A uniform ladder 5.0 m long rest against a frictionless, vertical wall with its

Question

A uniform ladder 5.0 m long rest against a frictionless, vertical wall with its lower end 3.0 m from the wall. The ladder weights 160 N and its bottom rest on a platform. A man weighing 740 N climbs slowly up the ladder. When the man has climbed 1.0 m along the ladder. Draw a free body diagram for the ladder. Write the equilibrium conditions applied to this situation. Calculate the lever arm for each force Find the normal and frictional forces at the bottom of the ladder. Find the magnitude and direction of the contact force on the base of the ladder.

Explanation / Answer

Let the man climb a distance d up the ladder.
Let the force on the ladder from the wall be F.
This is horizontal and so is equal to the frictional force.
Taking moment about the foot of the ladder:
740d*3/5 + 160*3/2 = 4F
F = 111d + 60
When d = 1, frictional force = 171 N
When the ladder starts to slip:
F = 0.40(160 + 740) = 360 = 111d + 60
d = (360 - 60)/111 = 2.7 m

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