Floating subs

Why do submarines float (and sink)? It's all a matter of controlling the sub's density. If the submarine is less dense than water, it will float. If it is more dense, it will sink. So let's start by looking at density. In words, density is how much stuff is in a certain amount of volume. Mathematically, density is as follows:

(Side note: if you were to measure density on the Moon, another planet, or deep in the ocean, you'd have to worry about the difference between weight and mass. Fortunately, for most people reading this post weight and mass are approximatively equivalent. For more information, check out this link.)

We're also in luck...water has a very easy density to remember: 1000 kg/m^3. Ocean water is slightly different due to it's salt content, but for our purposes we're just going to ignore some of those subtle nuisances.

When a submarine is floating on the water, its ballast tanks are filled with air. So let's pretend the bottle below is a submarine with air-filled ballast tanks and measure it's weight.

Next the volume of the bottle needs to be deterimed. Normally this would be done by sticking the whole bottle into a graduated cylinder filled with water, but I do not have one. So I estimated the number of teaspoons that the bottle held with a measuring cup. There were about 78 teaspoons.

So now that we've found the weight and volume (and converted them to practical units), we can find the density of the empty bottle.

So here's the big question...will the bottle float?? Do you remember what we said about density up above?

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It floats!

It floats because the density of the bottle (601.5 kg/m^3) is less than water (1000 kg/m^3).

Next let's fill the bottle with blue water and see what happens. We already know the volume, but we need to find the new weight.

With the new weight we can find the density of the bottle filled with blue water:

So, is the bottle with water going to float?

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No!

The bottle sank because its density of 1573 kg/m^3 is more than that of water.

Can you figure out how full the bottle should be so that it will hover in the water?

Here are some more interesting links:

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