A submarine is at a depth of 96.0 m under the ocean surface. The inside of the submarine is kept at atmospheric pressure. What is the net force being exerted on a circular window of the submarine that has a radius of 35 cm? The density of the ocean water is 1030 kg/m3

To find the net force exerted on the circular window of the submarine, we need to consider the pressure difference between the inside and outside of the window.

Let's start by calculating the pressure at the given depth. Using the formula for pressure in a fluid:

Pressure = density * gravity * depth

where:
density = 1030 kg/m^3 (density of ocean water)
gravity = 9.8 m/s^2 (acceleration due to gravity)
depth = 96.0 m (depth of the submarine)

Plugging in the values, we get:

Pressure = 1030 kg/m^3 * 9.8 m/s^2 * 96.0 m
= 9991680 Pa (Pascals)

Now, we can calculate the net force on the circular window. The net force is the pressure difference multiplied by the area of the window.

The pressure on the inside of the window is atmospheric pressure, which is approximately 101325 Pa.

Pressure difference = pressure inside - pressure outside
= 101325 Pa - 9991680 Pa
= -9880355 Pa

Since the pressure inside is larger than the pressure outside, the pressure difference is negative.

Finally, we calculate the net force using the formula:

Net Force = Pressure difference * Area

Given that the radius of the window is 35 cm, we convert it to meters:

radius = 35 cm * (1 meter / 100 cm)
= 0.35 m

Area = π * radius^2
= π * (0.35 m)^2

Plugging in the values and using the pressure difference calculated earlier, we can find the net force:

Net Force = -9880355 Pa * π * (0.35 m)^2

Calculating this expression will give you the net force being exerted on the circular window of the submarine.