Measuring Density (Cambridge O Level Physics)

Equipment List

Apparatus	Purpose
Regular and irregular shaped objects	To determine the density of
A suitable liquid e.g. water	To submerge the object in and measure the displacement
30 cm ruler	Used to measure objects up to 30 cm in length
Vernier caliper	Used to measure the diameter of objects
Micrometer	To measure small objects (up to around 3 cm)
Digital balance	To measure the mass of objects
Displacement (or eureka) can	To place the water and object in
Measuring cylinder	To measure the volume of the displaced water

• Resolution of measuring equipment:
  • 30 cm ruler = 1 mm
  • Vernier calipers = 0.01 mm
  • Micrometer = 0.001 mm
  • Digital balance = 0.01 g

Experiment 1: Measuring the Density of Regularly Shaped Objects

• The aim of this experiment is to determine the densities of regular objects by using measurements of their dimensions

Variables:

• Independent variable = Type of shape / volume
• Dependent variable = Mass of the object

Method

Vernier Caliper & Digital Balance

Vernier calipers are used to measure the diameter of a cylindrical shaped object to calculate its volume, and the digital scales are used to measure the object's mass

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

• An example of a results table might look like this:

Results Table

A results table should include areas to record all the relevant data i.e. measurements and calculations

Analysis of Results

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

Volume Formulae for Common Shapes

Calculating the volume of an object depends on its shape

• Remember to convert from centimetres (cm) to metres (m) by dividing by 100

1 cm = 0.01 m

50 cm = 0.5 m

• Using the mass and volume, the density of each can be calculated using the equation:

• Where:
  • ρ = density in kilogram per metres cubed (kg/m³)
  • m = mass in kilograms (kg)
  • V = volume in metres cubed (m³)

Experiment 2: Measuring the Density of Irregularly Shaped Objects

• The aim of this experiment is to determine the densities of irregular objects using a displacement technique

Variables:

• Independent variable = Different irregular shapes / mass
• Dependent variable = Volume of displaced water

Method

Apparatus for Measuring the Volume of Irregularly Shaped Objects

The volume of an irregularly shaped object can be found using the displacement of water. The object's mass can then be measured and these values used to calculate the object's density

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

 

• Alternatively, the object can be placed in a measuring cylinder containing a known volume of liquid, and the change in volume then measured
• Once the mass and volume of the shape is known, its density can be calculated

• An example of a results table might look like this:

Results Table

A results table should contain areas for all the required data in a logical format

Analysis of Results

• The volume of the water displaced is equal to the volume of the object
• Once the mass and volume of the shape are known, the density can be calculated using:

Experiment 3: Measuring Density of Liquids

• The aim of this experiment is to determine the density of a liquid by finding a difference in its mass

Variables:

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

Method

Measuring the Mass of Liquid in a Container

Mass of liquid = (mass of liquid + container) − (mass of container) 

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

• An example of a results table might look like this:

Results Table

A results table should have spaces for all the measurements and calculations required

Analysis of Results

• Find the mass of the liquid by subtracting the final reading from the original reading

Mass of liquid = Mass of cylinder with water – mass of cylinder

• Remember to convert between grams (g) and kilograms (kg) by dividing by 1000

1 g = 0.001 kg

78 g = 0.078 kg

• Once the mass and volume of the liquid are known, the density can be calculated using the equation:

Evaluating the Experiments

Systematic Errors:

• Ensure the digital balance is set to zero before taking measurements of mass
  • This includes when measuring the density of the liquid – remove the measuring cylinder and zero the balance before adding the liquid

Random Errors:

• A main cause of error in this experiment is in the measurements of length
  • Ensure to take repeat readings and calculate an average to keep this error to a minimum

• Place the irregular object in the displacement can carefully, as dropping it from a height might cause water to splash which will lead to an incorrect volume reading

Safety Considerations

• There is a lot of glassware in this experiment, ensure this is handled carefully
• Water should not be poured into the measuring cylinder when it is on the electric balance
  • This could lead to electric shock

• Make sure to stand up during the whole experiment, to react quickly to any spills