Mass and density

Inertia of bodies, mass as a measure of inertia, density of a substance, finding mass and volume, converting g/cm³ to kg/m³; how density relates to the structure of matter (molecules, lattice, states of matter).

Terms

Studied 0 of 8

Formulas

Density

\rho = \dfrac{m}{V}

Quantities
Symbol	Name	Unit
$\rho$	density of the substance	kg/m³
$m$	mass of the body	kg
$V$	volume of the body	m³

Solved for another quantity:

m = \rho V

V = \dfrac{m}{\rho}

Note. The formula holds for a uniform body (one substance, no cavities). Volume in $\text{m}^3$ : $1\ \text{cm}^3 = 10^{-6}\ \text{m}^3$ , $1\ \text{L} = 1\ \text{dm}^3 = 10^{-3}\ \text{m}^3$ .

Converting g/cm³ ↔ kg/m³

\rho_2 = 1000\,\rho_1

Quantities
Symbol	Name	Unit
$\rho_1$	density in g/cm³	g/cm³
$\rho_2$	the same density in kg/m³	kg/m³

Solved for another quantity:

\rho_1 = \dfrac{\rho_2}{1000}

Note. Where 1000 comes from: $1\ \dfrac{\text{g}}{\text{cm}^3} = \dfrac{10^{-3}\ \text{kg}}{10^{-6}\ \text{m}^3} = 1000\ \dfrac{\text{kg}}{\text{m}^3}$ . For example, $2.7\ \text{g/cm}^3 = 2700\ \text{kg/m}^3$ .

Lab

Set the quantities with the sliders. The graphs and the formulas with your numbers update at once.

Gas in a cylinder under a piston

The number of particles does not change (always 8). A diagram, not to scale.

The mass is the same, the volume is smaller → the density is greater.

m

7.2 g = 0.0072 kg

V

6,000 cm³ = 6000·10⁻⁶ m³

\rho

1.2 kg/m³

Formulas with your numbers

\rho = \dfrac{m}{V} = \dfrac{0.0072}{6000\cdot 10^{-6}} = 1.2

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Terms

Studied 0 of 8

Formulas

Density

\rho = \dfrac{m}{V}

Quantities
Symbol	Name	Unit
$\rho$	density of the substance	kg/m³
$m$	mass of the body	kg
$V$	volume of the body	m³

Solved for another quantity:

m = \rho V

V = \dfrac{m}{\rho}

Note. The formula holds for a uniform body (one substance, no cavities). Volume in $\text{m}^3$ : $1\ \text{cm}^3 = 10^{-6}\ \text{m}^3$ , $1\ \text{L} = 1\ \text{dm}^3 = 10^{-3}\ \text{m}^3$ .

Converting g/cm³ ↔ kg/m³

\rho_2 = 1000\,\rho_1

Quantities
Symbol	Name	Unit
$\rho_1$	density in g/cm³	g/cm³
$\rho_2$	the same density in kg/m³	kg/m³

Solved for another quantity:

\rho_1 = \dfrac{\rho_2}{1000}

Lab

Set the quantities with the sliders. The graphs and the formulas with your numbers update at once.

Gas in a cylinder under a piston

The number of particles does not change (always 8). A diagram, not to scale.

The mass is the same, the volume is smaller → the density is greater.

m

7.2 g = 0.0072 kg

V

6,000 cm³ = 6000·10⁻⁶ m³

\rho

1.2 kg/m³

Formulas with your numbers

\rho = \dfrac{m}{V} = \dfrac{0.0072}{6000\cdot 10^{-6}} = 1.2