The ancient Greek mathematician Archimedes was the first to figure out when something is going to float or sink. Supposedly, he made this discovery while taking a bath and was so excited that he jumped out of the tube, exclaimed, “Eureka, Eureka!” and ran out into the streets to tell the king.

His insight, now known as Archimedes’ Principle, states that an object will sink if the weight of the water displaced by the object is less than the weight of the object. Floating occurs when the weight of the water displaced equals the weight of the object. Ok, but why?

What Archimedes really figured out is that gravity acts both on water and submerged objects and there is effectively a competition to sink between submerged objects and the water that would be there if the submerged object was not. Both the water and a submerged object are both being pulled to the center of the Earth by gravity, but because water is a fluid, objects can move through the water and sink unless the water itself weighs more. Practically speaking, if an object has a greater mass than the water that would fill the same size as the object, then the object will displace the water and sink. In other words, it’s about density. (Related IFOD on Density!)

The key is that it is the average density of the overall object that counts. If you want an object to float, you don’t have to change the object’s mass – instead, just change the density of the object relative to the water. Illustration of this:

Fun Fact: Cans of diet soda, sparkling water and beer all float. Cans of regular soda sink. Why? The few grams of sugar in the regular soda add to the density of the water, other ingredients in soda and the aluminum can to be denser than water. Diet soda’s artificial sweeter weighs nearly nothing so its just water, carbonation and a few other ingredients.  The bubbles of the carbonation reduce the density so that the liquid and can together are less dense than water. Same concept for beer and sparkling water.

Based on Archimedes’ Principle, here’s a fun thought experiment. Imagine you are floating in a canoe in a small pond. On your lap is a decent sized rock that weighs 50 pounds.  What happens to the level of the water in the pond if you throw the rock overboard? Does  the water level rise, fall or stay the same?  Think about it for a bit.

The answer: the water level in the pond falls. Seems counter-intuitive. Here’s why: while in the canoe the 50 pound rock caused the canoe to displace 50 pounds of water, which caused the pond water level to rise as compared to the rock sitting on land. When the rock was tossed in the water the rock merely displaced an amount of water equal to the size of the rock. Since the rock is denser, much less water is displaced by the rock submerged as compared to the rock in the canoe. In other words, if the rock is about 2.5x as dense as water, moving from the canoe where the rock caused 50 pounds of water to be displaced, submerged in the water the rock only caused 20 pounds of water to be displaced, resulting in the overall level of water to fall.

So, how do large steel ships float on water – their overall average density is less than water because their hulls are designed to spread the weight of the ship and contents over a large enough area.