Density

Density tells you how much mass is squeezed into a given space. The formula is simple: density equals mass divided by volume, or rho = m/V. A kilogram of feathers and a kilogram of lead have the exact same mass, but the lead atoms sit close together in a tight lattice, while the fluffy feather structure traps huge amounts of empty air between fibers. Same mass, wildly different volume, so wildly different density.

At the molecular level, density comes down to packing. Heavier atoms packed closely together, like in lead or gold, give high density. Light atoms spread far apart, like in a gas or a foam, give low density. This is why squeezing a gas into half its volume doubles its density: you haven't added any molecules, you've just forced the same mass into half the space, so mass over volume doubles. Gases respond dramatically to compression because their molecules start out far apart; solids and liquids barely compress because their molecules are already packed close.

This idea sets up everything else in the fluids unit. Pressure in a fluid depends on the fluid's density, so a denser fluid pushes harder at the same depth. Buoyancy compares the density of an object to the density of the fluid it sits in: objects less dense than the fluid float, objects denser sink. Every later calculation in the unit quietly assumes you can find and compare densities first.