A glass bottle of soda is sealed with a screw cap. The absolute pressure of the carbon dioxide inside the bottle is 1.60 105 Pa. Assuming that the top and bottom surfaces of the cap each have an area of 3.70 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.

Question

Physics

Brycen Pruitt

17 August, 09:58

A glass bottle of soda is sealed with a screw cap. The absolute pressure of the carbon dioxide inside the bottle is 1.60 105 Pa. Assuming that the top and bottom surfaces of the cap each have an area of 3.70 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.

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Gabriela Choi · Answer 1

F tread = 21.8N

Explanation:

In order to find the force that the screw thread exert on the cap, use equation 11.3 taking into consideration that the cap is in equilibrium

Making the vertical net force equal zero.

Sum Fy = - F tread + Inside - F outside=0

F tread = F inside - F out side = P inside A - P out side A =

(P inside - P outside) A.=

((160000pa) - (101000pa)) * 0.00037

21.8N