Physics Problem

Question

A circular swimming pool has a diameter of 10 m. The circular side of the pool is 4 m high, and the depth of the water is 3.5 m. (The acceleration due to gravity is 9.8 m/s^2 and the density of water is 1000 kg/m^3 .)

How much work (in Joules) is required to:

(a) pump all of the water over the side?

(b) pump all of the water out of an outlet 1 m over the side?

Answer 1

Work is defined as Force * Distance .... in this case imagine infinitesmally thin disks of water being lifted up over the edge of the pool. Each disk will have a weight (dm) = ρgπ(10²)/4dh where h varies from 0 to 4 m. The distance each disc will be lifted 4-h with h=0 at bottom. The allows us to write Work = ρgπ(10²)/4∫(4-h)dh (h from 0 to 3.5) for part a). (6.16E6 joules).

for part b note that each disc will be lifted 5+1 = 5 meters for a total of work to be 3.85E5 joules

Answer 2

W = mgh/2 because you are taking the mass of the vertical-sided pool up an average of h/2 (The bottom material goes up h, the top material goes up 0. The amount of mass at any level has a corresponding level that averages to h/2)

W - ρVgh/2 and all units are in MKS, so you get Joules.

Part b just changes the height to h/2 + 1 (This is how far you are raising the center of mass of the pool)