Finding Earth's atmosphere mass from atmospheric pressure

[Nubcake]

1.Atmospheric pressure is 101kPa
a) Calculate the total force exerted by the atmosphere on the surface of the Earth. Radius of Earth is 6.4 Mm
b)Calculate the mass of the Earth's atmosphere , State any assumptions made.



P = F/A ρ = m/v [\b]



a) Surface area of a sphere is 4∏r^2

A = 4 x ∏ x (6.4 x 10^6)^2
A = 5.147 x 10^14 m^2

P = 101 x 1000 Pa

F = (101 x 1000) x (5.147 x 10^14) N
F = 5.2 x 10^19 N

b) Not sure what to do here , I've only got force , pressure and area , maybe volume too.

 

[gneill]

b) Not sure what to do here , I've only got force , pressure and area , maybe volume too.

You've also got the acceleration due to gravity. Make some reasonable assumptions about the average 'g' acting on a 'lump sum' model of the atmosphere.

- What's a reasonable approximation for the height of the atmosphere?
- How does it compare to the radius of the Earth?
- How much does g vary from the bottom to the top of the atmosphere? Is it significant for your purposes?

 

[Nubcake]

Why doesn't F = ma work in this situation ?

 

[gneill]

Why doesn't F = ma work in this situation ?

Who says it doesn't?

 

[Nubcake]

Who says it doesn't?

Well I used it and got a different answer to the right answer , instead of F = ma , W = mg is used.

 

[gneill]

Well I used it and got a different answer to the right answer , instead of F = ma , W = mg is used.

W, weight, is a force. g is an acceleration. It's just f = ma using different variable names.

You'll have to show your work so that we can see what it means when you say
you "got a different answer". Be sure to make your assumptions clear.

 

[Nubcake]

I guess I must have made a mistake with F = ma now that I think about it , I didn't rearrange the formula for mass .