Question

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

Answer 1

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`