Solve the following :
Question:

The angle between the resultant contact force and the normal force exerted by a body on the other is called the angle of friction. Show that if $\lambda$ be the angle of friction and $\mu$ the coefficient of static friction, $\lambda$ $\leq \tan -1 \mu$

Solution:

Angle of friction, $\tan \lambda=\frac{f f}{N}$

The value of friction force depends upon external force applied. If the body does not move then

$(f f=F)<(f f(I m)=\mu N)$

When body is about to move or moves then $\mathrm{ff}=f_{(l m)}=\mu \mathrm{N}$

So,

$\mathrm{ff}<=\mu N$

$\therefore \tan \lambda \leq \frac{\mu N}{N}$

$\tan \lambda \leq \mu$

$\lambda \leq \tan ^{-1}(\mu)$