Question

A book of mass 5 kg rests on a plank. You tilt one end of the plank and slowly increase the angle of the tilt. The coefficient of static friction between the book and the plank is 0.24. What is the maximum angle of tilt for which the book will remain stationary and not slide down the plank?

Answer 1

For the block not to slide, the maximum static friction μ_smg cosθ must at least balance the downslope component mg sinθ:

mg sinθ ≤ μ_s mg cosθ → tanθ ≤ μ_s.

Thus θ_max = arctan(0.24) ≈ 13.5° (about 0.235 rad). The mass cancels and does not affect the result.