But you already know about this, because Fg is what normies call an object’s “weight,” and for a given volume, weight depends only on the density. Now, if you dropped these blocks in a lake, obviously the styrofoam would float and the steel would sink. So clearly it has something to do with density.
What if you had a block of water with the same volume? If you could somehow hold this cube of water, it would feel pretty heavy, about 62.4 pounds. Now, if you place it carefully in a lake, will it sink or bob on the surface like styrofoam? Neither, right? It’s just going to sit there.
Since it doesn’t move up or down, the total force on the block of water must be zero. That means there has to be a force counteracting gravity by pushing up with equal strength. We call this buoyancy, and for any object, the buoyancy force is equal to the weight of the water it displaces.
So let’s think about this. The steel block displaces the same amount of water, so it has the same upward-pushing buoyancy force as the block of water. But because it’s denser and has more mass, down it goes.
In general, an object will sink if the gravitational force exceeds the buoyancy force, and it will float if the buoyancy force exceeds the gravitational force. Another way of saying that is, an object will sink if it’s denser than water and it will float if it’s less dense.
And right in the middle an object will neither sink nor rise to the surface—we call that neutral buoyancy. Humans are pretty close to neutral because our bodies are 60 percent water. That’s why you feel weightless underwater—the buoyancy force pretty much offsets the gravitational force.
Avast! Hold on there, matey. Aircraft carriers are made of steel and weigh 100,000 tons, so why do they float? Can you guess? It’s because of their shape. Unlike a block of steel, a ship’s hull is hollow and filled with air, so it has a large volume relative to its weight.
But what if you start filling it with cargo? The ship gets heavier, which means it must displace more water to reach that equilibrium point. In general, when you launch a boat or ship into the water, it’ll sink down until the weight of the water it pushes aside equals the boat’s total weight.