Question

webwork/mat 187h1 f lec0101/week 1/6 Week 1: Problem 6 Previous Problem Problem List Next Problem (1 point The tank shown below is full of water. Using the fact that the density of water is 1000 kg/m2, find the work (in joules) required to pump the water out of the outiet. Make sure your answer is correct to within one thousand joules. ' 1 m 6 m 1.5 m joules Work Submit Answers Preview My Answers You have attempted this problem O times. You have unlimited attempts remaining.

Answer 1

Given density of water is 1000 kg/m^3 and radius of tank = 1.5m length of tank = l = 6m Consider an horizontal strip of breadth 'dy' and length '2x' therefore Volume of strip V = (2x)middot dy middot 6 work required to pump water out of the tank is W = Force times distance = mg times d = rho times v times g times d = rho times 2 times g times (2.5 - y) [because m = rho times V] we know equation of circle, x^2 + y^2 = 1.5^2 x = squareroot 1.5^2 - y^2 implies W rho integral^1.5_-1.5 2 squareroot 1.5^2 - y^2 times 9.8(2.5 - y) dy W = (6)49 rho integral^1.5_1.5 squareroot 1.5^2 - y^2 - (6))9.6 rho integral^1.5_1.5 y squareroot 1.5^2 - y^2 Since integral^1.5_1.5 y squareroot 1.5^2 - y^2 is an odd function its value is zero. Therefore W = (6)49 rho integral^1.5_-1.5 squareroot (1.5)^2 - y^2 [because integral^a_-a squareroot a^2 - x^2 = [a^2/2 sin^-1 x/a]^a_-a = 1/2 pi a^2]