Buoyancy and Archimedes’ Principle (4B) - MCAT Chemical and Physical Foundations of Biological Systems

$0.80,\text{kg}$. Maximum mass for floating occurs when object density equals oil density, so mass is oil density times volume.

$6000,\text{N}$. Buoyant force equals fluid density times submerged volume times gravity for fully submerged objects.

$0.80$. Submerged fraction equals object density divided by water density for floating objects.

$600,\text{kg/m}^3$. Object density is the submerged fraction times water density for floating equilibrium.

$7,\text{N}$. Apparent weight equals actual weight minus buoyant force, reducing effective downward force.

$5,\text{N}$. Buoyant force depends on displaced water volume and water density, independent of object mass.

$20,\text{N}$. Buoyant force equals the weight of displaced water, calculated as density times volume times gravity.

It depends on fluid density, not object density. Buoyant force arises from fluid pressure differences and scales with fluid density for constant displaced volume.

$\text{N}=\text{kg}\cdot\text{m}\cdot\text{s}^{-2}$. Buoyant force, a force, has units of Newtons, equivalent to kg m s^{-2} in SI base units.

$F_B=\rho_{\text{fluid}}V_{\text{disp}}g$. Archimedes' principle states that the buoyant force equals the weight of the fluid displaced by the submerged volume.

Buoyant force equals weight of displaced fluid. Archimedes' principle quantifies the upward force on an object as equal to the weight of the fluid it displaces.

$W_{\text{disp}}=\rho_{\text{fluid}}V_{\text{disp}}g$. Weight equals mass times gravity, where mass is the product of fluid density and displaced volume.

Floats if $\rho_{\text{obj}}<\rho_{\text{fluid}}$. An object floats when its average density is less than the fluid's, causing buoyant force to exceed weight when partially submerged.

Sinks if $\rho_{\text{obj}}>\rho_{\text{fluid}}$. An object sinks when its average density exceeds the fluid's, resulting in weight greater than maximum buoyant force.

$\rho_{\text{obj}}=\rho_{\text{fluid}}$. Neutral buoyancy occurs when the object's density matches the fluid's, balancing buoyant force and weight.

$F_B=W$. At equilibrium, the buoyant force upward equals the object's weight downward for a floating object.

$\frac{V_{\text{sub}}}{V_{\text{obj}}}=\frac{\rho_{\text{obj}}}{\rho_{\text{fluid}}}$. The submerged fraction equals the ratio of object density to fluid density for equilibrium in floating objects.

$V_{\text{disp}}=V_{\text{obj}}$. For fully submerged objects, the displaced volume equals the entire object volume.

$V_{\text{disp}}=V_{\text{sub}}$. Displaced volume for floating objects is the submerged portion, balancing buoyant force with weight.

$\Delta P=\rho gh$. Pressure increases linearly with depth due to the weight of the overlying fluid column.

$P=P_0+\rho gh$. Hydrostatic pressure adds the contribution from the fluid column to the surface pressure.

It is independent of depth for fixed $V_{\text{disp}}$. In incompressible fluids, buoyant force depends on displaced volume and fluid density, remaining constant with depth.

$W_{\text{app}}=W-F_B$. Apparent weight is the actual weight reduced by the opposing buoyant force.

$F_B=\rho V g$. Buoyant force equals the weight of displaced fluid, calculated as fluid density times object volume times gravity.