Question

An aquarium 3 m long, 2 m wide, and 1 m deep is full of water. Find the work needed to pump half of the water out of the aquarium. (Use the fact that the density of water is 1000 kg/m3, and use 9.8 m/s2 for g.)

Answer 1

Answer:

work is 29430 J

Explanation:

Given data

long = 3 m

wide = 2 m

deep = 1 m

to find out

work needed to pump

solution

first we find out horizontal cross section area

i.e. area = long × wide

cross section area = 3  × 2 = 6

we can say if thickness dx is infinite than volume will be

dv that is equal to 6  × dx

so dv = 6 dx

and here force due to gravity will  be

df =  ρ × g × dv

that will be

df = 6 × ρ × g × dx

and work will be to lift distance x is

dw = df × (x)

so dw =  6 × (x) × ρ × g × dx

now we calculate work half of water out

we consider here full tank is top half so take derivative 0 to 1

so work = 6 × ρ × g ×$\int_{0}^{1} (x)dx$

work = 6 (1000) (9.81) (1/2)

work is 29430 J