# Metallic Plate on Cylinder (A/B/2/2014)

Classical Mechanics Level 4

A uniform metallic plate of negligible thickness, mass $$2m$$ and length $$4R$$ is twisted in the middle forming a right angle.The twisted plate is then placed on a cylinder of radius $$R$$ which lies fixed (unable to move ) on the horizontal plane. There is static friction between the cylinder and the plate.

The minimum coefficient of static friction $$\mu_s$$ in order the plate to be in equilibrium can be expressed as:

$$\mu_s = \sqrt{a} - b$$

Where $$a$$ and $$b$$ are co-prime square free integers.

Find the value of $$a+b$$

Assumptions

Use $$g$$ , the gravitational acceleration $$9.8 m/s^2$$ if needed.

Note: This problem was part of the Greek National Physics Contest 2014.

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