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$F = μN$ will fail because of the excessive heat generated if the normal force or the speed of motion gets too big. Why is that?

"$F = μN$, where μ is called the coefficient of friction (Fig. 12-1). Although this coefficient is not exactly constant, the formula is a good empirical rule for judging approximately the amount of force that will be needed in certain practical or engineering circumstances. If the normal force or the speed of motion gets too big, the law fails because of the excessive heat generated. It is important to realize that each of these empirical laws has its limitations, beyond which it does not really work."

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    $\begingroup$ Extreme case: the surface melts, potentially reducing its friction dramatically. $\endgroup$ – eyeballfrog Jun 25 at 2:10
  • $\begingroup$ Thanks, it helps $\endgroup$ – Vivien dong Jun 25 at 2:12
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The friction coefficient, $\mu$, varies with temperature, so if excessive heat is generated, the coefficient would change. This doesn't explain why the relationship $F = \mu N$ would fail, however, as the relationship should still hold under these circumstances.

As a general rule of thumb, empirical relationships tend to fail when excess heat is generated for a variety of reasons, and a common reason is material deformation. In the case of friction, the reason is often surface deformations. A common example is a copper pin sliding on a copper plate, in which the heat generated at high speeds would begin to melt the surface, which will cause $F = \mu N$ to fail since it is no longer a simple scenario in which a solid is sliding against another solid.

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  • $\begingroup$ I could be wrong but I don’t think Feynman is saying the relationship would fail, just the assumption that the coefficient of friction is constant will fail. $\endgroup$ – Bob D Jun 25 at 8:02

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