Question

A glass bottle of soda is sealed with a screw cap. The absolute pressure of the carbon dioxide inside the bottle is 1.50 x 105 Pa. Assuming that the top and bottom surfaces of the cap each have an area of 4.40 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

Answer:

$F \approx 19.5 N$

Explanation:

From the question we are told that:

Pressure of  $P_{CO_2}=1.50 * 105 Pa.$

Bottle cap area $A_b= 4.40 * 10-4 m^2$

 

Generally the equation for Resultant pressure $P_r$ is give as is mathematically given by

$P_r=P_{CO_2}-P_a$

Where

$P_a=atmospheric\ pressure = 1.013*10^5 pa$

$P_r=1.50 * 105 Pa-1.013*10^5 pa$

$P_r=0.487*10^5 pa$

Generally the equation for Force exerted by screw F is give as is mathematically given by

$F = P*A\\F = 0.487*10^5*4.00*10^-4\\ F = 19.48 N$

$F \approx 19.5 N$