Floating and Sinking

An object floats when its density is less than the density of the fluid it is placed in. An object sinks when its density is greater than the fluid’s density.

The rule

Condition	Result
Object density < fluid density	Floats
Object density > fluid density	Sinks
Object density = fluid density	Neither rises nor sinks (neutral buoyancy)

A block of wood ($\rho \approx 600\ \text{kg/m}^3$) floats in water ($\rho = 1000\ \text{kg/m}^3$) because the wood is less dense. An iron nail ($\rho \approx 7800\ \text{kg/m}^3$) sinks because iron is denser than water.

Why do ships made of steel float?

Steel is denser than water, but a ship is not solid steel. The hull encloses a large volume of air. The average density of the ship (steel + air) is less than the density of water, so the ship floats. If the hull is breached and water fills the air space, the average density rises above 1000 kg/m³ and the ship sinks.

What is upthrust?

When an object is submerged (or partly submerged) in a fluid, the fluid pushes upward on it. This upward force is called upthrust. An object floats when the upthrust equals its weight.

For a floating object: upthrust = weight of the object = weight of fluid displaced.

Common errors and how to correct them

• Saying heavy objects sink. A large ship is very heavy but floats because its average density is low. It is density, not mass alone, that determines floating.
• Confusing weight and density. A small lead pellet (low weight, high density) sinks. A large beach ball (higher weight, very low density) floats.
• Ignoring the fluid. Whether an object floats depends on the fluid. An egg sinks in fresh water but floats in very salty water (which is denser).

How to apply this in an exam

To predict whether an object floats: compare its density to the fluid density. If asked to explain why it floats, state that its density is less than the fluid density, and that the upthrust equals its weight.