A uniform ladder of mass 10 kg leans against a smooth vertical wall making an angle of `53^0` with it. The other end rests on a rough horizontal floor. Find the normal force and the frictional force that the floor exerts on the ladder

Explanation

The force acting on the ladder are shown in ure. They are
a. its weight W
b. normal force `N_1` by the vertical wall
c. normal force `N_2` by the floor and
d. frictioN/Al force f by the floor.
Taking horizontal and vertical components
`N_1=f`.............i
`N_2=W`...........ii
Taking torque about B
`N_1(AO)=W(CB)`
`or, N_1(AB)cos53^0=W(AB)/2sin53^0`

or, `N_13/5=W/2 4/5`
`or N_=2/3W`.....iii
The normal force by the floor is
`N_2=W(10kg)(9.8m/s^2)=98N`.
The frictioN/Al force is
`f=N_1=2/3W=65N`