A glass bottle of soda is sealed with a screw cap. The absolute pressure of the carbon dioxide inside the bottle is 1.80 x10^5pa. Assuming that the top and bottom surfaces of the cap each have an area of .0004M^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.
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physics - drwls, Sunday, April 8, 2007 at 6:48am
(Area)*(Poutside - Pinside) = Force
Pinside = 1.80*10^5 N/m^2
Poutside = 1 atm = 1.013*10^5 N/m^2
Area = 4*10^-4 m^2
Solve for Force, F
Physics please check - CJ, Sunday, April 8, 2007 at 11:12pm
F = (4.0^-4m^2)(1.013*10^5 N/m^2 - 1.80*10^5 N/m^2)
F = (0.0004)(-78799)
F = -31.5196
Correct procedure, I didn't check calc math. Units?
F= +31.5196
total forces = 0
PA(Co)-PA(atm)-F(thread)=0
F=PA(CO)-PA(atm)
To obtain the magnitude of the force that the screw thread exerts on the cap, we can use the formula:
Force = (Area) * (Poutside - Pinside)
where:
- Area is the combined area of the top and bottom surfaces of the cap, given as 0.0004 m^2.
- Poutside is the air pressure outside the bottle, given as 1 atmosphere, which is equivalent to 1.013 * 10^5 N/m^2.
- Pinside is the absolute pressure of the carbon dioxide inside the bottle, given as 1.80 * 10^5 N/m^2.
Now let's plug these values into the formula:
Force = (0.0004 m^2) * (1.013 * 10^5 N/m^2 - 1.80 * 10^5 N/m^2)
Force = (0.0004) * (-78,799)
Force = -31.5196 N (rounded to 4 decimal places)
The magnitude of the force that the screw thread exerts on the cap is 31.5196 N. Note that the negative sign indicates that the force is directed towards the cap, keeping it on the bottle.
Please note that the given solution didn't mention the units explicitly; however, based on the calculations, the obtained unit of force is Newtons (N).