Concept of density

Density is the measure of how tightly the particles of a substance are packed within a given volume. In simple terms, density tells us how much mass exists in a given volume.

1. A substance with tightly packed particles has high density
2. A substance with loosely packed particles has low density

Concept of density

The density (ρ) of a substance is given by:

$\rho = \frac{m}{V}$

Where:

• ρ (rho) = density
• m = mass of the substance
• V = volume of the substance

• The SI unit is kilogram per cubic metre (kg/m³)
• Other common units include gram per cubic centimetre (g/cm³)

Note: 1 g/cm³ = 1,000 kg/m³

To easily remember the relationship between mass, volume, and density, use the density triangle:

The density-mass-volume triangle

From the triangle:

1. To find density: $\rho = m \div V$
2. To find mass: $m = \rho \times V$
3. To find volume: $V = m \div \rho$

Density does not depend on the amount of substance you have. Even a small sample of gold or a large lump has the same density, because it depends only on the material, not its size.

A glass block has dimensions of 0.12 m × 0.04 m × 0.10 m and a mass of 1.2 kg. Find its density.

Solution:

$\text{Volume} = 0.12 \times 0.04 \times 0.10 = 0.00048 \, \text{m}^3$

$\text{Density} = \frac{1.2}{0.00048} = 2500 \, \text{kg/m}^3$

Answer: the density of the glass block is 2,500 kg/m³.

Given:

1. Mass of aluminium = 5.4 g
2. Density of aluminium = 2.7 g/cm³
3. Density of glass = 2.5 g/cm³

Step 1: find the volume of aluminium:

$V = \frac{5.4}{2.7} = 2 \, \text{cm}^3$

Step 2: use that volume to find the mass of glass:

$\text{Mass of glass} = 2.5 \times 2 = 5 \, \text{g}$

Answer: a 5.4 g aluminium block has the same volume as a 5 g glass block.

Aim: to determine the mass-to-volume ratio (density) for different solid objects.

Materials:

• Vernier caliper
• Beam balance
• Blocks of aluminium, copper, and iron

Procedure:

1. Measure the length, height, and width of each block.

2. Measure the mass of each block.

3. Use the formula:

   $\text{Volume} = \text{Length} \times \text{Height} \times \text{Width}$

4. Calculate the mass-to-volume ratio (density) for each.

Data table:

Questions:

1. Compare the density values of each substance.
2. Are they equal or different? Why?
3. What physical quantity does this ratio represent?