Mass, Weight and Density
Measurement · Mass, Weight and Density
Syllabus tag: KCSE | Mathematics | Form 1 | Topic 15 Mass, Weight and Density
Lesson objectives
By the end of this topic, you should be able to:
- State the units of mass and convert from one to another.
- Define weight and distinguish it from mass.
- State the units of weight.
- Define density and solve problems involving mass, volume and density.
Mass, Weight and Density
These three are often confused in ordinary speech. In mathematics and science they mean different things.
a) Mass
Mass is how much matter an object contains.
It is measured in milligrammes, grammes, kilogrammes and tonnes.
1 kg = 1 000 g, and 1 tonne = 1 000 kg.
Mass does not change when you move an object. A 2 kg bag of sugar has a mass of 2 kg on earth. It has the same mass on the moon.
b) Weight
Weight is the force of gravity pulling on an object.
Because it is a force, it is measured in newtons, not kilogrammes.
Weight changes with gravity. The same 2 kg bag weighs about 20 N on earth. On the moon it weighs only about 3 N, because gravity there is weaker.
Weight = mass × gravity. On earth gravity is about 10 N per kg.
So a 2 kg mass weighs about 20 N here.
c) Why the distinction matters
In everyday speech we say a bag "weighs 2 kg". Strictly that is its mass.
A balance compares masses, so it gives the same reading anywhere.
A spring scale measures force, so it would read differently on the moon.
Exam questions test this. If a question asks for weight but gives a mass in kilogrammes, multiply by 10. Answer in newtons.
d) Density
Density is the mass contained in each unit of volume.
The units follow from the formula: g/cm³ or kg/m³.
e) Rearranging
The formula rearranges two ways.
Mass = density × volume.
Volume = mass ÷ density.
Cover the quantity you want and read off what remains.
f) Comparing materials
| Material | Density |
|---|---|
| Cork | 0.24 g/cm³ |
| Water | 1 g/cm³ |
| Aluminium | 2.7 g/cm³ |
| Iron | 7.9 g/cm³ |
| Lead | 11.3 g/cm³ |
| Gold | 19.3 g/cm³ |
Anything with a density below 1 g/cm³ floats on water. Anything above sinks.
That single fact explains why cork floats and iron does not, and it follows directly from the numbers.
g) Where this is used
Identifying a metal from its mass and volume. Judging whether a load will float. Costing material by weight when only volume is known.
Words to know
- Mass -- the quantity of matter in a body, measured in kilograms.
- Weight -- the force of gravity on a mass, measured in newtons.
- Density -- mass per unit volume.
- Beam balance -- an instrument measuring mass by comparison.
- Spring balance -- an instrument measuring weight by extension.
:::checkpoint Check yourself
- What is the difference between mass and weight?
- In what unit is weight measured?
- A block has mass 500 g and volume 250 cm³. Find its density.
- Will a material of density 0.8 g/cm³ float on water? :::
Bridge to practice
The exercises begin with units of mass and the mass-weight distinction, move through calculating weight and the density relationship, and finish with unit consistency and applied problems. Before any density calculation, check that mass and volume belong to the same system of units.