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 = 7.8 m. The ladder is propped up at an angle theta = 62o. The coefficient of static friction between the ground and the ladder is mus = 0.40, 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 = 6.8 m up the ladder. (The painter's mass might be so low that only Lilliputian painters can safely ascend the ladder.)

Explanation / Answer

Let m = mass of the man.

Summing vertical forces,

Nfloor - M1g - mg = 0

Summing horizontal forces,

uk Nfloor - Nwall = 0

Summing torques about the floor,

Nwall L sin 62 - M1 g (L/2) cos 62 - m g (6.8 m) cos 62 = 0

Solving for m using these three equations,

m = 29.6 kg [ANSWER]

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