Question

Consider a tank of water shaped like a rectangular prism with triangular sides, as shown in the following diagram: Assume that the tank is completely full. How much work is done to pump the water out of the tank from the top? Enter your solution in Joules. (For simplicity, assume that the acceleration due to gravity is g = 10 m/s2, and that the density of water is D = 1000 kg/m.) Select one: 800000 2. 3 b. 300000 c.800000 d. 360000 O

Answer 1

12m m- 6 work done = Force x dispacement Force = density x gravity x volume. Force = (1000) x (10) x volume. .. work= Force x displacement = (1000) (10) volume x displacement iiw = 10000 x volume x displacement - 0 consider a small slice of height, by at a distance y from the base. Then volume of slice = length x breadth x height ... suce = x x 6 x 4 –(2) 24 2 B 2 from the figure, VABE ~ JCDE (similar triangles

=) X= 44 :: Vslice = 2 x 6 x D4 [from @) -44x6x04 Vslice = 84 ay from 0, W = 10000 x volume x displacement i. Wslece = 10000 x Uslice * (3-4) . W Suice = 20000 x 84 AY +(3-4) work = S Wslice: ai = 3 10000 x 84 (3-4) dy 2000 [$ 403-4) dy ] = 80000 $ (34-4²) dy

0 - 50000 [ 21. De - 80000 [ 3 (3)-(32) -01 = 80000 [ 27-9] L 2 = 80000 | 27-187- 40000 x 10 = 360000 i work = (360000] Joules,