Floatation

An object floats when the buoyant force is equal to or greater than its weight.

Mathematically:

\( F_b \geq W \)

Floating objects displace fluid equal to their own weight.

An object sinks when its weight is greater than the buoyant force:

\( W > F_b \)

This usually happens when the object is denser than the fluid.

When the buoyant force equals the weight exactly, the object stays suspended at a constant depth. Submarines achieve this by adjusting their density through ballast tanks.

The density of an object relative to the fluid decides its behaviour:

• If object density < fluid density → it floats.
• If object density > fluid density → it sinks.
• If object density = fluid density → it stays suspended.

Large hollow objects like ships float even if made of dense materials (like steel) because their overall density, including the air inside, is less than that of water.

According to Archimedes' principle, the buoyant force is equal to the weight of the displaced fluid:

\( F_b = \rho V g \)

Where \(V\) is the displaced fluid volume. Floating objects adjust themselves so that displaced water weighs exactly the same as the object.

A floating object displaces just enough fluid so that the buoyant force matches its own weight. This is why only part of the object stays underwater.

A floating object remains stable when its centre of gravity is below its centre of buoyancy. This arrangement prevents it from toppling easily.

Boats and ships have wide bases to keep the centre of buoyancy aligned with the centre of gravity, improving stability on water.

Ships float because their shape ensures that they displace enough water to balance their weight. Their hollow design lowers their overall density.

Ice is less dense than water, so it floats with about 90% of its volume submerged. This behaviour protects aquatic life in cold climates.

Life jackets increase a person's effective volume while keeping mass low, making the overall density less than water so the person floats.

Hot-air balloons float in air because hot air inside the balloon has lower density than surrounding cooler air, creating upward buoyant force.

A stone sinks because it is denser than water, and the buoyant force is not large enough to balance its weight.

A piece of wood floats because its density is lower than water. It submerges only enough to displace water equal to its weight.

An ice cube in a glass of water floats with a small part above the surface. This is due to the lower density of ice compared to liquid water.