Static friction resists relative motion. The maximum friction force before slipping is $F_{\max }={\mu }_{s}N$, where ${\mu }_s$ is the coefficient of static friction and $N$ is the normal force. For a block on an incline with no other forces, $N=W\cos \theta$ and the component of weight down the incline is $W\sin \theta$. At impending slip, $W\sin \theta ={\mu }_{s}N={\mu }_{s}W\cos \theta$, so $\tan \theta ={\mu }_s$.

Notation: ${\mu }_s$ = coefficient of static friction, $N$ = normal force, $\theta$ = angle of incline from horizontal.

A block of weight W rests on a rough incline. The coefficient of static friction between the block and the incline is μ_s = 0.35.

Find:

The maximum angle θ (in degrees) that the incline can have before the block is on the verge of slipping.

Maximum angle before slipping: $\theta \approx 19.3°$ (from horizontal).