Consider the vertically submerged rectangular plate. We are going to determine the total force due to liquid pressure on the plate. The dimensions of the plate are W = 12 ft, L = 8 ft . The top of the plate is at a depth of D = 5 ft below the surface. The weight density of water is 6 = 62.4 lbs/ft? | i ' AX This problem depends on the vertical coordinate system to the left. The force, E , on the ith strip of the plate = weight of the 2'1th " column of water" (diagram on right) = 6 - vi, where v;- = volume of the ith " column of water". For this problem, Adding up the force on all the subintervals and allowing n > oo, where n represents the number of subintervals, gives the integral for total force due to liquid pressure, F. (Don't forget 6) :1 f :dm :1 0 Question 2 [Z 10 pts '0 1 6) Details 1 11' The region R in the any-plane is bounded by the graphs of y : 4sin(a:), y : Em and a: : E, and just touches the origin. The centroid of R is located at