A glass bottle of soda is sealed with a screw cap. The absolute pressure of the carbon dioxide inside the bottle is 1.60 x 105 Pa. Assuming that the top and bottom surfaces of the cap each have an area of 3.60 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 calculate the magnitude of the force that the screw thread exerts on the cap, we need to consider the pressure difference between the inside of the bottle and the outside.

Step 1: Calculate the pressure difference
The pressure difference is the absolute pressure inside the bottle minus the atmospheric pressure outside the bottle. Given that the absolute pressure inside the bottle is 1.60 x 10^5 Pa and the atmospheric pressure is one atmosphere (which is approximately 1.013 x 10^5 Pa), we can calculate the pressure difference:

Pressure Difference = Absolute pressure inside the bottle - Atmospheric pressure
= (1.60 x 10^5 Pa) - (1.013 x 10^5 Pa)
= 0.587 x 10^5 Pa

Step 2: Calculate the force
The force exerted by the screw thread on the cap is equal to the pressure difference multiplied by the total area of the cap.

Force = Pressure Difference x Total Area

Given that the top and bottom surfaces of the cap each have an area of 3.60 x 10^-4 m^2, the total area is the sum of these two areas:

Total Area = 2 x Area of one surface
= 2 x (3.60 x 10^-4 m^2)
= 7.20 x 10^-4 m^2

Now, we can calculate the force:

Force = (0.587 x 10^5 Pa) x (7.20 x 10^-4 m^2)
= 4.2304 x 10^1 N
≈ 42.304 N

Therefore, the magnitude of the force that the screw thread exerts on the cap to keep it on the bottle is approximately 42.304 newtons.