A ladder weighing 20kg wt rests with its one end against a smooth vertically wall and the other end against the smooth floor. If the inclination of the ladder to the horizontal is 60^(@) then calculate the horizonatl force required at the lower end so that is does not slip.

A ladder weighing 20kg wt rests with its one end against a smooth vert

1.	A ladder weighing 20kg wt rests with its one end against a smooth vertically wall and the other end against the smooth floor. If the inclination of the ladder to the horizontal is 60^(@) then calculate the horizonatl force required at the lower end so that is does not slip.
Answer» SOLUTION : `BE=AE=L/2` `cos60^(@)=(AB)/(AC)` `:. Bar(AC)=bar(AB)costheta^(@)=L/2` `sin60^(@)=BC//AB` i.e., `bar(BC)=bar(AB)sin60^(@)` `bar(BC)=0.866L` `cos60^(@)=(AD)/(AE)` i.e., `bar(AD)cos60^(@)=L/2xx1/2=L/4` Taking moments about 'B' We write `Hbar(BC)+Hbar(DC)=R_2bar(AC)`,but AC-AD=DC Moment of `R_1` about B=O `:. H(0.866L)+20xxL/4=20xxL/2"":.bar(DC)=L/2-L/4=(2L-L)/4=L/4` `0.866HcancelL=20(cancelL)/4=5"":.H=5(0.866)=5.774N`