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

Question

1. A painter wishes to know whether or not he can safely stand on a ladder. The ladder has a mass M1 = 10 kg which is uniformly distributed throughout its length L = 6.8 m. The ladder is propped up at an angle theta = 62o. The coefficient of static friction between the ground and the ladder is mus = 0.35, 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 = 4.7 m up the ladder. (The painter's mass might be so low that only Lilliputian painters can safely ascend the ladder.)

Explanation / Answer

a) normal force exerted by floor N = M'g + m*g

b) force exerted by wall on ladder Nw = u*N

net torque = 0

Nw*L*sin theta = (m*g*d*costheta

us*(M'+m)*g*L*sintheta = m*g*d*costheta + M'*g*(L/2)*costheta

0.35*(10+m)*6.8*sin62 = m*4.7*cos62 + 10*3.4*cos62

2.101*(10 + m) = 2.207 m + 15.962

m = 47.662 kg

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