Define density as mass per unit volume; recall and use the equation ρ = m / V

1.4 Density 📏

What is Density? 🏗️

Density, denoted by ρ, is the amount of mass packed into a given volume. Think of it like how crowded a room is. If many people (mass) fit into a small room (volume), the density is high. If only a few people fit into a large room, the density is low.

The Density Formula 💧

\$\rho = \frac{m}{V}\$

where m is mass (kg) and V is volume (m³).

Examples & Analogies 🌊

  • Water has a density of about 1 kg m⁻³, so 1 kg of water occupies about 1 L.

  • Lead is much denser than water, so a small lead block can weigh a lot.

  • Imagine a sponge (low density) vs. a steel ball (high density).

Sample Calculation 📐

Mass (kg)Volume (m³)Density (kg m⁻³)
2.50.55

Exam Tips ✏️

• Always check units: mass in kg, volume in m³, density in kg m⁻³.

• If the problem gives density and mass, find volume: V = m/ρ.

• If it gives density and volume, find mass: m = ρV.

• Remember to convert units if needed (e.g., cm³ to m³).

• Use the crowded‑room analogy to decide if density is high or low.

Key Takeaways 📌

  1. Density = mass ÷ volume.

  2. Units: kg m⁻³.

  3. Higher density means more mass in the same volume.

  4. Use the formula to solve for any missing quantity.