Why does normal force help find kinetic/static friction coefficients?

I am confused why the normal force can find the kinetic/static friction coefficients. If anyone can help me understand why, that would be much appreciated.

Easy Math Editor

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Comments

Suppose you had a block of mass $m$ sitting on a rough surface. The maximum possible static friction force is:

$F_{max} = \mu \, N = \mu \, m g$

You could apply a horizontal force to the side of the block. Start with a very small force and increase it gradually, keeping track of the magnitude of the applied force at all times. The block starts to move when the applied force is equal to $\mu \, m g$ . Divide the value of the applied force at that instant by $m g$ to get the static friction coefficient.

Steven Chase - 1 year, 10 months ago

So is there some mathematical/scientific proof for this direct proportionality, or was this discovered by repeated observation? I don't quite understand why these two forces going in completely different directions different directions relate to one another. I hope you understand my question. Thank you for the assistance.

Dacota Sprague - 1 year, 10 months ago

I think the coefficients are determined empirically. And I agree that it is not entirely obvious that the friction should be proportional to $N^1$ rather than $N^2$ , for example.

Steven Chase - 1 year, 10 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$