Determining Density (WJEC GCSE Physics: Combined Science)

• Methods for regular and irregular objects are described, and a method for the density of liquids
• The equipment list for the first two investigations are similar:

Equipment List

List of Equipment Used to Investigate the Density of a Range of Objects

Equipment	Purpose
Regular and irregular shaped objects	To determine the density of
Liquid (e.g. salt or sugar solution)	To determine the density of
30 cm ruler	To measure straight sides up to 30 cm
Vernier caliper	To measure objects up to about 15 cm
Micrometer	To measure objects smaller than a few cm
Digital balance	To measure the mass of the objects and liquid
Displacement ("eureka") can	To displace water equal to the volume of the object
Measuring cylinder	To measure the volume of liquid and displaced water

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Experiment 1: Measuring the Density of Regularly Shaped Objects

Aim of the Experiment

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

Method

Vernier Caliper and Digital Balance

A vernier caliper and a digital balance are used to take more accurate measurements

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 and shape of the object 
3. Repeat these measurements and take an average of these readings before calculating the density

• Measurements should be recorded in a suitable results table

Example Results Table 

A results table should have space to include all the measurements taken and any calculations required (such as averages) presented in a clear and logical way

Analysis of Results

• Calculate the volume of the regularly shaped object 
• 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:

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

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Experiment 2: Measuring the Density of Irregularly Shaped Objects

Aim of the Experiment

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

Method

Apparatus for Measuring the Volume of Irregular Shaped Objects

A displacement can (or eureka can) is used for measuring the volume of irregular 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

• Measurements should be recorded in a suitable results table

Example Results Table 

A results table with spaces for repeat readings of measurements and spaces for calculations of averages

Analysis of Results

• The volume of the water displaced is equal to the volume of the object
  • 1 ml = 1 cm³
• Once the mass and volume of the shape are known, the density can be calculated

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Experiment 3: Measuring Density of Liquids

Aim of the Experiment

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

Method

Apparatus used to Determine the Mass of a Liquid

The mass of the empty measuring cylinder is found, and then the mass of the liquid in the cylinder. By subtracting the mass of the empty cylinder from the mass of the liquid-filled cylinder, the mass of the liquid can be found

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. Place the liquid-filled cylinder on the digital balance record the mass
4. Repeat these measurements and take an average before calculating the density

• Measurements should be recorded in a suitable results table

Example Results Table 

The results table has spaces to record the mass of the empty cylinder and the mass of the liquid-filled cylinder as well as spaces for repeat measurements and calculated averages

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

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

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Evaluating the Experiments

Systematic Errors:

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

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