20-10-09 Leaning sticks and circles

A large number of sticks (with mass density per unit length ρ) and circles (with radius R) lean on each other, as shown in the figure . Each stick makes an angle θ with the horizontal and is tangent to the next circle at its upper end. The sticks are hinged to the ground, and every other surface is frictionless (unlike in the previous problem). In the limit of a very large number of sticks and circles, what is the normal force between a stick and the circle it rests on, very far to the right? Assume that the last circle leans against a wall, to keep it from moving.

Src: Introd to classical mechanics