Good morning. I know I have posted this question several times but I am still getting the wrong answer. So I decided to repost it to get a fresh start.
Thanks for your help!
A glass bottle of soda is sealed with a screw cap. The absolute pressure of the carbon dioxide inside the bottle is 1.95 x 10^5 Pa. Assuming that the top and bottom surfaces of the cap each have an area of 4.75 x 10^-4 m^2, 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.
Force + atmospheric pressure*area=inside pressure*area
force= (insidepressure-atmosphericpres)area
force=(1.95E5N/m^2 - 101E3 N/m^2)4.75E-4m^2= ?
I never saw anything wrong with your work.
Good morning! It seems that you are trying to determine the magnitude of the force that the screw thread exerts on the cap in order to keep it on the bottle. You have correctly identified that the force can be obtained using the formula:
Force + atmospheric pressure * area = inside pressure * area
To calculate the force, you need to subtract the atmospheric pressure from the inside pressure and then multiply it by the area:
Force = (inside pressure - atmospheric pressure) * area
Let's calculate the force using the values given:
Inside pressure = 1.95 x 10^5 Pa
Atmospheric pressure = 101 x 10^3 N/m^2
Area = 4.75 x 10^-4 m^2
Substituting these values into the formula, we have:
Force = (1.95 x 10^5 Pa - 101 x 10^3 N/m^2) * 4.75 x 10^-4 m^2
Now, let's do the calculations:
Force = (1.95 x 10^5 - 101 x 10^3) * 4.75 x 10^-4
= (1.95 x 10^5 - 101 x 10^3) * 4.75 x 10^-4
= (1.95 - 0.101) * 4.75 x 10^-4
= 1.848 x 4.75 x 10^-4
= 0.8782 x 10^-3
= 8.782 x 10^-4
Therefore, the magnitude of the force that the screw thread exerts on the cap in order to keep it on the bottle is approximately 8.782 x 10^-4 N.
Please note that I have used the values you provided in your question. Double-check them to ensure they are correct.