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

Question

A uniform ladder 5.0 m rests against a frictionless, vertical wall with its lower end 3.0 m from the wall. The ladder weight 720 N the coefficient static friction between the foot of the ladder and the ground is 0.4 . A man weighing 180 N climbs slowly up the ladder. Start by drawing a free body-diagram of the ladder. What is the maximal frictional force when the man has climbed 1.0 m along the ladder? A uniform ladder 5.0 m rests against a frictionless, vertical wall with its lower end 3.0 m from the wall. The ladder weight 720 N the coefficient static friction between the foot of the ladder and the ground is 0.4 . A man weighing 180 N climbs slowly up the ladder. Start by drawing a free body-diagram of the ladder. What is the maximal frictional force when the man has climbed 1.0 m along the ladder?

Explanation / Answer

= cos^-1(3/5) = 53.13 deg

h=sqrt(5^2 - 3^2) = 4

By Newton’s second law along horizontal,

Ff = Fn2 ……………..(1)

Applying law of conservation of torque at the bottom of the ladder,

Fn2*h - mgxcos - Mg*L/2*cos = 0

Fn2*h = mgxcos + Mg*L/2*cos

Fn2 = (mgxcos + Mg*L/2*cos)/h

Fn2 = (180*cos53.13 + 720*2.5*cos53.13)/4

Fn2 = 297 N

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