Floating and Sinking

Introduction

Why does a coin sink while a huge wooden log floats? Why can a steel ship weighing thousands of tonnes carry cargo across oceans? The answer to all these questions is density. By comparing the density of an object with the density of the liquid it is placed in, you can predict whether it will float or sink — without ever doing the experiment.

Core explanation

The rule. An object placed in a fluid (liquid or gas):

- sinks if its density is greater than the fluid's density; - floats if its density is less than the fluid's density; - stays suspended at any depth if the densities are equal .

Water has a density of 1.00 g/cm³. Wood (about 0.5 g/cm³), ice (0.92 g/cm³) and most plastics used for packaging float; stone (about 2.6 g/cm³), iron (7.9 g/cm³) and glass (2.5 g/cm³) sink.

Why density decides. A fluid pushes up on anything placed in it with a force called upthrust . The upthrust equals the weight of the fluid the object pushes aside. If the object is less dense than the fluid, it only has to sink part of the way before the fluid it displaces weighs as much as the object — then it floats. If the object is denser, even complete submersion cannot displace enough fluid to support it, so it sinks.

How much floats above the surface. The lower an object's density compared with the liquid, the higher it floats. Ice (0.92 g/cm³) in water floats with about 92% below the surface — which is why most of an iceberg is hidden. Cork (0.24 g/cm³) floats with only about a quarter under water.

Average density: ships and submarines. A steel ship floats because it is not solid steel. Its hull encloses a large volume of air, so its average density (total mass ÷ total volume) is less than that of water. If the hull fills with water, the average density rises above 1 g/cm³ and the ship sinks. Submarines control their depth by pumping water in or out of ballast tanks, changing their average density.

Changing the liquid. Salt water is denser than fresh water (sea water is about 1.025 g/cm³). Objects float higher in the sea than in a river, and in the very salty Dead Sea (about 1.24 g/cm³) people float with ease.

Step-by-step reasoning

To predict whether an object floats in water:

1. Find the object's density (from data, or mass ÷ volume). 2. Find the liquid's density. 3. Compare: object denser → sinks; object less dense → floats. 4. For hollow objects, use average density: total mass ÷ total volume.

Visual explanation

Picture a tall jar of water with several objects: a cork bobbing high at the surface, an ice cube floating low, a plastic bead hovering mid-way (same density as the water) and a stone on the bottom. Beside each, a small label shows its density compared with 1.00 g/cm³.

Real-world analogy

A crowd at a concert: a person on someone's shoulders "floats" above the crowd because they are supported, while someone who drops a heavy bag will see it disappear to the floor. Lighter-for-their-size things are held up by the surrounding crowd; heavier-for-their-size things fall through.

Real-world example

Ships are painted with load lines, called Plimsoll lines, showing how deep they can safely sit in fresh water, summer sea water or winter sea water. Because fresh water is less dense, a fully loaded ship sits lower in a river than in the ocean, and the markings prevent overloading in each case.

Why?

Why can a heavy log float while a light pebble sinks? Floating depends on density, not on mass. The log has a large volume, so its density (about 0.5 g/cm³) is less than water's. The pebble is small but dense (about 2.6 g/cm³), so it sinks however light it is.

Common misconception

"Heavy things sink and light things float." A tiny grain of sand sinks, but a massive oil tanker floats. What matters is how mass compares with volume — density — and for hollow objects, the average density including the air inside.

Worked example

Question: A plastic toy has a mass of 45 g and a volume of 50 cm³. Will it float in fresh water (1.00 g/cm³)? In ethanol (0.79 g/cm³)?

Reasoning: Density = 45 ÷ 50 = 0.90 g/cm³. This is less than 1.00 but greater than 0.79.

Answer: It floats in water but sinks in ethanol.

Quick check

1. An object has a density of 1.10 g/cm³. Does it float in fresh water? In the Dead Sea (1.24 g/cm³)? Answer: It sinks in fresh water but floats in the Dead Sea.

Exam focus

Always compare two densities — the object's and the liquid's — and state which is greater. For ships and boats, refer to average density including air. Questions may give mass and volume, requiring you to calculate density first.

Advanced insight

Hydrometers measure liquid density by how deep a weighted glass float sinks: the less dense the liquid, the deeper it sinks. They are used to check the strength of battery acid, the sugar content of fruit juices and the progress of fermentation in brewing.

Summary

Objects float in a fluid if they are less dense than it and sink if they are denser. Floating happens because the upthrust equals the weight of fluid displaced. Hollow objects such as ships float because their average density, including the enclosed air, is below that of water. Denser liquids, such as salt water, make objects float higher.

Practice questions

1. Will aluminium (2.70 g/cm³) float in mercury (13.5 g/cm³)? Explain. Answer: Yes, because aluminium is less dense than mercury. 2. Explain why a steel ship floats but a steel bolt sinks. Answer: The ship contains a large volume of air, giving it an average density below that of water; the bolt is solid steel, which is much denser than water. 3. An egg sinks in fresh water but floats in strong salt water. What does this tell you about the egg's density? Answer: It is greater than the density of fresh water but less than that of the salt water. 4. Why does a larger fraction of an ice cube lie above the surface in sea water than in fresh water? Answer: Sea water is denser, so less of it needs to be displaced to support the ice, and the ice floats higher.