Question

Calculate the work (in joules) required to pump all of the liquid out of a full tank. Assume a=6 m, b=12 m, liquid exits through the spout, c=3 m, and density of the liquid is 1000 kg/m3. (Use decimal notation. Give your answer to two decimal place.)

Answer 1

`3.18*10^(5)J`

Step-by-step explanation:

From the expression of workdone, we no that

Workdone= force * distance

also

force=pressure *area

since pressure = density*height* gravity

we have

work done=pressure * area * distance

from the question, the workdone will be a dependent function on the height

hence we can write

`dw=pgh*A*dh\\A=a*b\\dw=pgh*(a*b)*dh\\`

to get the absolute workdone, we have to integrate both sides

Hence we have

`\int\limits^ {} dw\, dx =pgab\int\limits^3_0 {hdh} \, dx \\w=1000*9.8*6*12((h^(2))/(2) )|_(0)^(3)\\w=1000*9.8*6*12((3^(2))/(2) )\\w=3175200J\\W=3.18*10^(5)J`