Батискаф витримує тиск 60 МПа. Чи можна провести дослідження в східній частині Атлантичного океану западини Монако глибиною 5440 м? З<

Question

Батискаф витримує тиск 60 МПа. Чи можна провести дослідження
в східній частині Атлантичного океану западини Монако глибиною 5440 м? З
якою силою вода тисне на батискаф в западині, якщо прийняти, що форма
батискафа – сферична, з радіусом 3 м? Атмосферний тиск 101,3 кПа, g=10 Н/кг.

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Thu Nguyệt 5 years 2021-07-20T01:32:37+00:00 1 Answers 78 views 0

Answers ( )

  1. thanhha
    0
    2021-07-20T01:33:37+00:00
    Reply

    1) Yes

    2) 6.34\cdot 10^9 N

    Explanation:

    1)

    To solve this part, we have to calculate the pressure at the depth of the batyscaphe, and compare it with the maximum pressure that it can withstand.

    The pressure exerted by a column of fluid of height h is:

    p=p_0+\rho g h

    where

    p_0 = 101,300 Pa is the atmospheric pressure

    \rho is the fluid density

    g=10 m/s^2 is the acceleration due to gravity

    h is the height of the column of fluid

    Here we have:

    \rho=1030 kg/m^3 is the sea water density

    h = 5440 m is the depth at which the bathyscaphe is located

    Therefore, the pressure on it is

    p=101,300+(1030)(10)(5440)=56.1\cdot 10^6 Pa = 56.1 MPa

    Since the maximum pressure it can withstand is 60 MPa, then yes, the bathyscaphe can withstand it.

    2)

    Here we want to find the force exerted on the bathyscaphe.

    The relationship between force and pressure on a surface is:

    p=\frac{F}{A}

    where

    p is hte pressure

    F is the force

    A is the area of the surface

    Here we have:

    p=56.1\cdot 10^6 Pa is the pressure exerted

    The bathyscaphe has a spherical surface of radius

    r = 3 m

    So its surface is:

    A=4\pi r^2

    Therefore, we can find the force exerted on it by re-arranging the previous equation:

    F=pA=4\pi pr^2 = 4\pi (56.1\cdot 10^6)(3)^2=6.34\cdot 10^9 N

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