Why are there 2 ways of predicting if an object will float or not?

I thought about it for a second, I have always thought that for an object to float it had to be less dense than water, and if it had more density then it would sink. But then if it sinks or floats also depends on the equilibrium of forces between the weight and the buoyant force? As in if the buoyant force $$F=m_{displaced}g=\rho_{water}V_{displaced}g$$ is greater than the weight $$w=mg$$ then it will float, if not, then it will sink.

But which of both ways is the correct one? Which one will I have it use if I want to predict if it will float an object or not? Or does both relate to each other in some way that I don't know of?

Both are the same. since the buoyant force $$F_b=\rho*V$$ where $$\rho$$ is the density of the fluid and V the volume of the subject. so if $$F_b>mg$$ it floats. So usually the first way is easier if you have a homogenous object with known $$\rho$$, the second if you only know weight and volume.
• Nice answer. So you can quickly tell if an non-homogenous object (such as boat hull or a hollow shell) will float using $F_b>mg$, but to determine the height at which it floats you need a more detailed calculation which calculates how the volume and mass of the submerged part of the object depend on the amount submerged. Aug 13, 2023 at 10:21