An rectangular above-ground swimming pool is 9 m long and 4 m wide. The pool wall has a constant height of 3 m above the ground. Take atmospheric pressure to be 1 atm = 105 Pa and g = 10 m/s2.
(a) Calculate the weight of the air that fills the pool when the pool is empty. (Take the density of air to be 2.17 kg/m3.)
note, it's supposed to be 1 atm=10^5 Pa
To calculate the weight of the air that fills the pool when it's empty, we first need to find the volume of the pool.
The volume of a rectangular pool can be calculated using the formula:
Volume = Length x Width x Height
In this case, the length of the pool is 9 m, the width is 4 m, and the height is 3 m (above the ground level).
Volume = 9 m x 4 m x 3 m = 108 cubic meters
Now, we need to calculate the mass of the air in the pool. To do this, we need to know the density of air, which is given as 2.17 kg/m³.
Mass = Density x Volume
Mass = 2.17 kg/m³ x 108 m³ = 234.36 kg
Finally, we can calculate the weight of the air using the formula:
Weight = Mass x Gravity
Weight = 234.36 kg x 10 m/s² = 2343.6 N
Therefore, the weight of the air that fills the pool when it's empty is 2343.6 N.