Question

The foot of a uniform ladder is on a rough horizontal ground, and the top rests against a smooth vertical wall. The weight of the ladder is 400 N, and a man weighing 800 N stands on the ladder one-quarter of its lenght from the bottom. If the inclination of the ladder to the horizontal is 30 0 , find the reaction at the wall and the total force at the ground.

Answer 1

The total force at the ground,

$N_g=400+800=1200(N)$

The reaction at the wall,

$\Sigma M_{gr}=0:-R\cdot l\sin30°+800\cdot\frac{1}{4}l\cos30°+400\cdot \frac{1}{2}l\cos30°=0$

$R\cdot l\sin30°=800\cdot\frac{1}{4}l\cos30°+400\cdot \frac{1}{2}l\cos30°$

$R=\frac{800\cdot\frac{1}{4}\cos30°+400\cdot \frac{1}{2}\cos30°}{\sin30°}=693(N)$