Measuring Density (CIE IGCSE Physics: Co-ordinated Sciences (Double Award))

Equipment

Equipment list

Apparatus	Purpose
Regular and irregularly shaped objects	Objects used to measure the density of
A suitable liquid (e.g. sugar or salt solution)	Liquid to use to measure the density
A 30 cm ruler	To measure objects up to 30 cm in length
Vernier Calipers	To measure objects to around 15 cm in length
Micrometer	To measure objects to around 3 cm in length
Digital Balance	To measure the mass of objects
Displacement "Eureka" can	To measure the displacement of water of irregularly shaped objects
Measuring cylinders	To measure the volume of liquid

• 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

Equipment needed to measure 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 callipers 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

Results

An example results table to measure the density of regularly shaped objects

A suitable results table must contain space for multiple readings and any calculations that need to performed

Analysis of results

• Calculate the volume of the object depending on whether it is a cube, sphere, cylinder (or other regular shape)
• Then use the formula for density to calculate the density of each object 
  • The formulae for volume and density are explained in the revision note Density

Experiment 2: measuring the density of irregularly shaped objects

• This experiment aims 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

Equipment needed to measure the density of irregularly shaped objects

Apparatus for measuring the density 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

 

• Alternatively, the object can be placed in a measuring cylinder containing a known volume of liquid, and the change in volume then measured

 

When an irregular solid is placed in a measuring cylinder, the level of the liquid will rise by an amount equal to the volume of the solid

• Once the mass and volume of the shape is known, its density can be calculated

Results

An example results table to measure the density of irregularly shaped objects

A suitable results table must contain space for multiple readings and any calculations that need to performed

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 the density of liquids

• This experiment aims 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

Equipment needed to measure the density of liquid

Apparatus for determining the density of a liquid

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

Results

An example results table to measure the density of a liquid

A suitable results table must contain space for multiple readings and any calculations that need to performed

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

• Once the mass and volume of the liquid are known, the density can be calculated using the equation for calculating density
  • This is explained in the revision note Density

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