# Minimum Force

Three weightless rods of length $$l$$ each are hinged at point $$A$$ and $$B$$ lying on the same horizontal and joint through hinges at points $$C$$ and $$D$$ (shown below).

The length $$A$$$$B$$ $$=$$ $$2$$$$l$$. A load of mass $$m$$ is suspended at hinge $$C$$.

Determine the minimum force $$F$$ applied to the hinge $$D$$ for which the middle rod remains horizontal.

If $$F$$ can be described as $$\dfrac{mg}{k}$$, determine $$k$$

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