Physics Class: Upthrust and Buoyancy

Upthrust

• An upward force exerted by a fluid (liquid or gas) on a partially or completely submerged object.
• Measured in Newtons (N).
• Acts in the upward direction.
• The point where upthrust acts is called the center of buoyancy.

Buoyancy

• The property of a fluid to exert an upthrust on an immersed object.

Characteristics of Upthrust

• Increases with the volume of the object submerged in the fluid.
• Increases with the density of the fluid the object is submerged in.
• Acts on a body in an upward direction and is equal to the weight of the displaced liquid.

Factors Affecting Upthrust

• Upthrust is proportional to the volume of the object submerged.
• Upthrust is proportional to the density of the fluid.

Upthrust and Objects Falling

• In a vacuum, objects of the same mass will fall at the same rate due to the absence of upthrust.
• In air, objects with larger volumes will experience more upthrust and fall slower.

Comparing Upthrust in Different Fluids

• A body will experience more upthrust in a denser fluid.
• A body submerged to the same level in sea water will experience more upthrust than in river water due to the higher density of seawater.

Upthrust and Objects in Liquids

• An object will experience more upthrust in a denser liquid.
• An object held completely submerged in glycerine will experience more upthrust than in water because glycerine is denser.

Calculating Upthrust

• The resultant upward thrust (buoyant force) on a cylindrical body immersed in a liquid is equal to the weight of the liquid displaced by the body.
• Upthrust formula: F_B = hρgA where:
  • F_B is the buoyant force.
  • h is the height of the cylinder.
  • ρ is the density of the liquid.
  • g is the acceleration due to gravity.
  • A is the cross-sectional area of the cylinder.

Upthrust and Apparent Weight

• The apparent weight of an object in a liquid is less than the actual weight due to upthrust.
• Apparent weight = Real weight - Weight of displaced liquid = V(ρ - ρ_L)g where:
  • V is the volume of the object.
  • ρ is the density of the object.
  • ρ_L is the density of the liquid.
  • g is the acceleration due to gravity.

Upthrust and Floating/Sinking

• A body will sink if its weight is greater than the upthrust.
  • This occurs when the density of the body is greater than the density of the liquid (ρ > ρ_L).
• A body will float if its weight is equal to the upthrust.
  • This occurs when the body is completely immersed but just below the surface of the liquid (ρ < ρ_L).
• A body will float partially immersed if its weight is equal to the upthrust.
  • This occurs when the body is partially immersed and the upthrust balances the weight (ρ = ρ_L).

Relation Between Density and Floating/Sinking

• A body will sink if the density of the substance is greater than the density of the liquid (ρ_s > ρ_L).
• A body will float completely immersed in a liquid if the density of the substance is equal to the density of the liquid (ρ_s = ρ_L).
• A body will float partially immersed in a liquid if the density of the substance is less than the density of the liquid (ρ_s < ρ_L).

Archimedes' Principle

• States that the upthrust experienced by a body immersed in a liquid is equal to the weight of the liquid displaced by the body.
• Upthrust (Buoyant force) = V × ρ_L × g where:
  • V is the volume of the body submerged in the liquid.
  • ρ_L is the density of the liquid.
  • g is the acceleration due to gravity.

Principle of Flotation

• States that the weight of a floating body is equal to the weight of the liquid displaced by the submerged part.
• The apparent weight of a floating body is 0.

Applications of Upthrust

• Icebergs: Icebergs float with 9/10th of their volume submerged in water.
• Ships: Ships are designed to displace a volume of water that is greater than their own weight.
• Hot air balloons: Hot air balloons rise because the hot air inside is less dense than the surrounding air, creating an upthrust.
• Submarines: Submarines control their buoyancy by adjusting the amount of water in their ballast tanks.
• Swimming: We float in water because our density is slightly less than the density of water.

Summary of Floating and Sinking

• Objects of density less than that of a liquid float.
• Objects of density greater than that of a liquid sink.
• Upthrust is the key factor in determining whether an object will float or sink.
• Upthrust is also responsible for the apparent loss of weight experienced by objects submerged in a liquid.

Law of Flotation

• A body will float in a liquid if the weight of the body is equal to the weight of the liquid displaced by it.

Volume of Submerged Part

• The volume of the submerged part of a floating body can be calculated using the following equation: V/V_s = ρ_L/ρ_s where:
  • V is the total volume of the body.
  • V_s is the volume of the submerged part.
  • ρ_L is the density of the liquid.
  • ρ_s is the density of the body.