Buoyant Force and Floating Conditions

Buoyant Force

• The buoyant force is the upward force exerted by a fluid that opposes the weight of an object submerged.
• It originates from the pressure difference between the top and bottom of the object submerged in a fluid.
• The formula for buoyant force is $F_b = V_d \rho_l g$, where:
  • $V_d$ is the displaced volume, the volume of fluid displaced by the object.
  • $\rho_l$ is the density of the liquid.
  • $g$ is the acceleration due to gravity.

Floating Conditions

• Floating occurs when the buoyant force is equal to the weight of the object ($F_b = W$)
• In a scenario where an object floats, it is in equilibrium.
• There are two types of floating:
  • Fully Immersed: The object is completely submerged.
  • Partially Immersed: Only a portion of the object is submerged.
• Fully Immersed: This happens when the density of the body is equal to the density of the liquid.
• Partially Immersed: This happens when the density of the body is less than the density of the liquid.
• The weight of the submerged portion of the body is equal to the buoyant force acting on it.
• The weight of the object is equal to the buoyant force acting on it ($W=F_b$).

Formulas and Notes

• The weight of the object is given by the formula: $W = mg$, where $m$ is the mass and $g$ is the acceleration due to gravity.
• For an object that is just floating (fully submerged):
  • The volume of the submerged object ($V_d$) is equal to the whole volume of the object ($V_b$).
  • The condition for this type of floating is given by: $\rho_b V_b g = V_d \rho_l g$
• For an object that is floating with some portion outside (partially submerged):
  • The displaced volume ($V_d$) is less than the total volume of the object ($V_b$).
  • The condition for this type of floating is given by: $\rho_b V_b g = V_d \rho_l g$

Explore the principles of buoyant force and the conditions for an object to float. This quiz covers key concepts such as the formula for buoyant force, types of floating, and equilibrium conditions. Test your understanding of how density and pressure differences affect floating behavior.