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30 August, 21:56

An ocean-going research submarine has a 10-cmcm-diameter window 8.6 cmcm thick. The manufacturer says the window can withstand forces up to 1.2*106 NN. What is the submarine's maximum safe depth?

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  1. 30 August, 23:08
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    15144.268 m

    Explanation:

    Pressure: This can be defined as the ratio of force to the surface area in contact. T²he S. I unit of pressure is N/m²

    P = F/A ... Equation 1

    Where P = pressure, F = Force, A = Area of the submarine.

    The pressure in water is

    P = ρgh ... Equation 2

    Where ρ = density of the water, g = acceleration due to gravity, h = depth.

    Therefore,

    ρgh = F/A

    F = Aρgh ... Equation 3

    Making h the subject of the equation,

    h = F / (Aρg) ... Equation 4

    Given: F = 1.2*10⁶ N, A = πd²/4 where d = diameter = 10 cm = 0.1 m

    A = 3.14 (0.1) ²/4 = 0.00785 m².

    Constant: g = 9.8 m/s². ρ = 1030 kg/m³

    Substitute into equation 4,

    h = 1.2*10⁶ / (1030*9.8*0.00785)

    h = 15144.268 m.

    Hence the submarine's maximum safe depth = 15144.268 m
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