Mechanics Marathon 2 -Sliding Plank

A uniform plank of length 2a and weight W rests with its middle point upon a rough horizontal cylinder with radius r and angle of friction x whose axis is perpendicular to the plank. find the greatest weight that can attached to the one end of the plank , without sliding it off the cylinder .

r x 2 a r x W \frac{rx}{2a-rx}W r x 4 a r x W \frac{rx}{4a-rx}W 2 r x a r x W \frac{2rx}{a-rx}W r x a r x W \frac{rx}{a-rx}W

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