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 mfrom 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 weighing740 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

Given datas are:

Length of the ladder=5 m

Weight of the ladder=160 N

Coeffecient of friction=0.40

Weight iof the man=740 N

Consider the man climb a distance d up the ladder

The force on the ladder from the wall be F.

Frictional force is acting horizontally and the force is also 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

Lower end is 3m

a)So the maximum frictional force=111*3+60=393 N

b)When d = 1, frictional force = 171 N

c)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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