Equilibrium: Uniform plank rests against a frictionless roller: coefficient of static friction

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Problem:

A uniform plank with a length L of 6.10 m and a weight of 445 N, rests on the ground and against a frictionless roller at the top of the wall of height
h = 3.05 m. The plank remains in equilibrium for any value of theta greater than or equal to 70 degress but slips if theta is less than 70 degrees. Find the coefficient of static friction between the plank and the ground

In this figure we will take L= 6.10 in place of 20 ft and h = 3.05 m in place of 10ft

Solution:

First, the Earth's gravity acts on the plank and pulls it down with a ...