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An electrical short cuts off all power to a submersible diving vehicle when it is 30m below the surface of the ocean. The crew must push out a hatch of area 0.75m^2 and weight 300 Non the bottom to escape. If the pressure inside is 1.0 atm, what downward force must the crew exert on the hatch to open it?

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Answer:

[tex]227046.75\ \text{N}[/tex]

Explanation:

h = Depth = 30 m

[tex]\rho[/tex] = Density of seawater = [tex]1030\ \text{kg/m}^3[/tex]

A = Area = [tex]0.75\ \text{m}^2[/tex]

W = Weight = [tex]300\ \text{N}[/tex]

g = Acceleration due to gravity = [tex]9.81\ \text{m/s}^2[/tex]

The force balance of the system is given by

[tex]F=\rho ghA-W\\\Rightarrow F=1030\times 9.81\times 30\times 0.75-300\\\Rightarrow F=227046.75\ \text{N}[/tex]

The downward force required to open the hatch is [tex]227046.75\ \text{N}[/tex].

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