Question

The block shown in the figure is just on the verge of slipping. The coefficient of static friction between the block and table is

Answer 1

The FBDs of the given system is as shown


From the FBD of the block, we have
$N=40\text{N}$
At limiting condition, $f=\mu N=40\mu \text{N}$
$\therefore f=F=40\mu \text{N}$

From the FBD of string-mass system, we have
$T\sin {30}^{\circ }=8$
and $T\cos {30}^{\circ }=F=40\mu$
From above two equations, we have
$\tan {30}^{\circ }=\frac{8}{40\mu }\Rightarrow \mu =\frac{8\sqrt{3}}{40}=0.35$