(c) Anthony K. Grafton 2003

Up, Up, and Away

Did you know that helium-filled balloons float in the air for the same reason that the 50,000 ton battleship USS Missouri floats on the water? Both of these things float because they have smaller densities than the air or water they float in.

Density is a measure of the amount of mass something has in a given volume of space. When we report densities, we usually use units like “grams per milliliter” or “grams per centimeter cubed” or “grams per liter” which look like g/ml, g/cm³, and g/L when written out. (Keep in mind that a milliliter and a centimeter cubed are the same thing, because the volume of a square box that is one centimeter on a side is one milliliter.) Usually, units of g/ml are used when talking about a liquid, g/cm³ are used to talk about a solid, and g/L are used to talk about a gas.

A helium-filled balloon rises and floats in the air because it has a density less than air. Any object will float in air or water as long as the object is less dense than the air or water in which it is floating. This is sometimes called the Archimedes (ark-e-mee-dees) principleafter the man who first discovered it more than 2200 years ago.

A helium balloon has a density of around 1 g/L and air has a density of about 1.3 g/L. Therefore, since a helium balloon is less dense than air, it floats.

The same thing is true even for the huge steel battleship USS Missouri. As heavy as it is, it floats on water because its overall density, the amount of mass per unit volume, is less than that of water (remember that ships are mostly hollow inside). Consider that the density of water is about 1 g/ml and then think how big the Missouri must be so that its overall density is less than that. In fact, the Missouri is bigger than the famous ship Titanic.

Now that you know something about density, try looking up the density of some common things such as wood, iron, concrete, and cork. Which of these would you expect to float in water? Next, look up the densities of each of the nine planets in our solar system. If you had a tub of water big enough, which ones would float?