- Explain mass as quantity of matter and inertia.
- Use W = mg and interpret gravitational field strength.
- Measure mass and weight with suitable instruments.
- Determine density of liquids and regular or irregular solids.
5.1 Mass and inertia
Mass is a measure of the quantity of matter in an object and of its resistance to changes in motion. This resistance is called inertia. A large-mass trolley requires a larger resultant force than a small-mass trolley to produce the same acceleration.
Mass is measured in kilograms using a balance. A beam balance compares the unknown mass with known masses and therefore gives the same result in different gravitational fields. An electronic balance is convenient but should be zeroed or tared before use.
5.2 Weight and gravitational field strength
Weight is the gravitational force acting on a mass. W = mg, where W is in newtons, m in kilograms and g in N kg⁻¹. Near Earth’s surface g is approximately 9.8 N kg⁻¹ and is numerically equal to the free-fall acceleration 9.8 m s⁻².
A gravitational field is a region in which a mass experiences gravitational attraction. Gravitational field strength at a point is force per unit mass. Mass remains constant when an astronaut travels from Earth to the Moon, but weight decreases because the Moon’s gravitational field is weaker.
5.3 Density
Density is mass per unit volume: ρ = m/V. It describes how much mass is packed into a given volume. Common units are kg m⁻³ and g cm⁻³. Since 1 g cm⁻³ = 1000 kg m⁻³, unit conversion must be handled carefully.
To find the density of a regular solid, measure mass and dimensions, calculate the volume and divide. For an irregular solid that sinks, use water displacement. For a liquid, find the mass of an empty container, then the mass of container plus liquid; the difference is the liquid mass. Measure the liquid volume in a measuring cylinder.
5.4 Floating and density reasoning
An object floats when the upward force from the fluid can balance its weight before the object is completely submerged. Average density is therefore important. A steel ship floats because its hollow structure gives the complete ship a lower average density than solid steel.
Density is a material property only when temperature and composition are specified. Heating generally expands a substance and lowers its density because mass is unchanged while volume increases.
Worked examples
A 2.5 kg object has weight W = 2.5×9.8 = 24.5 N.
Mass = 540 g. Dimensions = 10.0 cm × 6.0 cm × 3.0 cm, so volume = 180 cm³. Density = 540/180 = 3.0 g cm⁻³.
Water rises from 35 cm³ to 57 cm³ when a 176 g stone is submerged. Volume = 22 cm³; density = 176/22 = 8.0 g cm⁻³.
Practical focus
Measure the density of a rectangular block and an irregular metal object. Repeat each dimension, record the range and use a mean. Dry the irregular object before measuring its mass so that adhering water does not increase the reading.
Examination guidance
- Do not write mass in newtons or weight in kilograms.
- In density calculations, convert all values into a consistent unit system before dividing.
- When using displacement, the rise in cylinder reading is the object volume, not the final reading alone.
Check your understanding
- What is inertia?
- A mass is taken to a planet where g is half Earth’s value. What changes?
- Convert 2.7 g cm⁻³ to kg m⁻³.
- The tendency of an object to resist a change in its state of rest or motion.
- Its weight halves; its mass is unchanged.
- 2700 kg m⁻³.
