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 = 5.0 kg which is uniformly distributed throughout its length L = 6.5 m. The ladder is propped up at an angle = 72°. The coefficient of static friction between the ground and the ladder is = 0.193, 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 = 3.9 m up the ladder.

A painter wishes to know whether or not he can safely stand on a ladder. The ladder has a mass M1 = 5.0 kg which is uniformly distributed throughout its length L = 6.5 m. The ladder is propped up at an angle = 72°. The coefficient of static friction between the ground and the ladder is ¼ = 0.193, 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 = 3.9 m up the ladder.

Explanation / Answer

Since the ladder is at rest, it satisfies the two conditions of equilibrium : 1) the net forces are zero and 2) the net torques are zero. The forces horizontally are the force of friction (f) and the force the wall exerts on the ladder (call it P). From Newton's 2nd law :

?F = 0 = f

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