Angle of friction: Angle between normal reaction and resultant of frictional force(F) and normal reaction(R) is called angle of friction(\(\theta\))
From OAB tan\(
\theta = \frac{{AC}}
{{OC}}
\)
\(
\Rightarrow \frac{F}
{R} \Rightarrow \mu _s
\) (from law of static friction Fs = µsR)
\(
\mu _s =
\)tan\(\theta\)
Ex 1: The angle of friction between two surfaces is 370 . if cas370=4/5 ,sin370=3/5 coefficient of static friction between those two surfaces is.
Sol : If \(\mu_s\) is coefficient of static friction and \(\alpha\) is angle of friction , tan\(\alpha\)=\(\mu_s\)
The coefficient of static frictions \(\mu_s\)=tan\(\alpha\) =tan370= sin370/cas370=3/4
Ex 2: A horizontal force of 4\(\sqrt 3\)kg.wt is just sufficient to pull a body of 8kg.wt on a horizontal surface. Find the coefficient of static friction between those two surfaces.
Sol: limiting frictional force \(
4\sqrt 3 x9.8N = \mu _s x8x9.8N
\)
The coefficient of static frictions \(
\mu _s = \frac{{4\sqrt 3 }}
{8} = \frac{{\sqrt 3 }}
{2}
\)