Question

A block is at rest at the top of a rough inclined plane of inclination ${30}^o$ with the horizontal. What is the coefficient of kinetic friction between the block and the plane, if the block sides down with an acceleration of $\frac{g}{5}$

Answer 1

$\begin{array}{c}\frac{mg}{2}-fr=\frac{mg}{5}\\ fr=\frac{3mg}{10}\\ {\mu }_k.mg\frac{\sqrt{3}}{2}=\frac{\sqrt{3}mg}{10}\\ {\mu }_k=\frac{\sqrt{3}}{5}\end{array}$