Matter: Properties, Fluids and Elasticity
Matter is anything that has mass and occupies volume. The particle model explains the three states: solids have closely packed vibrating particles, liquids have particles that can slide past one another, and gases have widely spaced fast-moving particles. Gases are compressible; liquids are almost incompressible.
Key quantities: density ρ = m/V in kg/m³, and relative density (specific gravity) = ρ_substance / ρ_water, which has no units. Pressure is p = F/A in pascals. In a static fluid, pressure increases with depth: p = ρgh, and at a given depth it acts equally in all directions (Pascal's principle). Archimedes' principle states that upthrust equals the weight of fluid displaced; a floating body displaces its own weight of fluid.
Elasticity: Hooke's law F = kx applies only within the elastic limit. Stress = F/A, strain = ΔL/L, and Young's modulus E = stress/strain. Thermal expansion follows ΔL = αLΔT; the area coefficient is about 2α and the volume coefficient about 3α.
Common traps: relative density has no units; liquid pressure depends on depth and density, not on the shape or total volume of the container; upthrust depends on displaced volume, not on the object's weight; Hooke's law fails beyond the elastic limit; and expansion coefficients must be used for the correct dimension.
Worked example: an aluminium rod of length 2.0 m has α = 23 × 10⁻⁶ K⁻¹ and is heated through 50 K. ΔL = αLΔT = (23 × 10⁻⁶)(2.0)(50) = 2.3 × 10⁻³ m = 2.3 mm.