A research submarine has a 30-cm-diameter window that is 8.1 cm thick. The manufacturer says the window can withstand forces up to 1.1*106 N. Part A Part complete What is the submarine's maximum safe depth in sea water? The pressure inside the submarine is maintained at 1.0 atm. Express your answer in meters.

The pressure at a certain depth underwater is:

P = ρgh

P = pressure, ρ = sea water density, g = gravitational acceleration near Earth, h = depth

The pressure exerted on the submarine window is:

P = F/A

P = pressure, F = force, A = area

The area of the circular submarine window is:

A = π (d/2) ²

A = area, d = diameter

Set the expressions for the pressure equal to each other:

F/A = ρgh

Substitute A:

F / (π (d/2) ²) = ρgh

Isolate h:

h = F / (ρgπ (d/2) ²)

Given values:

F = 1.1*10⁶N

ρ = 1030kg/m³ (pulled from a Google search)

g = 9.81m/s²

d = 30*10⁻²m

Plug in and solve for h:

h = 1.1*10⁶ / (1030 (9.81) π (30*10⁻²/2) ²)

h = 1540m