Ch 2 · Mass, Weight, Density and Pressure · IGCSE Physics 0625
Topic 2 of 5 in Motion, Forces and Energy — IGCSE Physics 0625 — 20 lessons.
Introduction
Why does an astronaut weigh less on the Moon but still have the same mass? Why does a steel ship float while a steel nail sinks? Why do snowshoes stop you sinking into snow? The answers come from three closely linked ideas: weight, density and pressure. They are short topics, but they turn up inside many longer questions about forces, floating, gases and the Solar System.
Key ideas
1. Mass. Mass is a measure of the quantity of matter in an object at rest relative to the observer. It is measured in kilograms (kg) and does not change when the object moves to a different planet.
🧑🏫 Teacher's explanation
Imagine you are holding a heavy backpack. The amount of 'stuff' or matter inside that backpack—the books, the pens, the laptop—is its mass. Even if you fly to the Moon, the number of books remains the same, so the mass is unchanged. However, because the Moon's gravity is weaker, the backpack feels much lighter to carry; this 'heaviness' you feel is the weight, which is the gravitational pull on that mass.
📖 Definitions
🔍 Worked example — Easy
A block of wood has a mass of 0.45 kg. Calculate its weight on Earth, taking g = 9.8 N/kg.
🔍 Worked example — Standard
An irregular stone is dropped into a measuring cylinder containing 50 cm^3 of water. The water level rises to 72 cm^3. If the mass of the stone is 135 g, calculate its density in g/cm^3.
🔍 Worked example — Exam-style
A hydraulic piston has an area of 0.02 m^2. A force of 500 N is applied to it. Calculate the pressure exerted. Then, calculate the change in pressure (Δ p) at the bottom of a tank of oil (rho = 900 kg/m^3) if the tank is 2.5 m deep. Use g = 9.8 N/kg.
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
(a) Calculate the density of the metal. (b) The block is placed at the bottom of a tank of water (rho = 1000 kg/m^3). Calculate the pressure exerted by the water at a depth of 0.5 m below the surface. Use g = 9.8 N/kg. [4 marks]
Practical notes
Density of a liquid. Measure the mass of an empty measuring cylinder on a balance. Pour in some liquid, read the volume at the bottom of the meniscus, and measure the new mass. Mass of liquid = difference in the two masses; then rho = m/V.
Worked example
Example 1 — mass and weight. An astronaut has a mass of 70 kg. Calculate her weight on Earth (g = 9.8\ N/kg) and on the Moon (g = 1.6\ N/kg).
🔍 Worked example — Easy
An object has a mass of 5.0 kg. Calculate its weight on Earth where g = 9.8 N/kg.
🔍 Worked example — Standard
A rectangular block has a mass of 450 g and a volume of 150 cm^3. Calculate its density in g/cm^3.
🔍 Worked example — Exam-style
A diver is at a depth of 25 m in a lake with a density of 1000 kg/m^3. Calculate the pressure exerted by the water alone. (Use g = 9.8 m/s^2)
⚠️ Common errors
Common mistakes and examiner tips
Practice
Answers: (1) W = 0.250 × 9.8 = 2.45\ N ≈ 2.5\ N. (2) V = 30\ cm^3, rho = 81/30 = 2.7\ g/cm^3 = 2700\ kg/m^3. (3) It floats, because its density is less than that of water (1.0\ g/cm^3). (4) A = 4 × 0.10 = 0.40\ m^2, p = 50 000/0.40 = 1.25 × 10^5\ Pa ≈ 1.3 × 10^5\ Pa. (5) V = 60\ m^3, m = rho V = 1.2 × 60 = 72\ kg. (6) Δ p = 1000 × 9.8 × 2.5 = 24 500\ Pa ≈ 2.5 × 10^4\ Pa. (7) The oil forms a separate layer on top of the water, because the oil is less dense than water.