For a submarine to stay submerged, it must be neutrally buoyant, which means it is maintaining a careful balance between its weight and the buoyant force of water pushing it toward the surface.

Question

If a submarine has an enclosed volume of 327.781 m3, how much must it weigh to stay submerged? (Use 1000 kg/m3 for the density of water.)

Answer 1

The density of the submarine has to be greater than or equal to the density of the water to submerge and sink. The more dense an environment is, the more it can hold something up that is less dense. Air can't hold a free-falling spherical ball, but it can hold up helium, as the air molecules are generally heavier in addendum.

Likewise...

ρ_sub ≥ ρ_water

ρ_sub = Mass / Volume

m_sub/V_sub ≥ ρ_water

Final Eq., just plug in the numbers below

m_sub ≥ ρ_water(V_sub)

Answer 2

The density of the submarine has to be greater than or equal to the density of the water to submerge and sink. The more dense an environment is, the more it can hold something up that is less dense. Air can't hold a free-falling spherical ball, but it can hold up helium, as the air molecules are generally heavier in addendum.

Likewise...

ρ_sub ≥ ρ_water

ρ_sub = Mass / Volume

m_sub/V_sub ≥ ρ_water

Final Eq., just plug in the numbers below

m_sub ≥ ρ_water(V_sub)