Undergrad Understanding forces on a balanced ladder

[issacnewton]

Hello

I have a question about the explanation given for the attached image about the balanced ladder on a wall. At the end the sentence says that, "Consequently the frictional force F at A passes through O". I am not able to understand why this is so. Can anybody please shed light on this statement ?

Thanks

 

[Stephen Tashi]

In an equilibrium situation, the net torque (about any point) of the applied forces is zero. For example, we can pick a point P on the page off to left of the diagram and unconnected to anything by a physical lever. If we draw imaginary levers from P to the points A,G,and B and compute the net torques on those imaginary levers cause by the forces at A,G, and B, then the net torque will be zero.

If we look at the point O, the net torques about O should be zero. The torques about O exerted by the forces W and R are zero because those R acts directly along the imaginary lever drawn from O to point B and W acts directly along the imaginary lever drawn from O to G. For the sum of torques to be zero, the torque exerted about O by force F must also be zero. Hence F must act directly along an imaginary lever drawn from O to A. This implies the direction of F is along the line AO.

 

[issacnewton]

Thanks Stephen... makes sense