Question

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

Answer 1

Answer

Given data in question

Floor volume V=$3y^2 m^3$

Weight of air W=500N

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

Now

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

The weight can written as

$W=mg$

$=\rho Vg$

$=\rho \times3y^2\times g$

So length of swimming pools floor

$y=\sqrt{\frac{W}{3\rho g}}$

Putting all values

$y=\sqrt{\frac{500}{3\times1.29\times 9.81}}\\y=3.63m$

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.