Buoyancy and floatation

Archimedes’ Principle

The buoyant force on an object immersed in a fluid equals the weight of the fluid displaced by that object.

Buoyant Force Formula

Fb = ρ g V.

Fb (Buoyant Force)

The upward force exerted by a fluid on an object immersed in it.

ρ (Density)

The mass per unit volume of a substance.

g (Acceleration due to gravity)

The acceleration caused by Earth's gravity acting on objects.

V (Volume displaced)

The volume of fluid pushed aside by a submerged object.

Meaning of Archimedes’ Principle

A fluid pushes an object upward with a force equal to the weight of the fluid displaced.

Fluid Pressure Formula

P = ρ g h.

Fluid Pressure

The force per unit area exerted by a fluid.

h (Depth)

The vertical distance below the surface of a fluid.

Why buoyant force exists

Because fluid pressure increases with depth causing pressure differences on objects.

Pressure at the top of a submerged object

Smaller because the top is closer to the surface.

Pressure at the bottom of a submerged object

Larger because the bottom is deeper in the fluid.

Cause of buoyant force

The pressure at the bottom of an object is greater than the pressure at the top.

Downward force on top surface

Fdown = ρ g htop A.

Upward force on bottom surface

Fup = ρ g (htop + hcylinder) A.

Net buoyant force formula derivation

Fnet = Fup − Fdown.

Result of buoyant force derivation

Fnet = ρ g hcylinder A.

Cylinder volume formula

V = A × h.

Final buoyant force result

Fb = ρ g V.

Important conclusion about buoyancy

Buoyant force depends on volume displaced not the depth of the object.

Object floating condition

Fb > W.

Object sinking condition

W > Fb.

Object suspended condition

Fb = W.

Weight of an object formula

W = mg.

Apparent weight in water

Wapparent = W − Fb.

Reason objects feel lighter in water

The buoyant force acts upward and reduces the measured weight.

Displaced fluid definition

The fluid pushed aside when an object is placed in a fluid.

Volume of displaced fluid

Equal to the volume of the submerged part of the object.

Example of displaced fluid

A rock with volume 0.002 m³ displaces 0.002 m³ of water.

Why ships float

Their hollow structure allows them to displace enough water so the buoyant force equals their weight.

Ship density principle

Ships float because their average density is less than water.

Why small metal objects sink

They are dense and displace too little water to generate sufficient buoyant force.

Buoyancy in gases

Buoyant force also occurs in gases like air.

Helium balloon explanation

Helium balloons rise because the weight of displaced air is greater than the balloon's weight.

True origin of buoyancy

Pressure difference between the top and bottom of an object in a fluid.

Key pressure relationship

Pressure increases with depth in fluids.

Final summary of buoyancy

Buoyant force equals the weight of displaced fluid and results from pressure differences in fluids.