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An electrical short cuts off all power to a submersible diving vehicle when it is a distance of 29 m below the surface of the ocean. The crew must push out a hatch of area 0.950 m2 and weight 390 N to escape.

If the pressure inside is 1.0atm, what downward force must they exert on the hatch to open it?

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Answer:

277983.465 N

Explanation:

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

g = Acceleration due to gravity = 9.81 m/s²

h = Depth = 29 m

w = Force = 390 N

A = Area = [tex]0.95\ m^2[/tex]

Force in the system would be

[tex]F=(\rho gh)A-w\\\Rightarrow F=(1030\times 9.81\times 29)\times 0.95-390\\\Rightarrow F=277983.465\ N[/tex]

The downward force must they exert on the hatch to open it is 277983.465 N

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