Question

A plank, of length L = 3.7 m and mass M = 19.6 kg, rests on the ground and on a frictionless roller at the top of a wall of height h = 1.70 m (see Figure). The center of gravity of the plank is at its center. The plank remains in equilibrium for any value of theta => 78o but slips if theta < 78o. Calculate the magnitude of the force exerted by the roller on the plank when theta = 78o.

Answer 1

calculating moments about the bottom contact point:
force on wall*L/2*sin78=19.6*L/2*cos78
force on wall= 19.6 ctan78