OPOpenPithMake curiosity visiblePhysics lab / Mass, density and pressure

About this lab

Four experiments, one habit: tell two quantities apart, then look at their ratio.

Mass and volume are two quantities; their ratio is density. Force and area are two quantities; their ratio is pressure. The first two experiments measure density with a balance and a cylinder, the last two read pressure from the dent in a sponge. Each has a common trap: watching only one of the two.

Every reading, dot and curve comes from the same physical model, not a pre-drawn animation. Change one parameter and all the data is recalculated together.

Four results

Four results

  • Mass and volume: for one substance the m–V graph is a line through the origin, and its slope is the density. A 5 cm aluminium cube weighs 337.5 g, a 2 cm iron cube only 63.2 g; the aluminium is heavier but its density is only 2.70 g/cm³, against 7.90 g/cm³ for iron.
  • Stone density: weigh first, then measure volume, and the granite gives 52.0 g, 20 mL, ρ = 2.60 g/cm³. Measure the volume first and the stone carries out about 1.4 g of water: 2.67 g/cm³, 2.7 % too high.
  • Pressing force: with the legs down the table touches 1/25 of the area it does top down, so the pressure is 25 times larger. The empty table on its legs pushes only 0.98 N and dents the sponge 8.4 mm; top down with 500 g added it pushes 5.88 N and dents just 2.3 mm.
  • Column pressure: an upright uniform cylinder presses with p = ρgh, whatever its thickness. An iron rod 1 cm in radius and 6 cm tall weighs only 149 g but presses 4645 Pa; an aluminium cylinder 3 cm in radius and 6 cm tall weighs 458 g and presses only 1588 Pa.

Model and sources

Model and sources

  • Density: aluminium 2.7 × 10³ kg/m³, iron 7.9 × 10³ kg/m³, pine 0.5 × 10³ kg/m³, from the PEP grade 8 textbook table (OpenStax lists iron or steel at 7.8 and wood at 0.3–0.9); the balance reads to 0.1 g.
  • Displacement: the cylinder starts with 40 mL of water, marked every 1 mL; a stone lifted out carries 1.4 g of water, a teaching assumption that in reality depends on the surface.
  • Pressure: p = F/S, 1 Pa = 1 N/m². The table is 100 g with a 10 cm × 10 cm top and four 1 cm × 1 cm legs; each weight disc is 100 g.
  • Sponge: dent depth d = 25 mm × (1 − e^(−p / 6000 Pa)), rising only with pressure. It is a teaching assumption for comparing dents, not a measured property of sponge.

g is the textbook value 9.8 N/kg. Liquid pressure and buoyancy are on the pressure and buoyancy bench and are not repeated here.

Back to physics ↑