# Fluids - A lost shipping container is found resting on the ocean floor

• crono_
In summary, the shipping container just begins to rise towards the surface when a spherical balloon is attached to it. The mass of the container is 60297.675 kg.
crono_

## Homework Statement

A lost shipping container is found resting on the ocean floor and completely submerged. The container is 6.3 m long, 2.1 m wide, and 2.6 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 1.8 m, the shipping container just begins to rise towards 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.

Container

L = 6.3 m
w = 2.1 m
h = 2.6 m
V = ?

Balloon / Air

r = 1.8 m
p = 1.29 kg / m3
V =
FB =

Water

p = 1025 kg / m3
FB =

## Homework Equations

Archimedes' Principle

FB = Wfluid

Vcontainer = L * w * h

Vballoon = 4/3 $$\pi$$r3

p = m / v

F = ma

## The Attempt at a Solution

First I found the volumes for the container and the balloon.

Vcontainer = L * w * h

Vcontainer = 6.3 * 2.1 * 2.6

Vcontainer = 34.398 m3

Vballoon = 4/3 $$\pi$$r3

Vballoon = 4/3 $$\pi$$1.83

Vballoon = 24.429

I then tried to find the buoyant force of the air.

FB = Wair

FB = mg

FB = pVg

FB = 1.29 * 24.429 * 9.8

FB = 308.83 N

And then for the sea water.

FB = Wwater

FB = mg

FB = pVg

FB = 1025 * 34.398 * 9.8

FB = 345527.91 N

After this, I used Newton's 2nd law...

F = ma

m = F / a

m = FBair + FBwater / g

m = 308.83 N + 345527.91 N / 9.80 m/s2

m = 35289 kg ----> 3.5 * 104 kg

But...this appears to be wrong...Um...thoughts?

Thanks!

Last edited:
Check the bouyancy of the balloon

You can ignore the mass of the air - otherwise it's the same calcuation as the container

Hmmm...

The buoyant force equals the weight of the displaced fluid which is the sea water, not the air. So the equation should have been:

FB = Wwater

= mg

= pVballoong

= 1025 * 24.429 * 9.8

= 245389 N

So, using that...

F = mg

m = F / g

m = 245389.30 N + 345527.91 N / 9.80 m/s2

m = 60297.67 kg ----> 6.0 * 104 kg

How is that?

Assuming you pressed the right buttons - yes.
You can simplify it a little by ignoring 'g' - since you cancel it out.
You just want the mass of seawater contained in the volume of shipping container and volume of balloon.

Didn't know what you meant by the g's cancelling, but I went back a few steps and tried this...Please excuse pi appearing as an exponent, I have no idea why that happens.

p(4/3 $$\pi$$r3)[STRIKE]g[/STRIKE] + p(L*w*h)[STRIKE]g[/STRIKE] = m[STRIKE]g[/STRIKE]

p(4/3 $$\pi$$r3) + p(L*w*h) = m

1025 kg/[STRIKE]m3[/STRIKE] (24.429 [STRIKE]m3[/STRIKE]) + 1025 kg/[STRIKE]m3[/STRIKE] (34.398 [STRIKE]m3[/STRIKE])

1025 kg (24.429) + 1025 kg (34.398)

25039.725 kg + 35257.95 kg

= 60297.675 kg ---> 6.0 * 104 kg

Do I pass?

Thats exactly it, since you are asked for the mass it doesn't really make sense to multiply the masses of seawater by g to calculate upward force then divide the weight by g to get mass
So you should get the same answer!

Great! Thanks a bunch for your help! :)

## 1. What type of fluids are typically found in shipping containers?

Shipping containers can hold a variety of fluids, such as water, oil, chemicals, and gases. It depends on what was being transported at the time of the accident.

## 2. How do shipping containers end up lost on the ocean floor?

Shipping containers can become lost on the ocean floor due to severe weather conditions, accidents during transportation, or improper stowing on the ship.

## 3. Can the fluids inside the container leak into the ocean and harm marine life?

Yes, if the container is damaged, the fluids inside can leak into the ocean and potentially harm marine life. This is why it is important to properly secure and transport fluids on ships.

## 4. How do scientists locate and retrieve lost shipping containers on the ocean floor?

Scientists use sonar technology and underwater robots to locate and retrieve lost shipping containers. They can also track the containers using GPS signals and data from shipping companies.

## 5. What are the potential environmental impacts of a lost shipping container on the ocean floor?

A lost shipping container can have various environmental impacts, including damage to marine life and habitats, pollution from leaked fluids or cargo, and disruption of ocean currents and ecosystems. It is important to properly handle and retrieve lost containers to minimize these impacts.