If $\mu$ is the coefficient of friction of a rough surface,then which of the following is true?
(1)$-1\le \mu\le1$
(2)$-\infty< \mu< -\infty$
(3)$0< \mu\le1$
(4)$0\le \mu\le1$
Solution:
Since $\mu=\tan\theta,$ where $\theta$=Angle of sliding friction.
and we know from trigonometry that $ tan\theta\in(-\infty,\infty).$So,$-\infty< \mu< -\infty$.
Hence,(2) is true.
Please check my argument.
Thank you
In the equation
$$\mu=\tan\theta$$
$\mu$ is the coefficient of static friction.
The equation tells you what the minimum value of the coefficient of static friction has to be between the object and the incline in order for the object to not slide. It doesn't necessarily tell what the actual coefficient of static friction is. So you should not interpret the equation to mean that the actual coefficient of static friction can approach infinity when $\theta$ approaches 90$^o$. So your "solution" and the conclusion (2) based on it are incorrect.
If you want an idea of the actual ranges of the coefficient of are, check this site: https://www.engineeringtoolbox.com/friction-coefficients-d_778.html
Hope this helps.
