density
Summary
Density is mass per unit volume of a substance, ρ = m/V, in kg/m³. The most testable point is that an object's average density compared with the fluid's density usually decides whether it floats or sinks.
Detail
Meaning: Density is the mass packed into a given volume of a substance. It is an intensive property: cutting a sample in half changes its mass and volume but typically not its density. Density does depend on temperature and pressure. Liquids and solids change little, while gases change a lot. Specific gravity is a substance's density divided by the density of water (1.00 × 10³ kg/m³, or 1.00 g/cm³), so it has no units.
Equation: ρ = m/V, where ρ is density (kg/m³), m is mass (kg), and V is volume (m³).
On the MCAT: Fluid passages use density to predict floating and sinking. An object floats if its average density is less than the fluid's, and a floating object has a submerged fraction equal to ρobject/ρfluid. Density also appears in buoyant force (Fbuoy = ρfluid Vsubmerged g) and in hydrostatic pressure (P = P0 + ρgh).
Common confusion: Density is not the same as mass or weight. A heavier sample of the same material has the same density. Buoyant force depends on the fluid's density and the displaced volume, not the object's own density. A steel ship floats because its average density, counting the air-filled hull, is below that of water.
Sources
- Physics (Giancoli)
- College Physics (Serway and Vuille)
- Physics (Cutnell and Johnson)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.