Topic 8.1 Internal Structure and Density: define a fluid and describe density as mass per unit volume, an intensive property of a substance.

What this topic is asking

The College Board (Topic 8.1) wants you to define a fluid and describe density as mass per unit volume, recognizing it as an intensive property that characterizes a substance independently of how much of it you have. This is the foundation for the pressure, buoyancy and flow topics that follow.

What a fluid is

The defining feature of a fluid is that it cannot maintain a fixed shape: unlike a solid, whose particles are held in place, a fluid's particles slide past each other, so the fluid flows and presses outward on its container. Treating fluids as ideal (incompressible and non-viscous) is the standard AP idealisation; it keeps the density constant and removes friction, which is what makes the pressure and flow relations of the later topics clean.

Density: mass per unit volume

Density is the single most-used quantity in the fluids unit. It appears in the pressure-depth relation, the buoyant force, and the continuity and Bernoulli equations of the later topics. Being fluent with $\rho = m/V$ and its rearrangement $m = \rho V$ is essential, because almost every fluids problem converts between a volume of fluid and the mass (and hence weight) of that fluid.

Density is an intensive property

A crucial and heavily tested point is that density is an intensive property: it characterizes the substance, not the amount. Cut a block of aluminum in half and each half has the same density as the whole; pour out half a glass of water and the remaining water is just as dense. This is because density is a ratio: halving the sample halves both the mass and the volume, leaving $m/V$ unchanged. Mass and volume themselves are extensive (they scale with the amount), but their ratio is not. This distinction matters for float-and-sink reasoning, which depends only on comparing densities (Topic 8.3): an object floats in a fluid if its average density is less than the fluid's, and sinks if it is greater, regardless of the object's size. The strategic insight for the unit is that density is the bridge between the geometry of a fluid (its volume) and the dynamics that act on it (its weight, through $m = \rho V$ and $W = \rho V g$). Establishing density firmly here is what makes pressure, buoyancy and flow tractable in the topics that follow.

Try this

Q1. A $2.0$ kg block occupies $8.0 \times 10^{-4}$ m cubed. Calculate its density. [2 points]

• Cue. $\rho = m/V = 2.0/(8.0 \times 10^{-4}) = 2500$ kg/m cubed.

Q2. A liter of water is poured into a larger tank of water. State whether its density changes. [1 point]

• Cue. No; density is intensive, so it stays at about $1000$ kg/m cubed.