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

Question

A uniform ladder 5.0 m long rests against a frictionless, vertical wall with its lower end 3.0 m from the wall. The ladder weighs 160 N. The coefficient of static friction between the foot of the ladder and the ground is 0.40. A man weighing 740 N climbs slowly up the ladder.

a. What is the maximum frictional force that the ground can exert on the ladder at its lower end?

b. What is the actual frictional force when the man has climbed 1.0 m along the ladder?

c.How far along the ladder can the man climb before the ladder starts to slip?

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

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.