Calculating Mass An Object Can Float In The Ocean

[SpearoWilso]

Homework Statement

This is a general question, not something I have been assigned for a subject. I am just wondering how you can calculate the mass a float can support in the ocean. I have no idea how to go about working this out, any help would be greatly appreciated

For example, how much mass can a 2lt milk bottle support before it sinks?

Homework Equations

Not Sure!

The Attempt at a Solution

 

[Feldoh]

Buoyancy would be a good place to start

 

[SpearoWilso]

all of the buoyancy formula's i have found are only used to calculate whether a material will float or not, how can I modify the formula to calculate the amount of weight required to submerge an object?

 

[SpearoWilso]

Perhaps some background into why I am interested in this question will spark a bit of interest.

I am a keen freediver and spearfisherman. When spearfishing, divers generally use a float attatched to a line which connects to the speargun. The reasoning behind this is that if a large fish is speared the diver can drop the gun and let the fish run, working the rope or float to tire the fish. This setup also allows the diver to string and tow fish along the rope at a reasonable distance from the diver to keep some level of safety from sharks.

When targeting large game spearfisherman use floats with large capacities to prevent fish from pulling floats underwater for extended periods of time and give them the best chance of landing the fish.

Now I have recently heard that some spearfisherman have lost fish when they have died because the dead mass of the fish is actually great enough to pull these large capacity floats underwater and sink them to the bottom.

Clearly the volume of air in the float is pivotal to calculating the mass it will support, i imagine the air pressure could also have some effect? I am interested in a general formula that will provide a rough idea of the dead mass it will take to sink a large float (e.g.70lt of air) in the ocean

Any help would be greatly appreciated!

 

[Pengwuino]

What you need to figure out is how high up the waterline can be before the vessel begins taking on water (or at a height you feel is acceptable for water to be incase of rough seas).

Let's say you want the waterline to be at the extreme and be right at the top of the perimeter of the boat (aka, a simple boat). What you do is you find the volume of the water that is displaced by the volume of the boat below that waterline. For example, if you have a cube shaped boat and its dimensions are 1m x 1m x 1m and when the water is 1m high, you consider it capsizing, the boat can displace a maximum of 1 cubic meter of water. If you have the water at sya, 0.5m high, it is only displacing 0.5 cubic meters. Now you need to figure out how much 1 cubic meter (or for the second example, 0.5) of water weighs. That way is how much of a load your cubic boat can support.

So in general, the boat can support as much as how much water it is capable of displacing before going under. For your milk carton example, it can basically support the mass of 2lt of water (minus the mass of the carton of course :) )

 

[SpearoWilso]

Thanks for your input, that is definitely helpful, but I am afraid I still don't understand the process fully, can you clarify what is meant by displacement in this instance?

Given that the density of seawater can be expressed as 1.027 kg/liter (for surface seawater)

Does this mean, roughly:

1ltr float will sink by a mass >1.027kg
2ltr float will sink by a mass >2*1.027kg

etc. etc. up to

35ltr float will sink by a mass >35*1.027kg

?

 

[SpearoWilso]

bump...any more help?

 

[diazona]

Displacement in the sense that Pengwuino was talking about refers to the amount of water that is displaced (pushed out of the way) by the milk bottle or whatever. The volume of water displaced is the same as the volume of the milk bottle that is below the waterline. For the kinds of floats you're talking about, since they are presumably fully closed up like a balloon (as opposed to, say, a boat, which has openings that will let in water if it sinks too low), the volume of water displaced can go as high as the volume of the object itself - that is to say, the float can be fully submerged and it will still exert its full lifting force. So the maximum weight it can support is equal to the amount of water that would fill the float's volume.

The point being, yes a 1L float will support a mass of 1.027kg, a 2L float will support 2*1.027kg, etc.

I actually made a couple of blog posts on just this topic recently:
http://www.ellipsix.net/blog/post.78.html
http://www.ellipsix.net/blog/post.79.html
Feel free to read them if you're interested.