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11 May, 06:50

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.

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  1. 11 May, 06:58
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    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
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