A lost shipping container is found resting on the ocean floor and completely submerged. The container is 6.5 m long, 2.5 m wide, and 2.7 m high. Salvage experts attach a spherical balloon to the top of the container and inflate it with air pumped down from the surface. When the balloon's radius is 1.4 m, the shipping container just begins to rise toward the surface. What is the mass of the container? Ignore the mass of the balloon and the air within it. Do not neglect the buoyant force exerted on the shipping container by the water. The density of seawater is 1025 kg/m3.

When the container just begins to rise, the upward and downward forces are equal. The upward forces are the buoyant force of the container [tex]B_c[/tex] and the buoyant force of the balloon [tex]B_b[/tex], while the downward force is the weight of the container. We write this as

[tex]B_c+B_b=W_c=m_cg[/tex]

A buoyant force is the weight of the displaced fluid [tex]B=m_{df}g=\rho_{sw}Vg[/tex], where the mass of the displaced fluid m_{df} is the density of the fluid multiplied by the volume displaced, in our case the density is that of seawater and the volume that of each of the objects for each buoyant force calculation, since they are completely submerged.

Our container has a volume [tex]V_c=(6.5m)(2.5m)(2.7 m)=43.875m^3[/tex].

The balloon has a volume [tex]V_b=\frac{4\pi r^3}{3}=\frac{4\pi (1.4m)^3}{3}=11.5m^3[/tex].

So our formula is:

[tex]m_cg=B_c+B_b[/tex]

[tex]m_cg=\rho_{sw}V_cg+\rho_{sw}V_bg[/tex]

[tex]m_c=\rho_{sw}(V_c+V_b)[/tex]

Which for our values gives:

[tex]m_c=(1025 kg/m^3)(43.875m^3+11.5m^3)=56759Kg[/tex]

okpalawalter8 okpalawalter8 · Answer 2 · 2022-03-31T14:57:05+02:00

Tthe mass of the container is mathematically given as

mc=56759Kg

What is the mass of the container?

Question Parameter(s):

The container is 6.5 m long, 2.5 m wide, and 2.7 m high

When the balloon's radius is 1.4 m

The density of seawater is 1025 kg/m3.

Generally, the equation for the weight of the container is mathematically given as

W_c=Bc+Bb

Where, buoyant force is

B=psw*Vg

The container volume

Vc=(6.5m)(2.5m)(2.7 m)

Vc=43.875m^3.

And

The balloon volume

[tex]V_b=\frac{4\pi r^3}{3}\\\\Vb=\frac{4\pi (1.4m)^3}{3}[/tex]

Vb=11.5m^3.

In conclusion, We sub into intial formula

m_cg=Bc+Bb

m_c=psw(V_c+V_b)

mc=(1025 kg/m^3)(43.875m^3+11.5m^3)

mc=56759Kg