Why do some things float in water?

It's All About Displacement

Objects in water displace some quantity of that water. The amount of water displaced on the mass and volume of the object. Objects float because the mass of the water they displace is greater than their own mass.

Take, for example, a 10 cubic foot barrel placed in a fresh water lake. Visualize a small barrel about 18 inches in diameter by just over 2 feet long. Let's assume that the barrel weighs 10 pounds when empty.

Water has a mass of about 62.4 pounds per cubic foot. The 10 cubic foot barrel, if sunk, would displace about 624 pounds of water. That is to say, before the barrel can sink, 624 pounds of water must be moved out of the way so the barrel can take its place. Another way to view this is that there is a 624 pound force trying to keep the barrel afloat.

Let's imagine that our barrel is empty. The term "empty" here on Earth doesn't really mean it has nothing in it. It actually means it's filled with air. Air weighs about .08 pounds per cubic foot. If the barrel is filled with air, it would weigh 10.8 pounds (10 for the barrel itself plus .8 for the air). Since the volume of water that would need to be displaced to sink the barrel weighs 624 pounds, the 10.8 pound air-filled barrel will float. In fact it can only displace 10.8/62 cubic feet of water, or about .17 cubic feet. The barrel would float very high in the water - most of it would be above the surface. We'd have to strap another 613.2 pounds to our barrel before it would begin to sink.

Imagine instead that the barrel is filled with something heavier - say Mercury. Mercury weighs about 849 pounds per cubic foot. Our ten cubic foot barrel of mercury weighs 8500 pounds! (10 pounds for the barrel and 8490 for the mercury). It will easily displace the 624 pounds of water and will sink like... well... like a barrel full of mercury. That is, assuming you could roll an 8500 pound barrel as far as the lake to begin with.

Let's turn the question around. How many cubic feet of mercury could we put into our barrel and have it continue to float? Remember that if our barrel sinks, it will displace 10 cubic feet of water and that water weighs 624 pounds. We need to keep our 10 pound barrel afloat, so that leaves us 614 pounds. Our mercury has to weigh less than 614 pounds if we expect our barrel to float.

Since mercury weighs 849 pounds per cubic foot, 614 pounds of it is about .723 cubic feet (614/849). If we put less than .723 cubic feet of mercury into our barrel and put it in the lake, it will float.

Alert readers might point out that the portion of the barrel that isn't holding mercury probably contains air, which we need to account for. That's true but mercury is so dense that the numbers don't change much.

I know what you're thinking. "What about beets?" you're thinking. Actually this exercise can be repeated with any substance we know the density of. That is, we know what's its mass is for a given volume. There's a link at the end of this answer to a table of densities and weights per cubic foot of scores of common substances. Will the barrel float if it's filled with beets? Check the table to figure it out.

It turns out that we don't need to imagine barrels filled with stuff to determine if that stuff will float in fresh water. We know that water weighs 62.4 pounds per cubic foot. Any material that weighs less than 62.4 pounds per cubic foot will float. If it weighs more, it will sink. That's pretty easy, but if we take a look at our table we'll notice something that will make our calculations even easier. That's something called specific gravity.

Specific gravity is a measure of how dense something is when compared to fresh water (remember that density is how much something weighs for some given volume). The specific gravity of pure water is always 1. If a substance has a specific gravity of less that one, it will float. A substance with a specific gravity greater than one will sink.

Our beets have a specific gravity of .72. They'll float. Birch wood, with a specific gravity of .71 floats even better than beets. Red brick, at 1.92, sinks like a brick. That's why it's somewhat easier to build a boat out of birch wood than it is out of brick. As for a boat made of beets, the mind boggles.