Lecture Notes: Understanding Density and Experimental Measurement

Introduction to Density

• Definition: Density is a measure of how much mass a substance has per unit of its volume.
• Formula:
  • Density ( \rho ) (rho) = ( \frac{\text{mass}}{\text{volume}} )
  • Units commonly used:
    • Kilograms per cubic meter (kg/m³)
    • Grams per cubic centimeter (g/cm³)

Conversion of Units

• Conversion between units:
  • 1 g/cm³ = 1000 kg/m³
• Example with Aluminium:
  • Density in kg/m³: 2710 kg/m³
  • Density in g/cm³: 2.71 g/cm³

Example Calculation

• Problem: Calculate the volume of 420 kg of Aluminium.
  • Given density: 2710 kg/m³
  • Formula: Volume = ( \frac{\text{Mass}}{\text{Density}} )
  • Calculation: ( \frac{420 \text{ kg}}{2710 \text{ kg/m}^3} = 0.155 \text{ m}^3 )

Experimental Determination of Density

• For Solids:

  • Mass Measurement: Use a balance to measure mass.
  • Volume Measurement:
    • Regular Shapes: Measure and multiply length ( \times ) width ( \times ) height.
      • Example: Volume of a cuboid with dimensions 4 cm, 3 cm, 2 cm = 24 cm³
    • Irregular Shapes: Use a eureka can and a measuring cylinder.
      • Fill eureka can with water up to the outlet.
      • Add the solid; water displacement equals the solid's volume.

• For Liquids:

  • Place an empty measuring cylinder on a balance and zero it.
  • Pour a known volume (e.g., 10 ml or 10 cm³) of liquid and measure its mass.
  • Calculate density: Mass/Volume.

Tips for Accurate Measurement

• Larger volume measurements lead to more accuracy by minimizing measurement uncertainties.
• Take multiple measurements to find anomalies and calculate a mean.

Conclusion

• Understanding density and its calculation is essential for analyzing substances in physics.
• Experimental methods vary slightly between solids and liquids but involve similar principles of measuring mass and volume.