Edexcel A Level (IAL) Physics-1.23 Density- Study Notes- New Syllabus
Edexcel A Level (IAL) Physics -1.23 Density- Study Notes- New syllabus
Edexcel A Level (IAL) Physics -1.23 Density- Study Notes -Edexcel A level Physics – per latest Syllabus.
Key Concepts:
- be able to use the equation density \( \rho = \dfrac{m}{V} \)
Density \( \rho = \dfrac{m}{V} \)
Definition of Density
Density is the mass per unit volume of a substance. It tells us how compact the matter inside an object is.
\( \rho = \dfrac{m}{V} \)
- \( \rho \) = density (kg m⁻³)
- \( m \) = mass (kg)
- \( V \) = volume (m³)
Key Points
- Higher density → particles are more closely packed.
- Different materials have different densities (e.g., iron is denser than wood).
- Objects float if their density is less than the fluid they are in.
- Volume can be measured using geometric formulas or displacement methods.
Rearranging the Density Formula
- Mass:
\( m = \rho V \)
- Volume:
\( V = \dfrac{m}{\rho} \)
Example (Easy)
A material has a mass of \( 200\, \mathrm{g} \) and a volume of \( 50\, \mathrm{cm^3} \). Find its density in \( \mathrm{kg\,m^{-3}} \).
▶️ Answer / Explanation
Convert units:
\( 200\, \mathrm{g} = 0.20\, \mathrm{kg} \)
\( 50\, \mathrm{cm^3} = 50 \times 10^{-6}\, \mathrm{m^3} = 5.0\times10^{-5}\, \mathrm{m^3} \)
Now use density formula:
\( \rho = \dfrac{m}{V} = \dfrac{0.20}{5.0\times10^{-5}} = 4000\, \mathrm{kg\,m^{-3}} \)
Example (Medium)
A rectangular block has dimensions \( 0.20\, \mathrm{m} \times 0.10\, \mathrm{m} \times 0.05\, \mathrm{m} \). If it has a mass of \( 3.0\, \mathrm{kg} \), find its density.
▶️ Answer / Explanation
Volume:
\( V = 0.20 \times 0.10 \times 0.05 = 0.001\, \mathrm{m^3} \)
Density:
\( \rho = \dfrac{3.0}{0.001} = 3000\, \mathrm{kg\,m^{-3}} \)
Example (Hard)
A metal cylinder has a radius of \( 0.04\, \mathrm{m} \) and a height of \( 0.30\, \mathrm{m} \). Its mass is \( 6.0\, \mathrm{kg} \). Find the density of the metal.
▶️ Answer / Explanation
Volume of a cylinder:
\( V = \pi r^2 h = \pi (0.04)^2 (0.30) \)
\( V = \pi (0.0016)(0.30) = 0.001507\, \mathrm{m^3} \) (approx.)
Density:
\( \rho = \dfrac{6.0}{0.001507} \approx 3980\, \mathrm{kg\,m^{-3}} \)