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 4.20 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.
To obtain the magnitude of the force that the screw thread exerts on the cap, we need to calculate the pressure difference between the inside and outside of the bottle and multiply it by the area of the cap.
1. First, let's calculate the pressure difference between the inside and outside of the bottle. This can be done using the formula:
Pressure difference = Pressure inside the bottle - Pressure outside the bottle
The pressure inside the bottle is given as 1.50 x 10^5 Pa, and since the air pressure outside the bottle is one atmosphere, we can convert it to Pascal by using the conversion factor: 1 atm = 101325 Pa.
Therefore, the pressure difference is:
Pressure difference = 1.50 x 10^5 Pa - 1 atm = 1.50 x 10^5 Pa - 101325 Pa = 4.9675 x 10^4 Pa
2. The force exerted on an object can be calculated using the formula:
Force = Pressure difference * Area
We have already calculated the pressure difference to be 4.9675 x 10^4 Pa, and the area of each surface of the cap is given as 4.20 x 10^-4 m^2.
Therefore, the magnitude of the force that the screw thread exerts on the cap is:
Force = 4.9675 x 10^4 Pa * 4.20 x 10^-4 m^2 = 20.8015 N
Thus, the magnitude of the force that the screw thread exerts on the cap in order to keep it on the bottle is approximately 20.8015 N.