Required practical

Determining density

There are different ways to investigate density. In this required practical activity, it is important to:

  • record the mass accurately
  • measure and observe the mass and the bigger volume of the different objects
  • use appropriate apparatus and methods to measure volume and mass and use that to investigate density

Aim of the experiment

To measure the density of various materials.

Method

Method 1: Regular solids

  1. Use a ruler to measure the length (l), width (w) and height (h) of a steel cube.
  2. Place the steel cube on the top pan balance and measure its mass.
  3. Calculate the volume of the cube using (l x w x h).
  4. Use the measurements to calculate the density of the metal.
  5. Use vernier callipers to measure the diameter of the sphere.
  6. Place the metal sphere on the top pan balance and measure its mass.
  7. Calculate the volume of the sphere using \frac{4}{3}\pi(\frac{\text{d}}{2})^{3}.
  8. Use the measurements to calculate the density of the metal.

Method 2: Stone or other irregular shaped object

  1. Place the stone on the top pan balance and measure its mass.
  2. Fill the displacement can until the water is level with the bottom of the pipe.
  3. Place a measuring cylinder under the pipe ready to collect the displaced water.
  4. Carefully drop the stone into the can and wait until no more water runs into the cylinder.
  5. Measure the volume of the displaced water.
  6. Use the measurements to calculate the density of the stone.
Displacement can used to measure the volume of an irregular shaped object.

Method 3: Water or any liquid

  1. Place the measuring cylinder on the top pan balance and measure its mass.
  2. Pour 50 cm3 of water into the measuring cylinder and measure its new mass.
  3. Subtract the mass in step 1 from the mass in step 2. This is the mass of 50 cm3 of water.
  4. Use the measurements to calculate the density of the water.

Results

Some example results could be:

ObjectMass / gVolume / cm³Density g/cm³Density kg/m³
Steel cube46860............
Steel sphere334.19............
Stone35668............
Water5050............

Analysis

Using the results from the table above, the densities can be calculated using:

Density = mass ÷ volume

Mass of steel cube = 468 g

Volume of steel cube = 60 cm3

Density = mass ÷ volume

468 ÷ 60 = 7.8 g/cm3 (= 7,800 kg/m3)

Diameter of steel sphere = 2 cm

Mass of steel sphere = 33 g

Volume of steel sphere = \frac{4}{3}\pi(\frac{\text{d}}{2})^{3} = 4.19 cm3

Density = mass ÷ volume

33 ÷ 4.19 = 7.9 g/cm3 (= 7,900 kg/m3)

For a stone of mass 356 g, the volume of water displaced into the measuring cylinder is 68 cm3.

Density = mass ÷ volume

356 ÷ 68 = 5.2 g/cm3 (= 5,200 kg/m3).

Mass of 50 cm3 of water is found to be 50 g.

Density = mass ÷ volume

50 ÷ 50 = 1 g/cm3 (= 1,000 kg/m3).

Evaluation

  • Density can be measured for regular solids, irregular solids and liquids.
  • Densities calculated from measurements are subject to experimental error. This could be because:
    • the top pan balances, when used by different people, may not be identically calibrated
    • the resolution of the measuring cylinders may be different, causing different values for the volume to be recorded
    • the displacement can may not have been set up correctly each time and any additional drops of water would cause some to dribble out of the spout before use
  • The experiment above shows steel to have two different values for density. One reason may be that some measurements are taken to different numbers of significant figures and this can create rounding errors. It can also mean that the actual value may be between 7.8 g/cm3 and 7.9 g/cm3.

Hazards and control measures

HazardConsequenceControl measures
Water spilled from displacement canSlip and fallUse a measuring cylinder to collect displaced water and prevent spills