Archimedes' principle states that any body fully or partially submerged in a fluid experiences an upward buoyant force equal to the weight of the displaced fluid.
The buoyant force can be described as: \[{F_e} = \rho_f \, g \, V_{\text{sub}},\] where:
- \( \rho_f \) is the density of the fluid (kg/m³),
- \(g\) is the gravitational acceleration (m/s²),
- \(V_{\text{sub}}\) is the volume of the displaced fluid (m³), which corresponds to the submerged volume of the object.
For an object with density \(\rho_o\) and total volume \(V_o\), when it floats in equilibrium, the fraction of the submerged volume is obtained by equating the object's weight to the buoyant force: \[ \rho_o \, g \, V_o \times \text{(submerged fraction)} \;=\; \rho_f \, g \, V_o \times \text{(submerged fraction)}. \] Simplifying: \[ \text{submerged fraction} \;=\; \frac{\rho_o}{\rho_f}. \]
However, when the object is free to move (as in this simulation), its equilibrium position is where the gravitational and buoyant forces balance; if displaced from this position, it may oscillate due to inertia and variations in the submerged portion.