The mass of 1 cubic meter of air at sea level is about 1.3kg. much does it weight in newtons? How much would a stack of 8000 such cubes weigh? If this total weight were all applied to an area of 1m^2, how much pressure would it produce on that surface? The answer should look familiar. (Although the atmosphere actually gets less dense with increasing altitude, the total amount of air is the same as these sea-level cubes were stacked some 8km high.)
weight= mg
pressure=weight/area
To find the weight of 1 cubic meter of air at sea level in newtons, we can use the formula: weight = mass × gravitational acceleration.
The mass of 1 cubic meter of air at sea level is given as 1.3 kg. The gravitational acceleration on Earth is approximately 9.8 m/s^2.
Using the formula, we can calculate the weight of 1 cubic meter of air:
Weight = 1.3 kg × 9.8 m/s^2 = 12.74 newtons (rounded to two decimal places).
To find the weight of a stack of 8000 such cubes, we can multiply the weight of 1 cube by the number of cubes in the stack:
Weight of stack = 12.74 newtons × 8000 = 101,920 newtons.
Now, let's calculate the pressure produced by this weight when applied to an area of 1 square meter. Pressure is defined as force per unit area.
Pressure = Force / Area
In this case, the force is the weight of the stack, which is 101,920 newtons, and the area is 1 square meter.
Pressure = 101,920 newtons / 1 square meter = 101,920 newtons per square meter.
This value, 101,920 newtons per square meter, is also known as 101,920 pascals (Pa). The pascal is the SI unit for pressure.
Therefore, the pressure produced by the weight of the stack of 8000 cubic meter cubes is 101,920 pascals, which should look familiar as it is the standard atmospheric pressure at sea level.