Theoretical and Experimental Analysis of Stable Equilibria of Floating Cylinders

In a typical physics course, students determine whether an object floats based on its density relative to that of the fluid. By discussing the orientation of the floating object, students can gain insights into the differences between equilibrium and stability. Here we show how a hollow cylindrical shell with radius R, and height H floats. The answer depends on H/R and the relative density of the cylinder to the density of the fluid: ρ. Assuming that ρ = 0.5, we identify stable equilibria and show what values of H/R produce stable equilibrium that are horizontal, vertical, or angled. The theory agrees well with experimental data from 3D printed cylinders. The experimental portion of this project is easily completed by introductory physics students and shows good agreement with the theoretical angle of stability for solid cylinders, suggesting a simple way to illustrate the stability of various objects.