Ch 4 · 1.4 Density · O Level Physics 5054

Topic 4 of 17 in Motion, Forces and Energy — O Level Physics 5054 — 20 lessons.

Introduction

A kilogram of feathers and a kilogram of iron have the same mass, but the feathers fill a sack while the iron fits in your hand. What differs is density: how much mass is packed into each unit of volume. Density lets you identify materials and explains why some things float. (Syllabus section 1.4.)

Key ideas

Density is mass per unit volume:

🧑‍🏫 Teacher's explanation

Imagine you have two identical boxes. One is filled with feathers and the other is filled with lead. Even though they take up the same amount of space (the same volume), the lead box is much heavier because the lead is more 'packed' or concentrated. This concept of how much 'stuff' is packed into a certain space is what we call density.\n\nDensity tells us how much mass is squeezed into every unit of volume. If an object is more dense than the liquid it is placed in, it will sink; if it is less dense, it will float. To find the density of an irregular object, like a small stone, we use the 'displacement method': we drop it into a measuring cylinder of water and see how much the water level rises. That rise in volume is exactly equal to the volume of the stone.

📖 Definitions

🔍 Worked example — Easy

A rectangular wooden block has a mass of 150 g and a volume of 200 cm^3. Calculate its density in g/cm^3.

🔍 Worked example — Standard

An irregular piece of metal is placed in a measuring cylinder containing 50 cm^3 of water. The water level rises to 72 cm^3. If the metal has a mass of 120 g, calculate its density in g/cm^3.

🔍 Worked example — Exam-style

A liquid has a density of 850 kg/m^3. A container with a volume of 0.02 m^3 is filled completely with this liquid. Calculate the mass of the liquid in kg.

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

Practical notes

All three methods find a mass with a balance and a volume; then rho = m/V.

Worked example

Example 1: a regular block. A metal block measures 2.0\ cm × 4.0\ cm × 5.0\ cm and has a mass of 316 g.

🔍 Worked example — Easy

A rectangular metal block has dimensions 2.0 cm × 4.0 cm × 5.0 cm and a mass of 316 g. Calculate its density in g/cm^3.

🔍 Worked example — Standard

An empty measuring cylinder has a mass of 82.0 g. When 50.0 cm^3 of oil is added, the total mass is 127.0 g. Calculate the density of the oil in g/cm^3.

🔍 Worked example — Exam-style

An irregular stone is dropped into a displacement vessel. The initial volume of water is 60 cm^3. After the stone is fully submerged, the volume rises to 110 cm^3. If the stone has a mass of 135 g, calculate its density in kg/m^3.

⚠️ Common errors

Common mistakes

Practice

Answers: (1) 240/400 = 0.60\ g/cm^3 = 600\ kg/m^3. (2) m = rho V = 1000 × 0.020 = 20\ kg. (3) Find its mass on a balance; find its volume by displacement in a measuring cylinder (V_2 - V_1); density = mass ÷ volume. (4) 85/10 = 8.5\ g/cm^3.

Summary

All chapters in Motion, Forces and Energy

1. 1.1 Physical Quantities and Measurement Techniques
2. 1.2 Motion
3. 1.3 Mass and Weight
4. 1.4 Density
5. 1.5.1 Balanced and Unbalanced Forces
6. 1.5.2 Friction
7. 1.5.3 Elastic Deformation
8. 1.5.4 Circular Motion
9. 1.5.5 Turning Effect of Forces
10. 1.5.6 Centre of Gravity
11. 1.6 Momentum
12. 1.7.1 Energy
13. 1.7.2 Work
14. 1.7.3 Energy Resources
15. 1.7.4 Efficiency
16. 1.7.5 Power
17. 1.8 Pressure