Question

A block of mass $15kg$ is resting on a rough inclined plane as shown in figure. The block is tied up by a horizontal string having a tension of $50N$. Calculate the coefficient of friction between the block and the inclined plane.

Answer 1

$M=15kg$

$T=50N$

Equating forces

$f=\mu [T\sin \theta +mg\cos \theta ]$

$mg\sin \theta =T\cos \theta +f$

$f=\mu [50/\sqrt{2}+150/\sqrt{2}]$

$150/\sqrt{2}=50/\sqrt{2}+f$

$\frac{100}{\sqrt{2}}=f$

$\mu \left[\frac{200}{\sqrt{2}}\right]=\frac{100}{\sqrt{2}}$

$\mu =0.5$