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 = 10^5 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.)
Weight = (Air Density)*Volume*g
Volume = (base area) x Height
The density of air that they told you to use is wrong. Are you sure you copied it correctly? It should be about 1.29 kg/m^3
I have my doubts about the quality of the physics education you are getting. They gave you a density of air with three significant figures that is 68% high and tell you to use a value of g that is 2% high.
The variables are supposed to be wrong so that you cannot take the problem and easily copy and paste them into the internet
To calculate the weight of the air that fills the pool when it is empty, we need to find the volume of the pool and then multiply it by the density of the air.
Step 1: Find the volume of the pool:
The volume of a rectangular prism (which represents the pool) is given by multiplying its length, width, and height. In this case, the length is 9 m, the width is 4 m, and the height is 3 m. So, the volume of the pool is:
Volume = length * width * height
Volume = 9 m * 4 m * 3 m
Volume = 108 m^3
Step 2: Calculate the weight of the air:
The weight of an object is given by its mass multiplied by the acceleration due to gravity. In this case, we can calculate the mass of the air by multiplying the density of the air by the volume of the pool:
Mass = density * volume
Mass = 2.17 kg/m^3 * 108 m^3
Now, we know the weight of an object is the product of its mass and acceleration due to gravity. The acceleration due to gravity is given as 10 m/s^2:
Weight = mass * acceleration due to gravity
Weight = (2.17 kg/m^3 * 108 m^3) * 10 m/s^2
By multiplying these values, we can find the weight of the air that fills the pool when it is empty.