Short on time? This page is the recap. For the particle diagrams, graphs and worked examples, use the full study guide. This is the algebra-based course: no calculus is needed.
Recap
- The properties of solids, liquids and gases come from how strongly their particles interact and how far apart they are.
- Solid: fixed shape and volume. Liquid: fixed volume, no fixed shape. Gas: neither fixed, and easy to compress.
- A fluid has no fixed shape and flows. Liquids and gases are fluids.
- Density describes a material, not a sample. Cutting a uniform object does not change its density.
- For an object made of several parts, use average density = total mass ÷ total volume.
- An ideal fluid is incompressible (constant density) and has no viscosity (no internal friction). Treat fluids as ideal unless told otherwise.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| ρ = m / V | ρ in kg/m³, m in kg, V in m³ | find density, mass or volume |
| 1 g/cm³ = 1000 kg/m³ | 1 mL = 1 cm³; 1 L = 10⁻³ m³ | convert lab units to SI |
| ρ_avg = m_total / V_total | kg/m³ | describe an object made of parts or with trapped air |
| slope of m–V graph | kg/m³ (or g/cm³) | find density from several samples |
| weight = mg | N | do not confuse with mass or density |
Assumptions behind the numbers
- Each sample is uniform: the same material all the way through.
- Volume by water displacement assumes the object is fully under water, does not absorb water and has no trapped bubbles.
- Liquids are treated as incompressible. Gases are not: their density changes when they are squeezed.
- Approximate densities: air 1.2 kg/m³, fresh water 1000 kg/m³, aluminium 2700 kg/m³.
Mistakes to avoid
- Swapping mass, weight, volume and density. Use the exact word, with its unit.
- “Heavy means dense.” Check the volume too.
- Forgetting to cube the length conversion. 1 cm³ = 10⁻⁶ m³, not 10⁻² m³.
- Saying fluids are only liquids. Air is a fluid.
- Using one data point when a graph is given. Use the slope of the best-fit line.
- Adding densities of parts. Add masses and add volumes, then divide.
Quick self-check
- A 250 cm³ block has mass 0.50 kg. What is its density in kg/m³? (2.0 × 10³ kg/m³)
- A uniform plank is sawn into three equal pieces. What happens to the density of each piece? (It stays the same.)
- What mass of water (1000 kg/m³) fills a 2.0 L bottle? (2.0 kg)
- Name the two properties of an ideal fluid. (Incompressible; no viscosity.)
Next: practice questions.