MCAT Chemical and Physical Foundations of Biological Systems Flashcards: 4b Buoyancy Archimedes

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This deck focuses on 4b Buoyancy Archimedes, giving you a quick way to review the definitions, rules, and examples that matter most for MCAT Chemical and Physical Foundations of Biological Systems.

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Flashcard 1: What is the net force on a fully submerged object (positive upward) in terms of $F_B$ and $W$?

Answer: $F_{\text{net}}=F_B-W$. Net force is the difference between upward buoyant force and downward weight.

Flashcard 2: A cube of volume $1.0\times10^{-3}\,\text{m}^3$ floats in oil with $\rho=800\,\text{kg/m}^3$. What is its maximum mass?

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

Flashcard 3: A $0.50\,\text{m}^3$ object is fully submerged in a fluid with $\rho=1200\,\text{kg/m}^3$. Find $F_B$ using $g=10\,\text{m/s}^2$.

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

Flashcard 4: An object has $\rho_{\text{obj}}=800\,\text{kg/m}^3$ in water. What fraction of its volume is submerged when floating?

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

Flashcard 5: An object floats in water with $60\%$ of its volume submerged. What is $\rho_{\text{obj}}$?

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

Flashcard 6: A $1.0\,\text{kg}$ object experiences $F_B=3\,\text{N}$. What is its apparent weight in the fluid using $g=10\,\text{m/s}^2$?

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

Flashcard 7: A $1.0\,\text{kg}$ object displaces $5.0\times10^{-4}\,\text{m}^3$ of water. What is $F_B$ using $g=10\,\text{m/s}^2$?

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

Flashcard 8: Find the buoyant force on $2.0\,\text{L}$ of displaced water using $\rho=1000\,\text{kg/m}^3$ and $g=10\,\text{m/s}^2$.

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

Flashcard 9: Which option is correct: buoyant force depends on object density or on fluid density (for fixed $V_{\text{disp}}$)?

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

Flashcard 10: Identify the correct unit for buoyant force in SI base units.

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

Flashcard 11: What is the formula for buoyant force on a fully submerged object in a fluid?

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

Flashcard 12: What does Archimedes’ principle state about the buoyant force on an object in a fluid?

Answer: 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.

Flashcard 13: What is the formula for the weight of a displaced fluid volume $V_{\text{disp}}$?

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

Flashcard 14: Which condition determines whether an object floats, in terms of average densities?

Answer: 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.

Flashcard 15: Which condition determines whether an object sinks, in terms of average densities?

Answer: 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.

Flashcard 16: What is the condition for neutral buoyancy (neither rising nor sinking) in a fluid?

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

Flashcard 17: What is the equilibrium force balance for a floating object (neglecting surface tension)?

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

Flashcard 18: What is the fraction of a floating object’s volume that is submerged in a fluid?

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

Flashcard 19: What is the volume displaced by an object that is fully submerged in a fluid?

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

Flashcard 20: What is the volume displaced by an object that is floating (partially submerged)?

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

Flashcard 21: What is the formula for the pressure difference across a vertical height $h$ in a static fluid?

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

Flashcard 22: What is the formula for hydrostatic pressure at depth $h$ below a fluid surface?

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

Flashcard 23: Which statement best describes how buoyant force changes with depth in an incompressible fluid?

Answer: 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.

Flashcard 24: What is the apparent weight of a fully submerged object in a fluid, in terms of $W$ and $F_B$?

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

Flashcard 25: What is the buoyant force on a fully submerged object of volume $V$ in a fluid of density $\rho$?

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