Have you ever wondered why a massive steel ship can float on water, while a tiny pebble sinks straight to the bottom? Or why a helium balloon rises in the air while a regular balloon falls? The answer to all these questions lies in a fundamental property of matter called density.

Density is a key concept in your IGCSE Physics course that helps explain the behavior of materials. It's not just about how heavy something is, but about how much "stuff" is packed into the space it occupies. Understanding density is crucial for making sense of everything from material science to the structure of planets.

This guide will walk you through what density is, how to calculate it, and how to measure it for different types of objects. We will also explore the principles of floating and sinking, so you can confidently tackle any related problems in your exams.

For a more visual and interactive exploration of these concepts, please see the embedded guide below. You can scroll within the frame to see all the content.

Density is defined as the mass per unit volume of a substance. In simpler terms, it's a measure of how tightly the matter (mass) is packed into a given space (volume).

Imagine two boxes of the same size. One is filled with feathers, and the other is filled with rocks. Even though they have the same volume, the box of rocks has much more mass and is therefore much denser.

Here are the key things to know about density:

• It's a Scalar: Like mass, density is a scalar quantity. It has a magnitude (a number) but no direction.
• Symbol and Units: Density is represented by the Greek letter ρ (rho).
• The standard SI unit for density is kilograms per cubic meter (kg/m³).
• A very common alternative unit is grams per cubic centimeter (g/cm³).
• It's useful to remember the conversion: 1 g/cm³ = 1000 kg/m³.
• Characteristic Property: Density is a characteristic property of a substance. For example, pure water has a density of approximately 1000 kg/m³ (or 1 g/cm³), and pure gold has a density of about 19,300 kg/m³. This can help in identifying materials.

The relationship between density, mass, and volume is expressed by a simple formula:

Density = Mass / Volume

ρ = m / V

Where:

• ρ (rho) is the Density in kg/m³ or g/cm³.
• m is the Mass in kg or g.
• V is the Volume in m³ or cm³.

Make sure your units are consistent! If you use mass in kg, your volume must be in m³ to get density in kg/m³.

You can use a formula triangle to easily rearrange the equation:

• To find mass: m = ρ × V
• To find volume: V = m / ρ

To find the density of an object, you always need to determine two things: its mass and its volume.

1. Measuring Mass: This is the easy part. You can measure the mass of any object (solid or liquid) using a top-pan balance (or digital scale). Remember to record the mass in kilograms (kg) or grams (g).
2. Measuring Volume: The method for measuring volume depends on the object's shape and state.

A. Volume of a Regularly Shaped Object

For objects with regular shapes like cubes, cuboids, spheres, or cylinders, you can:

1. Use a ruler or vernier calipers to measure its dimensions (length, width, height, radius).
2. Calculate the volume using the appropriate mathematical formula (e.g., for a cuboid, V = length × width × height).

Example: Finding the density of a wooden block

1. Mass: Place the block on a digital scale. Let's say its mass is 240 g.
2. Volume: Measure its dimensions with a ruler. Let's say it is 10 cm long, 6 cm wide, and 4 cm high.

• Volume = 10 cm × 6 cm × 4 cm = 240 cm³.

1. Density:

• ρ = m / V = 240 g / 240 cm³ = 1 g/cm³.

B. Volume of an Irregularly Shaped Object (like a stone)

You can't use a ruler to find the volume of an object like a stone. Instead, you must use the displacement method.

1. Fill a measuring cylinder with enough water to fully submerge the object. Record the initial volume of the water (V₁).
2. Carefully lower the object into the water, ensuring it is fully submerged and no water splashes out.
3. Record the new, final volume of the water with the object in it (V₂).
4. The volume of the object is the difference between the final and initial readings: V = V₂ - V₁.

Example: Finding the density of a rock

1. Mass: The rock's mass is measured as 150 g.
2. Volume:

• A measuring cylinder is filled to 50 cm³ (V₁).
• The rock is submerged, and the water level rises to 80 cm³ (V₂).
• Volume of the rock = 80 cm³ - 50 cm³ = 30 cm³.

1. Density:

• ρ = m / V = 150 g / 30 cm³ = 5 g/cm³.

Note: For larger objects, a eureka can (or displacement can) can be used. The object displaces water, which flows out of a spout and is collected in a measuring cylinder. The volume of collected water is equal to the volume of the object.

C. Density of a Liquid

1. Mass:

• Place an empty measuring cylinder on a digital scale and record its mass (m₁).
• Pour the liquid into the measuring cylinder and record the new total mass (m₂).
• The mass of the liquid is the difference: m = m₂ - m₁.

1. Volume: Read the volume of the liquid directly from the scale on the measuring cylinder (V).
2. Density: Calculate ρ = m / V.

Density is the key to understanding why objects float or sink in a fluid (a liquid or a gas).

The rule is simple:

• An object will float if its average density is less than the density of the fluid.
• An object will sink if its average density is greater than the density of the fluid.
• An object will remain suspended (neutrally buoyant) if its density is equal to the fluid's density.

Examples:

• Wood on Water: Wood has a density of about 600-800 kg/m³, while water has a density of 1000 kg/m³. Since the wood is less dense than the water, it floats.
• A Steel Ship: A block of steel is very dense (~8000 kg/m³) and will sink. However, a ship is shaped to displace a huge volume of water. Its hollow structure means its average density (the total mass of the ship divided by its total volume, including the air inside) is less than the density of water, so it floats.
• Helium Balloon: Helium gas is much less dense than the surrounding air, so the upward buoyant force from the air is greater than the balloon's weight, causing it to rise.

• Density is the mass per unit volume (ρ = m/V), telling you how 'compact' a substance is.
• To find density, you must measure both mass (with a balance) and volume.
• Volume measurement depends on the object: ruler and formula for regular shapes, water displacement for irregular shapes.
• An object floats if it is less dense than the fluid it is in. It sinks if it is more dense.

Mastering density will give you a powerful tool for analyzing the physical world and is a guaranteed topic in your IGCSE exams.