static - dynamic transition). My understanding as to why ...
There are some vital considerations you are not including in your initial analysis. One is the performance and response (due to 'jiggling/vibration' of the tire at low pressure) of the tire depending on its shape.
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