Archimedes' Principle Calculator

Archimedes' principle states that any object, wholly or partially immersed in a stationary fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. Mathematically, the buoyant force ($F_b$) is calculated as $F_b = V_f \times \rho_f \times g$, where $V_f$ represents the volume of the displaced fluid, $\rho_f$ is the density of the fluid, and $g$ is the acceleration due to gravity. Furthermore, an object's apparent weight ($W_{app}$) when submerged is equal to its true weight ($W_{true}$) minus the upward buoyant force: $W_{app} = W_{true} - F_b$. By rearranging these relationships, you can solve for unknown variables such as object density, volume, or displaced fluid mass.

Let us calculate the apparent weight of an object with a true mass of 5 kg and a volume of 0.004 cubic meters submerged entirely in fresh water, which has a density of $1,000 \text{ kg/m}^3$. Assume standard gravitational acceleration ($g = 9.81 \text{ m/s}^2$). First, find the true weight: $W_{true} = 5 \text{ kg} \times 9.81 \text{ m/s}^2 = 49.05 \text{ N}$. Next, calculate the buoyant force using the displaced volume (which equals the object's volume): $F_b = 0.004 \text{ m}^3 \times 1000 \text{ kg/m}^3 \times 9.81 \text{ m/s}^2 = 39.24 \text{ N}$. Finally, subtract the buoyant force from the true weight to find the apparent weight: $W_{app} = 49.05 \text{ N} - 39.24 \text{ N} = 9.81 \text{ N}$. Thus, the object feels significantly lighter underwater.

When performing manual calculations alongside this tool, always ensure your units are consistent—convert grams to kilograms and centimeters to meters before plugging values into equations. Pay close attention to fluid density variations, as temperature and salinity can alter water density significantly. Finally, remember that if an object's density is greater than the fluid density, it will sink, whereas a lesser density results in floating.