A block is at rest on an inclined plane makin | vedclass

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(C) When a block is placed on an inclined plane,the forces acting on it are the gravitational force $(mg)$,the normal force $(N)$,and the static frict

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$	an 	heta$

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(C) When a block is placed on an inclined plane,the forces acting on it are the gravitational force $(mg)$,the normal force $(N)$,and the static frictional force $(f_s)$.The component of weight acting down the plane is $mg \sin \alpha$ and the component perpendicular to the plane is $mg \cos \alpha$.For the block to be at rest,the frictional force $f_s = mg \sin \alpha$ and the normal force $N = mg \cos \alpha$.The block starts slipping when the angle of inclination reaches the angle of repose,$	heta$. At this point,the static friction reaches its maximum value,$f_{s,max} = \mu_s N$.Equating the forces at the point of slipping: $mg \sin 	heta = \mu_s (mg \cos 	heta)$.Dividing both sides by $mg \cos 	heta$,we get $\mu_s = \frac{\sin 	heta}{\cos 	heta} = 	an 	heta$.Thus,the coefficient of static friction is $	an 	heta$.

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