An aquarium is 2 m long, 1 m wide, and 1 m deep is full of water weighing 9,800 n/m3.(a) find the work needed to pump half of the water out of the top of the aquarium

Sagot :

In an aquarium 2 m long, 1 m wide, and 1 m deep, the work needed to pump half of the water is 2452.5 J

Calculation

Work done is defined as the integral of force multiplied with distance.

So, the formula goes as W=[tex]\int\limits^a_b {Fx} \, dx\\[/tex]

Force can be written in terms of density as

F = m * g = ρVg

v = 2x1x1 = 2[tex]m^{3}[/tex]

so, work done will be

W = [tex]\int\limits^{0.5}_0 2*1000*9.81* {x} \, dx[/tex]

= 19620[tex](\frac{x^2}{2} )\left \{ {{0.5} \atop {0}} \right.[/tex]

W = 19620 [tex]\frac{(0.5)^2}{2}[/tex]

W= 2452.5 J

Thus, the work that is needed to be done to pump half the water = 2452.5 J

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