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Sergio039 [100]
3 years ago
15

An aquarium 2 m long, 1 m wide, and 1 m deep is full of water. Find the work (in J) needed to pump half of the water out of the

aquarium. Use the fact that the density of water is 1000kg/m3.
Mathematics
1 answer:
Nitella [24]3 years ago
8 0

Answer:

W=2452.5 J

Step-by-step explanation:

The work is define as the integral of the force times distance. So we have:

W=\int^{a}_{b}Fxdx

Now, we can write the force in terms of density.

F=m*g=\rho Vg

V is the volume (V=2*1*1=2 m³)

So the work will be:

W=\int^{0.5}_{0} 2*1000*9.81*xdx=\int^{0.5}_{0} 2*1000*9.81*xdx=\int^{0.5}_{0}19620xdx=19620(\frac{x^{2}}{2})|^{0.5}_{0}

The limit of integration is between 0 and 0.5 because we want to pump half of the water out of the aquarium.

W=19620(\frac{x^{2}}{2})|^{0.5}_{0}=19620(\frac{0.5^{2}}{2})

W=2452.5 J

I hope it helps you!

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