A 8 m ladder of negligible (zero) mass leans against the side of a house, with t

Question

A 8 m ladder of negligible (zero) mass leans against the side of a house, with the bottom of the ladder 2.2 m from the wall. The contact interaction between the ladder and the ground is able to exert a horizontal static friction force of no more that 0.36 mg, where mg is the weight of the person on the ladder. Assume that the contact interaction between the wall and the top of the ladder is frictionless. How high can a person safely climb on this ladder without running the risk of this ladder slipping?

Explanation / Answer

Let: h be the height of the person (measured along the ladder). F be the force of friction at the foot of the ladder. (This will be toward the wall, as the ladder tends to slip away.) R be the normal reaction of the ground at the foot of the ladder, S be the normal reaction of the frictionless wall at the top of the ladder. The meaurements given tell you the ladder is at 30deg. to the wall For vertical equilibrium: mg = R For horizontal equilibrium: S = F ...(2) Given: F

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