A block is at rest on a frictionless horizontal plane. As one end of the plane is slowly raised, the block eventually "breaks loose" when the plane makes an angle, $\theta$ , with the horizontal. At this moment the coefficient of static friction is
A) sin $\theta$
B) cos $\theta$
C) tan $\theta$
D) cot $\theta$

Question

Quizplus · Accepted Answer

The coefficient of static friction ($\mu_s$) is given by the ratio of the force of friction to the normal force. When the block breaks loose, the force of friction equals the component of gravity parallel to the plane, and the normal force equals the component of gravity perpendicular to the plane. Thus, $\mu_s = \frac{mg\sin\theta}{mg\cos\theta} = \tan\theta$, making the correct answer tan $\theta$.

A Block Is at Rest on a Frictionless Horizontal Plane θ\thetaθ

A Block Is at Rest on a Frictionless Horizontal Plane $\theta$