Question

A vertical dam retains 15 m of water. It is pierced at its base witha semi-circular door 6m in diameter (the base of the door is its diameter), as indicated in the figure below. 15 door 6 a) Let y denote the height in meters measured from the base of the dam. The hydrostatic force exerted by the water on the portion of the door comprised between y m and y+ Ay m is approximately p (y) Ay N.What is p (y)? Note that the density of water is p 1000 Kg/m3 and the acceleration due to gravity on the Earth's surface is g 9.8 m/ s2. Express your answer as a formula. Answer: 19600(15-y)(sqrt(9-y^2)) b) In Newtons, what is the total hydrostatic force exerted on the door? Give the answer correct to three significant digits. Answer: Number

Answer 1

Tadius door 2m ea enor =2 1 Total id diitance from Mydrestatic presswu at any paid PYPCA) 9-y21 mmall becta on for 13600 015-)-y2 dy 3 19600 015-)3-Y2 dy 3 294ooo 19 600 dy=3sim 0g 4000*12t9-9 coso)ine- 19 60 30os 3-9(o50 odo (-3aholds 2 Cer 9sino do gin do -196o6y21) -894000x t5292 0D L*) wa*+ of + 764 00 264G o00 20781635 +17649D 1901763 54 f 1901763 5N