Final answer:
The mass of the column of air can be found by using the pressure and area to calculate the force, and then using the force to find the mass. The calculation yields a mass of 15219.39 kg for the column of air.
Step-by-step explanation:
To calculate the mass of the column of air, we can use the relationship between pressure, area, and force. The pressure exerted by the column of air can be thought of as the force it applies per unit area. This force is equal to the weight of the air.
The formula to relate pressure (P), force (F), and area (A) is:
P = F/A
Given:
- Pressure (P) = 1.57 x 10µ Pa
- Area (A) = 0.95 m²
- Acceleration due to gravity (g) = 9.8 m/s²
We can rearrange the formula to find the force (weight) of the air:
F = P x A
Then, calculate the force:
F = (1.57 x 10µ Pa) x (0.95 m²)
= 149150 N
Next, we calculate the mass (m) using Newton's second law F = m x g, or rearranged, m = F/g:
m = 149150 N / 9.8 m/s²
The mass of the air column is thus:
m = 15219.39 kg