Physics Density and Volume Calculation

Density

• Density is a measure of how much mass a substance has per unit of its volume.
• Formula for density: Density (ρ) = Mass (m) / Volume (V)
• In physics, density is usually measured in kilograms per cubic meter (kg/m³).
• One gram per cubic centimeter (g/cm³) is equivalent to 1000 kilograms per cubic meter (kg/m³).

How to find the volume of a solid

• Regular shape:
  • Measure the length, width, and height of the solid.
  • Multiply the length, width, and height to calculate the volume.
  • Example: For a cuboid with dimensions 4 cm x 3 cm x 2 cm, the volume is 24 cm³.
• Irregular shape:
  • Use a Eureka can filled with water and a measuring cylinder.
  • When an irregular object is submerged in the Eureka can, the volume of water displaced is equal to the volume of the object.
  • Collect the displaced water in the measuring cylinder.
  • The volume of the water in the measuring cylinder is the volume of the object.

How to experimentally calculate the density of a solid

• Step 1: Measure the mass.
  • Place the solid on a balance and measure its mass.
• Step 2: Measure the volume.
  • Use the method for calculating volume described above based on the shape of the solid.
• Step 3: Calculate the density.
  • Divide the mass by the volume.

How to experimentally calculate the density of a liquid

• Step 1: Measure the mass of the empty measuring cylinder.
  • Place an empty measuring cylinder on a balance and zero the balance.
• Step 2: Measure the mass of the liquid.
  • Pour a known volume of liquid (e.g., 10 ml = 10 cm³) into the measuring cylinder.
  • Record the mass of the liquid in the measuring cylinder.
• Step 3: Calculate the density.
  • Divide the mass of the liquid by the volume (which you already know).
• Accuracy: Using a larger volume of liquid to measure will typically give a more accurate density measurement as it minimizes the impact of uncertainties in measurements.
• Multiple measurements: Taking multiple measurements of density helps identify anomalies and permits calculating a mean, allowing for more reliable results.