Question $5$

A $52m$ gate, $AB,$ is hinged at A and is held in position by rod $CD,$ which is provided with a roller at C$.$ End $D$ of the rod pushes against a spring having a spring constant $k.$ The spring is undeformed when the gate is vertical. The gate is a solid, flat plate with a thickness of $165$ mm and is made of steel having a density $r=7,850k\frac{g}{m^3}.$ The gate retains fresh water with a depth $d=8m.$ Assuming that rod $CD$ remains horizontal, determine the spring constant of the spring for the case when, under the conditions presented, the bottom of the gate will move to the end of the curved portion of the floor, at $E,$ making contact with the housing of the spring $($so point $B$ coincides with point $C).$

Answer:

$k=5\mathrm{.}96k\frac{N}{m}$