Buoyancy and Archimedes' Principle

Archimedes' Principle states that any object fully or partially submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces:

$F_b = \rho_{\text{fluid}} \cdot g \cdot V_{\text{submerged}}$

where $g = 9.81\,\text{m/s}^2$.

Floating and Sinking

An object floats when the buoyant force equals or exceeds its weight ($F_b \geq mg$). For a floating object in equilibrium, the fraction of its volume that is submerged equals the ratio of its density to the fluid density:

$\frac{V_{\text{sub}}}{V_{\text{total}}} = \frac{\rho_{\text{object}}}{\rho_{\text{fluid}}}$

If this ratio exceeds 1, the object sinks (it cannot displace enough fluid to support its own weight).

Net Force

The net vertical force on a fully submerged object (positive = upward) acting downward is:

$F_{\text{net}} = W - F_b = mg - \rho_{\text{fluid}} \cdot g \cdot V_{\text{total}}$

A negative net force means the buoyant force exceeds gravity — the object will rise or float.

Examples

Your Task

Implement:

• buoyancy_force(rho_fluid, V_submerged) — upward buoyant force (N)
• submerged_fraction(rho_object, rho_fluid) — fraction of volume submerged
• net_force(mass, rho_fluid, V_total) — net downward force on a fully submerged object (N)