Matter and Pressure
Density and pressure
SEC Physics tests density, pressure in solids, liquids and gases, atmospheric pressure, floating and Hooke's law.
- Density ρ = m/V (kg/m³); to compare with water, 1000 kg/m³ = 1 g/cm³.
- Pressure p = F/A (Pa = N/m²); force is perpendicular to the area.
- Pressure in a liquid: p = ρgh, where h is vertical depth below the surface. Pressure depends on depth and density, not on the shape or width of the container.
- Atmospheric pressure decreases with height and is measured with a barometer; a manometer measures pressure differences.
- Hooke's law: extension is proportional to load up to the limit of proportionality; spring constant k = F/x.
Worked example
A rectangular block has mass 2.4 kg and volume 0.0030 m³. It rests on a face of area 0.020 m². Taking g = 10 N/kg, find its density and the pressure on the surface.
ρ = m/V = 2.4/0.0030 = 800 kg/m³.
Weight = mg = 2.4 × 10 = 24 N; p = F/A = 24/0.020 = 1200 Pa.
Reasoning: density uses volume; pressure uses the contact area, not the volume.
Traps
Using cm² or cm³ without converting to m² or m³; using the block's height instead of the contact area; thinking liquid pressure depends on total volume; adding atmospheric pressure when only gauge pressure is asked; measuring extension beyond the proportional limit.