Homework SourseThe Deligne Dam on the Cayley River is built so that the wal
The Deligne Dam on the Cayley River is built so that the wall facing the water is shaped like the region above the curve y=0.6x^2 and below the line y=300 . (Here, distances are measured in meters.) The water level is 34 meters below the top of the dam. Find the force (in Newtons) exerted on the dam by water pressure. (Water has a density of 1000kg/m^3 , and the acceleration of gravity is 9.8m/sec^2 )
Solution
dam ends at y=300m and starts at y=300-34 = 266m
so area = 2* area between x=0 and 0.6x^2 from y=266 to 300
=integrate( .6x^2dy) = .6x^2*y = y^2 so
value of integral = (300)^2 - (266)^2 = 19244
VOLUME = 19244*width(W)
mass =
1000*19244*width(W)
force = weight = 9.8*1000*19244*width(W)
