Definition 6.1.1. Mass Density.
The mass density of an object, \(\rho\text{,}\) can be found by dividing the object’s mass by its volume:
\begin{equation*}
\rho = \frac{m}{V}
\end{equation*}
Section 6.1 Density
In The Law of Inertia (Newton’s First Law), you learned about the mass as a property of an object. In some situations, you may care about how that mass is distributed in space, which is useful to describe using a new quantity known as density.
Note 6.1.2. 1D and 2D Density.
The symbol \(\rho\) represents the volume (three-dimensional) mass density. Physics also commonly makes use of surface (two-dimensional) mass density, symbolized by \(\sigma\text{,}\) and linear (one-dimensional) mass density, symbolized by \(\lambda\text{.}\)
Exercises Activities
1. Sensemaking: Units.
Determine the units for mass density.
Answer.
\(\mathrm{kg/m^3}\)
2. Sensemaking: Numbers.
One cup of water has a mass of approximately \(240 \mathrm{~g}\text{.}\) Use this to estimate the density of water. Make sure to convert your final answer to SI units, and comment on whether or not this number makes sense.
3. Sensemaking: Covariation.
Density depends on two quantities: mass and volume. Use the covariational reasoning sensemaking strategy to check that the definition for density makes sense given your everyday experience.
