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 = 11.0 kg which is uniformly distributed throughout its length L = 9.9 m. The ladder is propped up at an angle ? = 68°. The coefficient of static friction between the ground and the ladder is µ = 0.242, and the wall against which the ladder is resting is frictionless.
a. Calculate the maximum mass of the painter for which the ladder will remain stable when he climbs a distance d = 6.1 m up the ladder.
b. If the painter does not stand on the ladder, what is the minimum angle ? for which the ladder will remain stable?

Explanation / Answer

Let the normal reaction that the vertical wall exerts on the ladder is N this has to be equal to the frictional force that tyhe floor exerts on the ladder let us make the net torque 0 by the point of contact with the ground we have the clockwise torques as mg*6.1cos68+11*9.8*9.9*cos68/2 and anti clockwise torques are µ(11*9.8+mg)*9.9sin68 for the extreme case µ is max and equate that equal to 0.242 and solve b) for this we have 11*9.8*9.9*cos/2

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