Density (Cambridge (CIE) A Level Physics): Revision Note

A paving slab has a mass of 73 kg and dimensions 40 mm × 500 mm × 850 mm.

Calculate the density, in kg m^-3 of the material from which the paving slab is made.

Answer:

Step 1: List the known quantities and convert to SI units

• Mass, m = 73 kg

• Length, $l$ = 0.850 m

• Width, w = 0.500 m

• Height, h = 0.040 m

Step 2: State the equation for density

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

Step 3: Calculate the volume

$\mathrm{volume}\mathrm{of}\mathrm{a}\mathrm{cuboid}=\mathrm{length}\times \mathrm{width}\times \mathrm{height}$

$V=lwh$

$V=0.850\times 0.500\times 0.040$

$V=0.017{\mathrm{m}}^3$

Step 4: Substitute the known values to calculate

$\rho =\frac{73}{0.017}$

$\rho =4300\mathrm{kg}{\mathrm{m}}^{-3}\left(2\mathrm{s}.\mathrm{f}.\right)$

• When converting a larger unit to a smaller one, you multiply (×)

  • E.g. 125 m = 125 × 100 = 12 500 cm

• When you convert a smaller unit to a larger one, you divide (÷)

  • E.g. 5 g = $\frac{5}{1000}$ = 0.005 or 5 × 10^-3 kg

• When dealing with squared or cubic conversions, cube or square the conversion factor too

  • E.g. 1 mm³ = $\frac{1}{{1000}^3}$ = 1 × 10^-9 m³

  • E.g. 1 cm³ = $\frac{1}{{100}^3}$ = 1 × 10^-6 m³