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 λ be the angle of friction and µ the coefficient of static friction, λ≤ tan-1µ .

Answer 1

Let the Resultant of the Friction and the Normal Reaction be giving the Force F.

∴ Component of the Force F towards the Normal Reaction = F Cosλ

Component of the Force F towards the Friction = F Sinλ

Normal force R = F.cosλ and frictional force f=F.sinλ  

But the limiting frictional force = µR

=µF × cosλ ,

which will be always greater than or equal to frictional force ,

f = F × sinλ,

∴  f ≤ µR  

F × sinλ ≤ µF × cosλ

tanλ ≤ µ

Hence, Proved.

Hope it helps .