A unifor ladder 5.0 m long rests against a frictionless, vertical wall with its
ID: 1505653 • Letter: A
Question
A unifor ladder 5.0 m long rests against a frictionless, vertical wall with its lower end 3.0 m from the wall. The ladder weighs 190 N. The coeffiencent of static friction between the foot of the ladder and the ground is {u}0. A man weighing 790 N climbs slowly up the ladder. Start by drawing a free-body diagram of the ladder. What is the actually frictional force when the man has climbed 1.0 m along the ladder? A unifor ladder 5.0 m long rests against a frictionless, vertical wall with its lower end 3.0 m from the wall. The ladder weighs 190 N. The coeffiencent of static friction between the foot of the ladder and the ground is {u}0. A man weighing 790 N climbs slowly up the ladder. Start by drawing a free-body diagram of the ladder. What is the actually frictional force when the man has climbed 1.0 m along 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:
790d*3/5 + 190*3/2 = 4F
F = 118.5 d + 71.25
When d = 1, frictional force = 190 N
When the ladder starts to slip:
F = 0.40(190 + 790) = 392 = 118.5 d + 71.25
d = (392 – 71.25)/118.25 = 2.71 m
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