Buoyancy and Archimedes’ Principle (4B) - Chem & Physics

1. What is the equilibrium force balance for a floating object (neglecting surface tension)?

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

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

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

3. What is the volume displaced by an object that is fully submerged in a fluid?

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

4. What is the formula for the weight of a displaced fluid volume $V_{\text{disp}}$?

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

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

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

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

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

7. 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?

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

8. What is the formula for buoyant force on a fully submerged object in a fluid?

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

9. What is the formula for the pressure difference across a vertical height $h$ in a static fluid?

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

10. What is the condition for neutral buoyancy (neither rising nor sinking) in a fluid?

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

11. Identify the correct unit for buoyant force in SI base units.

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

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

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

13. Which statement best describes how buoyant force changes with depth in an incompressible fluid?

    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.

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

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

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

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

16. Which condition determines whether an object sinks, in terms of average densities?

    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.

17. What is the volume displaced by an object that is floating (partially submerged)?

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

18. What is the apparent weight of a fully submerged object in a fluid, in terms of $W$ and $F_B$?

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

19. What is the formula for hydrostatic pressure at depth $h$ below a fluid surface?

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

20. What does Archimedes' principle state about the buoyant force on an object in a fluid?

    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.

21. Which condition determines whether an object floats, in terms of average densities?

    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.

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

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

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

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

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

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

25. What is the fraction of a floating object's volume that is submerged in a fluid?

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

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