Question $3$

The cross$-$section of a $3\mathrm{.}0$ m $-$wide $($in the plane of the figure$),$ fresh$-$water tank with a slanted bottom is presented. A rectangular door in the bottom of the tank, $1\mathrm{.}6$ m by $0\mathrm{.}8$ m $($normal to the plane of the figure$),$ is hinged at $\backslash ($ A $\backslash )$ and can be opened by the vertical cable under a tension $\backslash ($ P $\backslash ),$ as shown. Determine the minimum tension force in the cable required to open the door. The door is fabricated from $16$ mm thick steel plate with a mass density of $\backslash (7,850\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ).$

Answer:

$\backslash [$

P$\_\{\backslash$min $\}=13\mathrm{.}36\backslash$mathrm$\{$kN$\}$

$\backslash ]$

Solve this with only two pressure forces please. No breaking into horizontal and vertical forces like the other answer