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.

1) Yes

2)

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:

where

is the atmospheric pressure

is the fluid density

is the acceleration due to gravity

h is the height of the column of fluid

Here we have:

is the sea water density

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

Therefore, the pressure on it is

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:

where

p is hte pressure

F is the force

A is the area of the surface

Here we have:

is the pressure exerted

The bathyscaphe has a spherical surface of radius

r = 3 m

So its surface is:

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