density
/ rho spelled 'row' /
Density tells you how tightly matter is packed into a given amount of space. A small lead fishing weight feels surprisingly heavy for its size, while a big foam cushion feels almost weightless: the lead is dense, the foam is not. Density answers the everyday puzzle of why a tiny thing can be heavy and a large thing can be light.
Precisely, density is the mass of a substance divided by the volume it occupies. Writing rho (the Greek letter, pronounced row) for density, m for mass, and V for volume, the defining relationship is rho = m / V. Its SI unit is the kilogram per cubic metre (kg/m^3). Density does not depend on how much of the stuff you have, only on what it is made of and its state: a drop of water and a bathtub of water have the same density. For reference, fresh water is about 1000 kg/m^3, air near the ground is about 1.2 kg/m^3, and lead is about 11 300 kg/m^3.
Density is the key that unlocks floating and sinking: an object floats in a fluid when its average density is less than the fluid's, which is why an oil layer rests on water and a helium balloon rises through air. One honest caution: do not confuse dense with heavy. A supertanker is enormously heavy yet floats, because when its steel hull is counted together with the air inside, its average density is less than that of water.
A cube of aluminium measuring 0.1 m on each side has a volume of 0.001 m^3 and a mass of about 2.7 kg, so its density is rho = m / V = 2.7 / 0.001 = 2700 kg/m^3, heavier than water but far lighter than lead.
Density compares mass to volume; the same material has the same density no matter how big the piece.
Dense is not the same as heavy: a huge low-density object can outweigh a tiny dense one. Density is about mass per unit volume, not total mass.