this is one of those things ive always accepted but never knew how it worked. i always assumed it was density, but a boat weighs more than a rock. so whats the deal?
True, a boat weighs more than a rock. But OTOH, a boat has a lot of empty space in it filled with air (which is lighter than water). As such, the total density is lower than water and the boat floats.
The rock, OTOH, is (mostly) solid and therefore has a greater total density than water. So it sinks.
The ultimate example of this is the planet Saturn. Saturn (which presumably weighs more than a boat) has a density of less than water. As such, if there was an ocean big enough to hold it, the planet would float.
Zev Steinhardt
It **is **density.
Your analysis neglects the density of the air in the boat. If you dismantled the (presumed) metal boat so that it can’t trap* air, those pieces would not float.
If something has a **net **density less than water it will float.
*or try to force air below the water level
You’re almost there, Hoss.
You just need to revisit your idea of density. As opposed to weight, I mean. Us regular folks need to think of density as a combination of weight and volume.
The short answer is that if you put something into a liquid, it will sink into that liquid. When it is sinking, it is *displacing * the liquid. Fill a pan with water. Carefully place an object into the water and catch every drop that overflows. As long as the object is floating, the *weight * of that water will equal the weight of the block of wood. The *volume * of the displaced water will be less than the wood. Because the wood has equal weight but greater volume, it is said to be less dense. If you could squeeze that same piece of wood into a chunk that took up less space than the water it displaces, it will sink like…a stone.
So if you take 1,000 tons of sheet steel and configure it in such a way as to create a space that would hold 1,000 tons or more of water–but don’t let any water in that space, it will float on water. Because the density (weight / volume) is less than the density of water–it is capable of displacing more than its own weight in water.
(is this horse dead yet?)
Or looking at it another way, an object displaces its own volume of water, but that water may weight more or less than the object itself; if the displaced water weighs more than the object, the object will float.
It is density, but it’s hard to see the difference between the boat and the rock because you don’t see the air within the boat hull as being part of the boat.
Technically, a boat floats because of displacement:
Take a 25 lb rock and a 25 pound boat. The rock is the same weight, but much more dense. Because of that, it displaces (takes up volume) that is less than its weight in water. That is, a 25 pound rock takes up as much volume as say 8 pounds of water. Drop the rock in water, it sinks.
Now take a 25 pound boat. That’s a pretty lightweight boat; let’s say it’s a canoe made of carbon fiber. It displaces a LOT more water than the rock, probably 5 gallons which is roughly 40 pounds of water. Since it displaces MORE weight in water than its own weight, it floats.
If you put the canoe in a car crusher and smash it to roughly the size of the rock, it will sink.
Back to density:
That this is related to density is not so obvious. You have to count in the air that’s inside the canoe. We don’t do that because the air doesn’t seem to be part of the boat, but it is; you’re just not used to seeing it that way.
Another way to look at this is to imagine a carbon-fiber ball filled with air, floating in the water. Remember, it floats because the whole ball, including the air, is less dense than the equivalent volume of water. Fill the think with liquid mercury and it will sink! The air is not “holding up the ball.”
Now cut the top off the ball. It still floats, because it’s still less dense than the equivalent volume of water. The air has been “let out,” but that doesn’t matter. Air means nothing, volume means everything.
Asides:
Some rocks DO float. Pumice, a volcanic rock, floats in water. Pumice is like a rocky sponge, filled with air vesicles. This leads to a great camping trick: making camp coffee. Pour ground coffee into boiling water and cook. If someone asks you when you know it’s ready, tell them “when a rock floats in it.” Good for a laugh. Reinforce the idea by tossing pebbles in, then when you think it’s ready, palm your trusty piece of pumice and toss it in…
The planet Saturn has a density less than that of water, according to our most reliable calculations. If you could find enough water, you could float Saturn in it. One heck of a beach ball!
A canoe that floats can be made out of concrete as a matter of fact. It’s a classic Mechanical Engineering student project.
Haj
Not sure if your post was directed at mine or at the OP…
Actually, density is Mass/Volume. People often confuse mass and weight. They aren’t the same, since weight depends on the strength of the gravitational field you are in. Most of the time this is OK, since we’re usually talking about stuff that happens on the surface of the earth, in which case you can pretty much ignore the difference (just a multiplicative factor).
Not directed at you, sir.
I figured I’d get something wrong if I started adding details. 
And that’s all you need to know to have a future as a political adviser! 
Eureka! <jumps out of tub and runs naked through the village>
So if she’s a witch, then she floats? Or is she a duck, or a piece of wood? 
Concrete pontoons and barges are also quite commonplace.
It only displaces its own volume of water if it sinks.
Stuff float?
Two scoops of stuff and some soda water…