Answer to Question #283448 in Electric Circuits for kocii

Question #283448

An empty swimming pool with a square floor dimension has a volume of 3y 2 m3 . Given the weight of air in the swimming pool is about 500 N and the air density is 1.29 kg/m3 . (a) Find the length of the swimming pool’s floor, y. (b) Determine the force exerted by air on the floor of the swimming pool


1
Expert's answer
2021-12-29T13:01:54-0500

Answer

Given data in question

Floor volume V=3y2m33y^2 m^3

Weight of air W=500N

Density ρ=1.29kgm3\rho=1.29\frac{kg}{m^3}

Now

a) length of the swimming pool’s floor, y

The weight can written as

W=mgW=mg

=ρVg=\rho Vg

=ρ×3y2×g=\rho \times3y^2\times g

So length of swimming pools floor

y=W3ρgy=\sqrt{\frac{W}{3\rho g}}

Putting all values

y=5003×1.29×9.81y=3.63my=\sqrt{\frac{500}{3\times1.29\times 9.81}}\\y=3.63m


b) now force exerted by air on the floor of the swimming pool is given by

The equivalent of weight of air

F=W=500N.




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