$1)$A rectangular gate of dimension $1$ m by $4$ m is held in place by a stop block at $B.$ This block

exerts a horizontal force of $40$ kN and a vertical force of $0$ kN $.$ The gate is pin$-$connected at A $.$

Find the depth $h$ of the water. Assume the center of pressure is the same as the center of

gravity $[$Figure $1]$

$2)$The concrete dam weighs $23\mathrm{.}6k\frac{N}{m^{}}$ and rests on a solid foundation. Determine the

minimum coefficient of friction between the dam and the foundation required to keep the dam

from sliding at the water depth shown. Assume no fluid uplift pressure along the base. Base

your analysis on a unit length of the dam. $[$Figure $2]$

Figure $1$

Figure $2$