(Solved): A vertical dam has a semicircular gate as shown in the figure. The total depth \( d \) of the figu ...

A vertical dam has a semicircular gate as shown in the figure. The total depth \( d \) of the figure is \( 24 \mathrm{~m} \), the height \( h \) of air above the water level is \( 4 \mathrm{~m} \), and the width \( w \) of the gate is \( 4 \mathrm{~m} \). () Set up an integral that can be used to find the hydrostatic force (in N) against the gate. (Use \( 9.8 \mathrm{~m} / \mathrm{s}^{2} \) for the acceleration due to gravity. Recall that the weight density of water is \( 1,000 \mathrm{~kg} / \mathrm{m}^{3} \).) \[ \int_{0} x(1,000)(9.8)(1) d x \] Find the hydrostatic force (in N) against the gate. (Round your answer to the nearest whole number.) \( \mathrm{N} \)