Archimedes

Archimedes' Principle: Any body completely or partially submerged in a fluid experiences an upward buoyant force equal to the weight of fluid displaced: $F_b = \rho_f \cdot V_{\text{disp}} \cdot g$.

Flotation Equilibrium: An object floats if $\rho_{\text{obj}} < \rho_f$, remains neutral if $\rho_{\text{obj}} = \rho_f$, and sinks if $\rho_{\text{obj}} > \rho_f$. Net force is $F_{\text{net}} = (\rho_f V_{\text{disp}} - m)g$.

Torricelli's Law: The efflux speed of liquid discharging through an orifice at depth $h$ under gravity is $v = \sqrt{2gh}$, derived from Bernoulli's conservation of energy.

Operating Instructions: Set fluid density ($\rho_f$), object mass, volume, and gravity. Observe sinking/floating equilibrium and efflux draining rates on the live stage.