Question

A glass bottle of soda is sealed with a screw cap. The

absolute pressure of the carbon dioxide inside the bottle
is1.80*105 Pa. Assuming that the top and bottomsurfaces
of the cap each have an area of 4.10*10-4m2,
obtain the magnitude of the force that the screwthread exerts on
the cap in order to keep it on the bottle. The air pressure outside
the bottle is one atmosphere.

Answer 1

32.25675 N

Step-by-step explanation:

1 atm = 101325 Pa

As the CO2 pressure inside the bottle and the atmospheric pressure has opposite direction, the net pressure on the cap is:

`1.8*10^5 - 101325 = 78675 Pa`

Then the pressurized force acting on the cap by CO2 is

`F = PA =  78675 * 4.1*10^(-4) = 32.25675 N`

This is also the magnitude of the force the the screw thread has to exert on the cap in order to keep it on the bottle