THE QUESTION IS POSTED ON THE ATTACHMENT FILE BELOW
1. The problem statement, all variables and given/known data
density of the gates is 4000 kg/m^3
width of the gate is 6m
2. Relevant equations
Static Equilibrium : every equation that sums up forces or moments equals zero
You also must find the force of the weight going down F=mg
but first you have to find the mass which is the volume multiplied by the density.
3. The attempt at a solution
I know the force that is produced by the pressure which is 265 KN that is obvious from that fact that Ax=265 KN (different direction)as well .
but if Ay=377 KN[up] and Cy=1389 KN[up]
that means force of the gate is 1012 KN(down)
now my main problem is
1. I've tried manipulating the height, base and width of the triangle to find the volumes for a hour now and I can't find any way you could get the right volume that leads to the forces of 1021 KN
-yes I know you have to multiply the mass by the 9.81 m/s^2 to get the force
-whats driving me crazy is the whole volume issue
2. If the force is 1012KN like they say how did they get the moment/torque arm from the force to point A to be 4.4 m (in order to solve for Cy)???
-I know you have to find the centroid, but I kind of keep getting stuck after that