contestada

A spherical submersible 1.87 m in radius, armed with multiple cameras, descends under water in a region of the Atlantic Ocean known for shipwrecks and finds its first shipwreck at a depth of 1.84 ✕ 103 m. Seawater has density 1.025 ✕ 103 kg/m3, and the air pressure at the ocean's surface is 1.013 ✕ 105 Pa.
(a) What is the absolute pressure at the depth of the shipwreck?
Pa

(b) What is the buoyant force on the submersible at the depth of the shipwreck? (Give the magnitude.)

Respuesta :

cjmejiab

The concepts that we need to apply in this problem are the Pressure in a liquid at a given depth, that is hydrostatic pressure and the force in terms of density, volume and gravity.

The hydrostatic pressure is given by,

[tex]P_h = P_0 +\rho gD[/tex]

Where

[tex]P_0[/tex] is the pressure at the top

[tex]\rho[/tex] is the density

g = gravity force

D = The distance from the top.

Part A )

[tex]P_h = P_0+pgD[/tex]

[tex]P_h = (1.013*10^5)+(1.025*10^3)(9.8)(1.84*10^3)[/tex]

[tex]P_h = 1.858*10^7Pa[/tex]

Part B) The force in terms of density, volume and gravity is

[tex]F = \rho Vg[/tex]

[tex]F = (1.025*10^3)(\frac{4}{3}\pi*R^3)(9.8)[/tex]

[tex]F = (1.025*10^3)(\frac{4}{3}\pi*(1.87)^3)(9.8)[/tex]

[tex]F = 2.75*10^5 N[/tex]

hamzaahmeds

This question involves the concepts of absolute pressure, atmospheric pressure, and buoyant force.

(a) The absolute pressure at the depth of the shipwreck is "18602.96 KPa".

(b) The buoyant force on submersible at the depth of shipwreck is "275.43 KN".

(a)

The absolute pressure is the sum of atmospheric pressure and the static pressure due to depth of water:

[tex]Absolute\ Pressure=Atmospheric\ Pressure+\rho gh\\Absolute\ Pressure=1.013\ x\ 10^5\ Pa+(1.025\ x\ 10^3\ kg/m^3)(9.81\ m/s^2)(1.84\ x\ 10^3\ m)[/tex]

Absolute Pressure = 101.3 x 10³ Pa + 18501.7 x 10³ Pa

Absolute Pressure = 18602.96 x 10³ Pa = 18602.96 KPa

(b)

The buoyant force can be calculated using the following formula:

[tex]F = \rho Vg\\F = (1.025\ x\ 10^3\ kg/m^3)(\frac{4}{3}\pi (radius)^3)(9.81\ m/s^2)\\F =(1.025\ x\ 10^3\ kg/m^3)(\frac{4}{3}\pi (1.87\ m)^3)(9.81\ m/s^2)\\[/tex]

F = 275.43 x 10³ N = 275.43 KN

Learn more about buoyant force here:

brainly.com/question/21990136?referrer=searchResults

The attached picture illustrates the buoyant force.

Ver imagen hamzaahmeds

Otras preguntas