A mass of 4 kg rests on a horizontal plane. The plane is gradually inclined until at an angle of 15°

Question

A mass of 4 kg rests on a horizontal plane. The plane is gradually inclined until at an angle of 15° with the horizontal, the mass just begins to slide. What is the coefficient of static friction between the block and the surface?

Professor PC Thomas Classes · Answer

At the angle of repose $	heta$, the component of weight down the plane balances the maximum static friction. $mg \sin	heta = \mu_s mg \cos	heta \implies \mu_s = 	an	heta = 	an 15^\circ$.