An electrical short cuts off all power to a submersible diving vehicle when it is a distance of 28 m below the surface of the ocean. The crew must push out a hatch of area 0.70 m2 and weight 200 N on 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?

to find the necessary force to escape we must make a free-body diagram on the hatch, taking into account that we will match the forces that go down with those that go up, taking into account the above we propose the following equation,

Fw=W+Fi+F

where

Fw= force or weight produced by the water column above the submarine.

to fint Fw we can use the following ecuation

Fw=h. γ. A

h=distance

γ= specific weight for seawater = 10074N / m ^ 3

A=Area

Fw=28x10074x0.7=197467N

w is the weight of the hatch = 200N

Fi is the internal force of the submarine produced by the pressure = 1atm = 101325Pa for this we can use the following formula

Fi=PA=101325x0.7=70927.5N

finally the force that is needed to open the hatch is given by the initial equation

Fw=W+Fi+F

F=Fw-W+Fi

F=197467N-200N-70927.5N

F=126339.5N

onyebuchinnaji onyebuchinnaji · Answer 2 · 2022-04-12T15:25:24+02:00

The downward force must the crew exert on the hatch to open it is 121,152.5 N.

Hydrostatic pressure of water at the given depth

The pressure of water at the given depth is calculated as follows;

P = ρgh

where;

ρ is density of water

P = 1000 (kg/m²) x 9.8 (m/s) x 28 (m)

P = 274,400 Pa

Total pressure inside submersible

1 atm = 101325 Pa

P(inside) = 101325 Pa

Net force on the submersible

F = PA

F = (outside pressure - inside pressure) x Area

F = (274,400 Pa - 101325 Pa) x 0.7

F = 121,152.5 N

Thus, the downward force must the crew exert on the hatch to open it is 121,152.5 N.

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