MHB Coefficient of friction and effects of

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The discussion centers on calculating tire wear based on the coefficient of friction between a polyester and rubber tire and the road surface. It highlights that while static friction is independent of weight, wear occurs due to slippage, which complicates calculations. Theoretical analysis of this wear is deemed complex, as it would require accounting for various factors, including tire material cohesiveness. An experimental approach to measure wear is suggested as a more practical solution. Overall, understanding tire wear involves intricate relationships between friction, slippage, and material properties.
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Not a question from a college course or anything like that, but one of interest to me:)

You take a car tyre made of polyester and rubber, the treads are cut to about 7mm deep, the roads coefficient of friction are normally about 0.7 in conjunction with contact of the tyre, if the weight is independant of the static friction between the tyre and road surface, how could a calculation be performed to work out how much wear takes place when a tyre rolls along the road surface?
 
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If the tyre were really "rolling", there would be NO friction and so no wear. In order that there be friction, there would have to be some slippage and the friction and wear would depend on the amount of slippage which is not given here.
 
I think it would also depend on the material of the tire itself - its "cohesiveness". I think the formula would be immensely complicated. That is, I think a theoretical analysis would be quite complicated. An a posteriori experimental result would naturally be much easier.
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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