Density and pressure

• Gases are less dense than solids because the molecules are more spread out (same mass, over a larger volume)
• Approximate Densities of Materials

  • This table gives some examples of densities of common materials
• Density is defined as the mass per unit volume of a material
• Worked example for calculating density

  1. Step 1: List the known quantities

  2. Step 2: Write out the equation for density

  3. Step 3: Substitute in values

  4. Step 4: Round the answer to two significant figures
• Units of density

  • Depend on what units are used for mass and volume
• Exam Tip: Make sure you are comfortable converting between units such as metres (m) and centimetres (cm) or grams (g) and kilograms (kg)
• If a material is more dense than water (1000 kg/m^3), then it will sink
• Similarly sized objects made from high density materials

  • Have a high mass
• Examples of density differences


  • A bag full of feathers is far lighter compared to a similar bag full of metal
  • A balloon is less dense than a small bar of lead despite occupying a larger volume
• Core Practical: Determining Density

  1. Equipment List

  2. Experiment 1: Measuring the Density of Regularly Shaped Objects
• Objects made from low density materials

  • Typically have a low mass
• The volume of an object may not always be given directly, but can be calculated with the appropriate equation depending on the object’s shape
• Density related to mass and volume

  Density is related to mass and volume by the following equation
• Units of density

  • If the mass is measured in g and volume in cm, then the density will be in g/cm
  • If the mass is measured in kg and volume in m, then the density will be in kg/m
• Calculating the volume of an object depends on its shape
• Experiment 2: Measuring the Density of Irregularly Shaped Objects

  1. Place the object on a digital balance and note down its mass

  2. Fill the eureka can with water up to a point just below the spout

  3. Place an empty measuring cylinder below its spout

  4. Carefully lower the object into the eureka can

  5. Measure the volume of the displaced water in the measuring cylinder

  6. Repeat these measurements and take an average before calculating the density
• Experiment 3: Measuring Density of Liquids

  1. Place an empty measuring cylinder on a digital balance and note down the mass

  2. Fill the cylinder with the liquid and note down the volume

  3. Note down the new reading on the digital balance

  4. Repeat these measurements and take an average before calculating the density
• Variables for Experiment 1

  • Independent variable = Type of shape / volume
  • Dependent variable = Mass of the object
• Analysis of Results for Experiment 1

  Calculate the volume of the object depending on whether it is a cube, sphere, cylinder (or other regular shape)
• Analysis of Results for Experiment 2

  1. The volume of the water displaced is equal to the volume of the object

  2. Once the mass and volume of the shape are known, the density can be calculated
• Using the mass and volume, the density of each can be calculated using the equation: ρ = m/V
• Experiment 1: Measuring the Density of Regularly Shaped Objects

  1. Place the object on a digital balance and note down its mass

  2. Use either the ruler, Vernier calipers or micrometer to measure the object’s dimensions (width, height, length, radius) – the apparatus will depend on the size of the object

  3. Repeat these measurements and take an average of these readings before calculating the density
• Analysis of Results for Experiment 3

  1. Find the mass of the liquid by subtracting the final reading from the original reading

  2. Mass of liquid = Mass of cylinder with
• Remember to convert from centimetres (cm) to metres (m) by dividing by 100
• Variables for Experiment 2

  • Independent variable = Different irregular shapes / mass
  • Dependent variable = Volume of displaced water
• An example of a results table might look like this
• Variables for Experiment 3

  • Independent variable = Volume of water added
  • Dependent variable = Mass of cylinder
• Random Errors

  1. A main cause of error in this experiment is in the measurements of length

  2. Ensure to take repeat readings and calculate an average to keep this error to a minimum
• The area for pressure calculation should always be the cross-sectional area of the object
• Pressure examples

  • When a drawing pin is pushed downwards
  • Tractors with large tyres
  • Nails with sharp pointed ends
• Mass of liquid calculation

  Mass of cylinder with water - mass of cylinder
• 78 g = 0.078 kg
• Calculate density of liquid


  Once the mass and volume of the liquid are known, the density can be calculated using the equation
• Place the irregular object in the displacement can carefully

  Dropping it from a height might cause water to splash which will lead to an incorrect volume reading
• Pressure calculation in fluids

  The pressure at the surface of a fluid can be calculated using the equation
• Remember to convert between grams (g) and kilograms (kg) by dividing by 1000
• Pressure formula triangle

  This equation can be rearranged with the help of a formula triangle
• Pressure

  The concentration of a force or the force per unit area
• Systematic Errors

  1. Ensure the digital balance is set to zero before taking measurements of mass

  2. When measuring the density of the liquid, remove the measuring cylinder and zero the balance before adding the liquid
• Find the mass of the liquid


  Subtract the final reading from the original reading