A ladder of length 5 m is placed against a smooth wall. The coefficient of friction is #mu# between ladder and ground. What is the minimum value of #mu#, if the ladder is not to slip?

Question

The point where the ladder touches the wall is at a height of 4m from ground the ground.

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Answer 1 · 2017-10-09T16:32:29

See below.

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The equilibrium equations are

#H_a-H_b = 0#
#V_a-P = 0#
#P 3/2-V_a 3 +4H_a= 0#
#H_a = mu V_a#

Solving we have

#H_a = (3 P)/8, V_a = P, H_b = -(3 P)/8, mu = 3/8#

then

#mu = 3/8#