A painter wishes to know whether or not he can safely stand on a ladder. The lad

Question

A painter wishes to know whether or not he can safely stand on a ladder. The ladder has a mass M1 = 14 kg which is uniformly distributed throughout its length L = 8.6 m. The ladder is propped up at an angle theta = 59 degree . The coefficient of static friction between the ground and the ladder is mu s = 0.38: and the wall against which the ladder is resting is frictionless. Calculate the maximum mass of the painter for which the ladder will remain stable when he climbs a distance d = 6.4 m up the ladder.

Explanation / Answer

Let the mass of the person be m Contact force ground = N1 contact force wall = N2 we get N1 = mg + 14*9.8 = mg + 137.2 Horizontal equilibrium = .38 * (mg + 137.2) = N2 = .38 mg + 52.136 Rotation equilbrium about point of contact mg*6.4 sin 59 + 14*9.8*4.3sin59 = [.38 mg + 52.136 ]* 8.6 sin 59 solving we get solve to get the value of mg

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