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, $\lambda \le {\tan }^{-1}\mu$.

Answer 1

Assuming F be the applied force

R be the frictional force'

R be the normal force

$u=tan\lambda =F/R$

When $F=\mu R$

F is the limiting friction.

When applied force increases, force of friction increases upto limiting friction.

Before reaching limiting friction:

$F<\mu R/F$

$tan\lambda =F/R<\mu R$

$tan\lambda \le \mu$

$\lambda \le ta{n}^{-1}\mu$