# The unending streak of circles and sticks

A large number of sticks (with mass density $$\rho$$ per unit length) and circles (with radius $$R$$) lean on each other, as shown in the figure below.

Each stick makes an angle $$\theta$$ with the horizontal and is tangent to a circle at its upper end. The sticks are hinged to the ground, and every other surface is friction less.

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? If you find result as $$S$$ give the as $$[S]$$ , where [.] represents the ceiling function.

Details and assumptions:

• The last circle, i.e. the circle at infinity is leaning against a wall (which has only the significance of stopping the whole system from moving)
• Take $$\rho = 1, R = 15, g = 10\text{ m/s}^2, \theta = 74^\circ$$.
• Every value is given is S.I. system.

Hint: As always, generalize the result for any $$N$$ and then take the limit as $$N$$ tends to infinity.

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