What is the reasoning behind µ < 1?

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jack action
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I know the coefficient of friction can be greater than one. But it seems that a lot of people were thought the opposite at some point through the school system. What was the reasoning behind that theory? I can't imagine how you could prove such a statement.
 

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I know the coefficient of friction can be greater than one. But it seems that a lot of people were thought the opposite at some point through the school system. What was the reasoning behind that theory? I can't imagine how you could prove such a statement.

It's a terrible idea to tell students that the coefficient of friction is less than or equal to 1. It's rarely greater than 1, but that doesn't mean it doesn't exist. I know a teacher who once told his students it can never exceed 1, and guess what, they ended up getting a question on their A level exam where the value of μ they were supposed to calculate was actually 1.27. Incidentally, this was the only year in which a coefficient of friction greater than 1 actually appeared on a CIE A level exam.
Anyway, you could imagine how terrible it was for students who obtained the correct answer but ended up erasing their work and wasting a lot of time, all because they were told a myth (or a misquoted fact) by their teacher.
 
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What was the reasoning behind that theory?
Interesting question, and probably no really clear answer. It did include contact area, forbade galling and adhesion (which would have wiped out any basis for proposing the "unit" limit in the first place), and made some strange appeal to intuition based on 45 degree frictionless (of all things) wedges, and it's just as well I can't recall the particulars. It made for entertaining evenings in college, listening to adherents vs. drag racing fans.
 
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