What is the Tension in a Ladder Challenge System?

[ashokmittal]

A ladder of length 2a and weight W, with its centre of gravity 3/8 of the way up it, stands on a smooth horizontal plane resting against a smooth vertical wall, and the middle point is tied to a point in the wall by a horizontal rope of length b. Find the tension in the rope.

 

[arildno]

1. "Smooth" means no friction between ladder and wall/floor.
2. Set up the equilibrium equations (all three of them).
Solve for the 2 unknown normal forces plus the tension

 

[Galileo]

Draw a diagram of the situation. Since the system is in equilibrium, the sum of all forces is zero. In addition, there is no net torque about the center of mass either.

The surfaces are smooth, implying no frictional force, but there is a normal force from both the horizontal plane and the vertical wall.