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Is the coefficient of friction always less than unity? What are the cases in which coefficient of friction is greater than unity?

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Coefficient of friction may be more than 1. It only implies that frictional force is greater than normal force. It does not violate any well established principle. This is in case of silicone rubber.

You can have a look at this at https://simple.m.wikipedia.org/wiki/Coefficient_of_friction

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