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The relation between coefficient of kinetic friction and static friction is the fact that coefficient of static friction is greater than coefficient of kinetic friction. But does a mathematical relation between these coefficients of friction exist?

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    $\begingroup$ You mixed some words up in your question, can you edit you answer, please. $\endgroup$
    – franz
    Commented Dec 17, 2021 at 8:02

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Each coefficient is determined by experiment by dividing the friction force by the normal force. It is then observed that the coefficient of kinetic friction is generally less than the coefficient of static friction. So the relationship between them is empirically determined. To my knowledge there is no direct mathematical relationship based upon theory.

Hope this helps.

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