Answer to Question #269092 in Classical Mechanics for joseph

Question

1. Determine the placement d of the pin on the 0.5-m-wide rectangular gate so that it is on the verge to rotate clockwise (open) when wastewater reaches a height h = 2.5 m. What is the resultant force acting on the gate?

2. The tank is filled to its top with an industrial solvent, ethyl ether. Determine the resultant force acting on the plate ABC, and its location on the plate measured from edge AB of the tank. Use the formula method. Take p_cc = 715 kg/m³.

Answer 1

1.

Since the gate is circular in shape, it is convenient to compute the resultant force as follows.

$F_{R} = \gamma _{w}\bar{h}A = 1984.86~ lb .$

The location of the center of pressure can be determined from

$Y_{p} =\frac{\bar{I}_{x}}{\bar{y}_{A}} + \bar{y} =4.625~ft.$

When the gate is on the verge of opening, the normal force at A and B is zero. Summing the moments about point C requires that F_R acts through C. Thus,

$d = y_{p} – 3 ft = 1.62 ~ft.$

2.

The resultant force is

$F_{R} = \gamma _{ee}\bar{h}A =18.5~klb.$

$\bar{I} =\frac{1}{36} bh^{3} = 480~ ft.$ Then

$y_{p} =\frac{\bar{I_{x}}}{\bar{y_{A}}} + \bar{y} = 9 ft.$ Thus,

$d = 12 ~ ft – y_{P} = 3 ~ft.$