In the figure a uniform plank with a length L of 786 m and a

In the figure, a uniform plank, with a length L of 7.86 m and a weight of 653 N, rests on the ground and against a frictionless roller at the top of a wall of height h = 4.70 m. The plank remains in equilibrium for any value of ? = 70.0° or more, but slips if ? < 70.0°. Find the coefficient of static friction between the plank and the ground.

Solution

mu_s = (L * sin² theta * cos theta) / (2h - (L * sin theta * cos² theta) )

= (7.86 * sin² 70 * cos 70) / (2 * 4.70 - (7.86 * sin 70 * cos² 70) )

= 2.37 / (9.4 - 0.863)

= 0.278