To solve this problem it is necessary to apply the concepts related to Pressure, Strength and Area.
We know by definition that Pressure is the amount of Force expressed per unit area, that is,
[tex]P = \frac{F}{A}[/tex]
Where,
F = Force
A = Cross-sectional Area
The net pressure on the bottle would be given by the difference between the internal pressure and the atmospheric pressure, therefore
[tex]P_{net} = P_{in}-P_{atm}[/tex]
[tex]P_{net} = 2.5atm-1atm[/tex]
[tex]P_{net} = 1.5atm (\frac{101325Pa}{1atm})[/tex]
[tex]P_{net} = 151987.5Pa[/tex]
The given radio is,
[tex]r = 3cm^2[/tex]
Hence the Cross-sectional Area would be
[tex]A= \pi r^2[/tex]
[tex]A = \pi(3*10^{-2})^2[/tex]
[tex]A = 2.827*10^{-3}m^2[/tex]
Applying the equation for Pressure we have that
[tex]P = \frac{F}{A}[/tex]
[tex]151987.5= \frac{F}{2.827*10^{-3}}[/tex]
[tex]F = 429.66N[/tex]
Therefore the frictional force on the cork due to the neck of the bottle is 429.66N.
