Question

The coefficient of static friction between a block of mass $m$ and an incline is ${\mu }_s=0.3$.
(a) What can be the maximum angle $\theta$ of the incline with the horizontal so that the block does not slip on the plane?
(b) if the inclined makes an angle $\theta /2$ with the horizontal, find the frictional force on the block.

Answer 1

(a) For no slip condition

Gravitation force component must be less than maximum Friction force

$mg\sin \theta \le \mu mg\cos \theta$

$\tan \theta \le \mu =0.3$

$\theta \le {\tan }^{-1}0.3$

(b) When angle is less than slipping angle than. Friction force equal to the gravitation force component.

Friction force $=mg\sin \left(\theta /2\right)$