Question

A glass bottle of soda is sealed with a screw cap. The absolute pressure of the carbon dioxide inside the bottle is 1.90 x 105 Pa. Assuming that the top and bottom surfaces of the cap each have an area of 3.90 x 10-4 m2, 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.

Answer 1

The magnitude of the force is 34.59 N.

Step-by-step explanation:

Given that,

Inside pressure
`P_(in)= 1.90*10^(5)\ Pa`

Area
`A=3.90*10^(-4)\ m^2`

Outside pressure = 1 atm

We need to calculate the magnitude of the force

Using formula of force

`F_(net)=F_(in)-F_(out)`

`F_(net)=(P_(in)-P_(out))A`

Where,
`P_(in)` =inside Pressure

`P_(out)` =outside Pressure

A = area

Put the value into the formula

`F_(net)=(1.90*10^(5)-1.013*10^(5))3.90*10^(-4)`

`F_(net)=34.59\ N`

Hence, The magnitude of the force is 34.59 N.