# Sliding Rod

A uniform rod of mass $$m$$ and length $$l$$ is placed vertically on the smooth horizontal floor. Now the rod is given a slight push so that it starts falling.

Find the Normal Reaction that the ground applies on it as a function of angle $$\theta$$ that the rod makes with the horizontal.

$$\large{N (\theta) = \frac{mg [a {(\sin\theta - 1)}^{b} + c]}{{( d - e{(\sin\theta)}^{2})}^{f}}}$$

Enter your answer as $$a + b + c + d + e + f$$

Details and assumptions:

• $$0 < \theta < \dfrac{\pi}{2}$$.

• There is no friction between the contact surfaces.

• Neglect air dra .

• Calculate the Normal reaction before the collision takes place.

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