An aquarium 2 m long, 1 m wide, and 1 m deep is half-filled with water. Find the work needed to pump the water out of the aquarium. (

Question

Use 9.8 m/s2 for g and the fact that the density of water is 1000 kg/m3.

Answer 1

Two ways to solve this.

1) If you concentrate all weight of the water to the center of mass of the half filled aquarium, just raise the

water weight 3/4 of a meter.

Work = Force × Distance = ρg(Volume)(3/4) = (3/4)9800(1)(2)(1/2) = 7350 N

2) Let the height, y, be at the base of the aquarium. Need to move 1×2×dy rectangular prisms from 0 to 1/2 meters to the top of the tank.

Work = ρg∫^1/2₀(1-y)(1)(2)dy = 2ρg[y-y²/2]^1/2₀ = 2(9800)[1/2-1/8] = 7350 N