Question

The ladder shown in figure has negligible mass and rests on a friction less floor. The crossbar connects the two legs of the ladder at the middle. The angle between the two legs is 60°. The fat person sitting on the ladder has a mass of 80 kg. Find the contanct force exerted by the floor on each leg and the tension in the crossbar.

Answer 1

The forces acting on different parts are shown in figure. Consider the vertical equilibrium of “the ladder plus the person” system. The forces acting on this system are its weight (80 kg) g and the contact force N + N = 2 N due to the floor. Thus

2 N = (80 kg) g or N = (40 kg) (9.8 m/s²) = 392 N

Next consider the equilibrium of the left leg of the ladder. Taking torques of the forces acting on it about the upper end,

N (2m) tan 30° = T (1m)