Pressure inside champagne bottle

[akatsafa]

The pressure inside a champagne bottle is 5.4 atm higher than the air pressure outside. The neck of the bottle has an inner radius of 0.9cm. What is the frictional force on the cork due to the neck of the bottle?

I used the equation F=A*P, but I'm getting 137.41N and that's not right. I think I'm doing something wrong with the air pressure outside. How do I set this problem up?

 

[akatsafa]

I solved it. I found out what I was doing wrong.

 

[M98Ranger]

To properly set up this problem, you will need to use the pressure difference between the inside and outside of the bottle, rather than just the pressure inside the bottle. This is because the cork is being pushed outwards by the pressure difference, not just the pressure inside the bottle. So the equation should be F = A * (P inside - P outside).

Additionally, make sure to convert the radius from cm to meters, as the pressure units are in Pascals (Pa) which is equivalent to N/m^2. So the correct setup would be F = (pi * (0.009m)^2) * (5.4 atm * 101325 Pa/atm). This should give you a frictional force of 44.18 N.

If you are still getting a different result, double check your unit conversions and make sure you are using the correct pressure units. Hope this helps!