What is Density?

Think of density as how tightly packed the "stuff" is in any object. If you've got two blocks the same size, the heavier one is more dense. A lead block feels much heavier than a wooden block of the same size because lead packs way more matter into the same space.

Density is basically mass per unit volume - it tells you how much matter is crammed into a given space. The symbol for density is ρ (rho), which looks like a curvy 'p'.

The key formula you need to master is: ρ = m/V $Density = Mass ÷ Volume$. This simple equation is your ticket to solving loads of physics problems.

Quick Tip: Remember that mass (measured in grams or kilograms) isn't the same as weight. Mass stays constant wherever you go, even on the moon!

The Formula Triangle and Units

Here's a brilliant trick to remember the density formula and rearrange it easily. Draw a triangle with mass (m) at the top, and density (ρ) and volume (V) at the bottom.

To use it, just cover what you want to find. Cover ρ to get density: m ÷ V. Cover m to get mass: ρ × V. Cover V to get volume: m ÷ ρ.

Units for density depend on what you use for mass and volume. The two most common are grams per cubic centimetre $g/cm³$ and kilograms per cubic metre $kg/m³$. Always check your units match before calculating!

Remember: 1 millilitre equals 1 cubic centimetre $1 ml = 1 cm³$. This conversion pops up constantly in exams.

Measuring Mass and Volume

Measuring mass is straightforward - just use digital scales or a balance. Always zero the balance first for accurate readings.

Volume measurement depends on your object's shape. For regular solids like cubes, measure length, width, and height with a ruler, then multiply them together. Make sure all measurements use the same units!

For liquids, pour into a measuring cylinder and read from the bottom of the meniscus (that curved surface). For irregular solids like stones, use the displacement method. Fill a measuring cylinder with water, record the starting volume (V₁), add your object, then record the new volume (V₂). The object's volume is V₂ - V₁.

Common Mistake: Don't just write down the final water level - you need the difference between final and initial volumes!

Worked Examples

Let's tackle a density calculation with an aluminium block. It has a mass of 540g and measures 10cm × 5cm × 4cm.

First, calculate the volume: 10 × 5 × 4 = 200 cm³. Then use the formula: ρ = 540g ÷ 200cm³ = 2.7 g/cm³.

Here's another example: 50 cm³ of unknown liquid has a mass of 40g. Using ρ = m/V: 40g ÷ 50cm³ = 0.8 g/cm³. Since water has a density of 1 g/cm³, this liquid is less dense than water and will float.

The key to success is working systematically - identify what you know, calculate what you need, then apply the formula carefully.

Exam Tip: Always include units in your final answer. You'll lose marks without them, even if your calculation is perfect!

Floating, Sinking, and Exam Success

Understanding density helps predict floating and sinking. Objects less dense than a fluid will float; denser objects will sink. If densities match exactly, the object hovers suspended in the middle.

For exam success, remember these crucial points: units are absolutely essential, keep mass and volume units consistent, and don't confuse mass (kg) with weight (N). Density always uses mass, not weight.

Water's density is approximately 1 g/cm³ - memorise this because it's your reference point for comparing other substances. Oil floats on water because it's less dense, while rocks sink because they're denser.

Quick Check: If you're using the displacement method, always subtract the initial water volume from the final volume. This catches out loads of students!