Find the coefficient of friction between ladder and floor, Mechanical Engineering

Find the coefficient of friction between ladder and floor:

A ladder of 5m long rests on horizontal ground and leans against smooth vertical wall at an angle of 70° with the horizontal. The weight of ladder is 900N and acts at middle. The ladder is at point of sliding, when the man weighing 750N stands 1.5m from the bottom of ladder. Calculate the coefficient of friction between ladder and floor.

Sol.: Forces acting on ladder is shown in the figure

By resolving all the forces vertically,

 

1417_Find the coefficient of friction between ladder and floor.png

RV = R - 900 - 750 = 0

R = 1650N                                                   ...(i)

Taking moment about the point B,

R × 5sin20° - Fr  × 5cos20° - 900 × 2.5sin20° - 750 × 3.5sin20° = 0

As Fr = µR, and R = 1650N; Fr  = 1650µ

Putting, value of R and Fr

µ = 0.127              .......ANS

Posted Date: 10/18/2012 2:39:03 AM | Location : United States







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