Question

A ladder leen again a perfectly smooth vertical wall at angle of 30 to the horizontal.,

A load of 800N placed 3/4 of the way up, the ladder if the ladder rest at a rough horizontal surfaces which prellent shipping. Find the magnitude and direction of the reaction between the ladder and the ground.

Answer 1

The total force at the ground,

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

The reaction at the wall,

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

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

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