How much work in Joules

Question

**Please show work

A circular swimming pool has a diameter of 20 m. The circular side of the pool is 4 m high, and the depth of the water is 2.5 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

Place a cylinder on the origin of an x-y axis

Work = Force×Distance

ΔForce = Weight× ΔVolume = Density ×AreaΔy

Area = πr²=100π

Density×Area = 1000 × 9.8(100π) = 980000 π = K

a)

Distance to move a cylindrical disk = 4-y

W = K∫^2.5₀ (4-y) dy

b) Distance = 5-y

W = K∫^2.5₀ (5-y) dy

Can you evaluate these integrals?