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,
R_{V} = R - 900 - 750 = 0
R = 1650N ...(i)
Taking moment about the point B,
R × 5sin20° - F_{r } × 5cos20° - 900 × 2.5sin20° - 750 × 3.5sin20° = 0
As F_{r} = µR, and R = 1650N; F_{r } = 1650µ
Putting, value of R and F_{r}
µ = 0.127 .......ANS