Question

A block of mass $15\text{kg}$ is resting on a rough inclined plane as shown in figure. The block is tied up by a horizontal string which has a tension of $50\text{N}$. Calculate the coefficient of friction between the block and inclined plane. Consider $g=10{\text{ms}}^{-2}$

Answer 1

Since the string is under tension, there is limiting friction acting between the block and the plane.

$\sum F_x=0\Rightarrow 50+\mu \text{N cos 45 = N cos 45}$
$(1-\mu )\frac{N}{\sqrt{2}}=50....\left(i\right)$
$\sum F_y=0\Rightarrow \mu Ncos45+Ncos45=150$
$(1+\mu )\frac{N}{\sqrt{2}}=150......\left(ii\right)$
Equation $\left(ii\right)/\left(i\right)\Rightarrow \frac{1+\mu }{1-\mu }=\frac{150}{50}$
$1+\mu =3-3\mu \Rightarrow 4\mu =2\mu =\frac{1}{2}$