Physics Class: Upthrust and Buoyancy

Study Notes

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.

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.

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.

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.

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.

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.

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.

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).

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).

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.

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.

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.

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.

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

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.