# You know it has something to do with Density, but what?

As the story goes, Archimedes was bathing in a public bathhouse several thousand years ago when he noticed the water level rise around him in the tub. Truly thrilled by his apparently miraculous realization, he jumped out of the tub and ran through the streets naked screaming "Eureka!!! Eureka!!!" (I've found it!!! I've found it). What Archimedes had discovered is now referred to as Fluid Displacement. He had noticed that when a body is submerged in a fluid, that body displaces a volume of the fluid equal to its own. That is, to say, that if I placed a cubic meter block of stainless steel into a pool (don't ask me how), the block would displace exactly one cubic meter of water. Simple, right?

Anyway, back to our naked friend. Archimedes also noticed that the objects felt lighter when they were submerged. This phenomena made him want to quantify this observation. After a while, Archimedes made the wonderful discovery that the objects were buoyed up by a force equal to the weight of the fluid that they displace.

So let's take a look at our block in the pool. That cube of stainless steel (which is more dense than water) would have a mass of approximately 8020 kg or would weigh 78596 N. As we learned before, the cube would displace one cubic meter of water, which has a mass of (quite conveniently) 1000 kg or a weight of 9800 N. So the cube would be pushed up, in effect, by 9800 N of water. 78596 (its real weight) - 9800 (what's pushing up on it) = 68796 N (its weight while submerged). Great, now you know this thing weighs 9800 N less while I try to get it out of my pool.

Now let's try something we know is less dense than water. We'll take, oh I dunno, cedar wood, which has a density of .49 g/cu cm. Keep in mind that water's density is 1 g/cu cm. So if I had one cubic meter of wood (if you haven't noticed by now,I go to Price Club), which has have a mass of 490 kg, it would, if forced underwater, displace, again, one cubic meter of water. This displaced water has a mass that is greater than the object being submerged, so in other words, the water is pushing up harder than the wood is pushing down. The wood will float at a position such that the submerged portion would displace a volume of water whose mass is equal to the mass of the entire block. Or the wood would displace its weight in water.

Humans are only slightly less dense than water, which is why we must submerge a large portion of our bodies to stay afloat (more displaced fluid means greater force pushing upwards). Women are less dense than men (due to a higher fat percentage), which is why it is easier for women to float than men. It's not our fault, it's science!