Mass, Weight, Density and Pressure for Singapore N(A)-Level Science (Physics) 5105/5106: mass versus weight and the gravitational field, density and how to measure it, and pressure in solids and liquids including how pressure increases with depth

What this module covers

Mass, Weight, Density and Pressure brings together three closely related ideas in N(A)-Level Science (Physics) 5105/5106. It first separates mass from weight, two quantities that are often confused, then defines density as how tightly matter is packed, and finally explains pressure as force spread over an area, both for solids and for liquids.

These ideas connect to forces (weight is a force) and to everyday life, from floating and sinking to hydraulic brakes. Each dot point below has full worked answers and practice questions.

Mass, weight and the gravitational field

Mass, weight and gravitational field distinguishes mass, the amount of matter in an object measured in kilograms, from weight, the gravitational force on it measured in newtons. They are linked by

where $g$ is the gravitational field strength, about $10\ \text{N kg}^{-1}$ near Earth. Mass stays the same everywhere, but weight changes if $g$ changes.

Density and its measurement

Density and its measurement defines density as mass per unit volume:

For a regular solid you find the volume from its dimensions; for an irregular solid you measure the rise in water level in a measuring cylinder; for a liquid you find the mass of a known volume. An object floats in a liquid if its density is less than that of the liquid.

Pressure in solids and liquids

Pressure in solids and liquids defines pressure as force per unit area:

measured in pascals ($\text{Pa}$), where $1\ \text{Pa} = 1\ \text{N m}^{-2}$. A small area gives a large pressure, which is why sharp blades cut. In a liquid, pressure increases with depth because of the weight of liquid above, following $P = \rho g h$, and it acts equally in all directions at a given depth.

How this module is examined

• Keep units straight. Mass in kilograms, weight in newtons, density in $\text{kg m}^{-3}$ or $\text{g cm}^{-3}$, pressure in pascals.
• Pick the right method. Use displacement for irregular solids and dimensions for regular ones when finding volume.
• Link depth to pressure. Explain liquid pressure rising with depth using the weight of liquid above.

Check your knowledge

Recall and calculation questions across the module. Attempt them, then check the worked solutions.

1. State the difference between mass and weight. (2 marks)
2. A block has mass $2.0\ \text{kg}$. Take $g = 10\ \text{N kg}^{-1}$. Calculate its weight. (2 marks)
3. A liquid has mass $500\ \text{g}$ and volume $250\ \text{cm}^3$. Calculate its density. (2 marks)
4. A force of $200\ \text{N}$ acts on an area of $4.0\ \text{m}^2$. Calculate the pressure. (2 marks)
5. State why pressure in a liquid increases with depth. (1 mark)