I need help! i don't know how to do this problem.
average atmospheric pressure at earth's surface is 1.01 x 10^5 N/m^2. Earth's radius is 6.37 x 10^6m. Show that the total weight of earth's atmosphere is about 5.15 x 10^19 N.
P=W/A= W/4πr²,
W=4πr²•P=
=4•3.14•(6.37•10⁶)²•1.01•10⁵=5.15•10¹⁹ N
To find the total weight of Earth's atmosphere, we need to calculate the pressure over the entire surface area of the Earth and then multiply it by the area.
Here's the step-by-step process to solve the problem:
Step 1: Calculate the surface area of Earth.
The formula to find the surface area of a sphere is given by: Surface Area = 4πr^2
In this case, Earth's radius (r) is given as 6.37 x 10^6 m. So, we substitute this value into the formula:
Surface Area = 4π(6.37 x 10^6)^2
Step 2: Calculate the pressure over the entire surface area.
Given that the average atmospheric pressure at Earth's surface is 1.01 x 10^5 N/m^2, we multiply this pressure by the surface area calculated in Step 1:
Pressure x Surface Area = (1.01 x 10^5 N/m^2) x Surface Area
Step 3: Multiply the pressure by the surface area to find the total weight.
To find the total weight of Earth's atmosphere, we need to multiply the pressure by the surface area:
Total Weight = Pressure x Surface Area
Step 4: Substitute the values and calculate.
Now, we substitute the values for the pressure and surface area calculated in Steps 1 and 2, respectively:
Total Weight = (1.01 x 10^5 N/m^2) x Surface Area
Finally, calculate the total weight of Earth's atmosphere using the values obtained in the previous steps.
Note: Please substitute the actual values into the formulas for accurate results.