How Does Screw Cap Pressure Keep a Soda Bottle Sealed?

[wbhphysics]

I have tried this question and cannot seem to figure it out:

A glass bottle of soda is sealed with a screw cap. The absolute pressure of the carbon dioxide inside the bottle is 1.90E5 Pa. Assuming that the top and bottom surfaces of the cap each have an area of 3.50E-4 m^2, obtain the magnitude of the force that the screw thread exerts on the cap in order to keep it on the bottle. The air pressure outside the bottle is one atmosphere.

I tried:
P=F/A
P=1.90E5 pa
A=3.50E-4 m^2 (x2)
F=?

CO2 (up): F1=1.90E5 Pa x 3.50E-4 m^2 = 66.5N
ATM (down): F2=1.013E5 Pa x 3.50E-4 m^2 = 35.5 N

F1-F2= F3
F3= 66.5-35.5
=131 N (this is not the correct answer)

Hint: There are 3 forces acting on the cap; the force of the CO2 pushing up; the force of the atmospheric pressure pushing down. Use eq. 11.3 and the fact that the cap is in equilibrium to solve the problem.
Eq 11.3: P=F/A
The SI unit for measuring pressure is the pascal (Pa); 1Pa=1N/m^2
Atmospheric pressure One atmosphere of pressure is 1.013E5 Pa or 14.7 lb/in^2

CO2 pushing up = 1.90E5 Pa
ATM pushing down = 1 atm


Thanks!

 

[uart]

F3= 66.5-35.5 = 131 N (this is not the correct answer) Yes it certainly is not. Do you want to re-check your maths there.

 

[wbhphysics]

Oh, haha thanks!