We can derive a neat relationship involving the density of a floating object. We start with a free-body diagram, showing that the downward force of gravity is exactly balanced by the upward buoyant force.

Let's take up to be positive. Applying Newton's Second Law gives:

+F_b - mg = ma = 0

Using Archimedes' principle gives:

ρ_fluidgV_disp = mg.

The object's mass, m, is its density ρ_obj multiplied by its volume. So:

ρ_fluidgV_disp = ρ_objVg.

Factors of g cancel, leaving:

ρ_fluid V_disp = ρ_obj V.

The density of the object is given by:

ρobj

=

Vdisp V

ρfluid

This means, for instance, that if the object floats with 40% of its volume submerged, the object's density is 40% of the fluid's density.