Question

The ladder shown in figure has negligible mass and rests on a frictionless floor. The crossbar connects the two legs of the ladder at the center as shown. The angle between the two legs is ${60}^{\circ }.$ The fat person sitting on the ladder has a mass of $80kg$. Find the contact force exerted by the floor on each leg and the tension in the crossbar.

Answer 1

REF.Image.

Solution

The FBD of the system is as

For Equilibrium of fat person

$2\left(\frac{\sqrt{3}N}{2}\right)=Mg$

$\sqrt{3}N=80\left(10\right)$

$\sqrt{3}N=8000N$

For equilibrium of equal leg

in vert. direction

$N^1-\frac{\sqrt{3}N}{2}=0$

$N^1=\frac{\left(\sqrt{3}N\right)}{2}=\frac{800N}{2}=400N$

So, the contact force exerted by

the floor on each leg $\left(N^1\right)$ is 400N.