Measuring Density | Physics for GCSE/IGCSE - Year 11 PDF Download

Measuring Density

Equipment List

Resolution

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 objective of this experiment is to ascertain the densities of standard objects by measuring their dimensions.

 Variables: 

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

Method:

1. Place the object on a digital balance and record its mass.
2. Measure the object's dimensions using appropriate tools such as a ruler, Vernier calipers, or micrometer based on the object's size.
3. Take multiple measurements and calculate the average before determining the density.

A sample of a results table could resemble the following:

Analysis of Results

• Compute the volume of the object based on its shape, whether it's a cube, sphere, cylinder, or another regular form.
  
• Remember to convert measurements from centimeters (cm) to meters (m) by dividing by 100.
  1 cm = 0.01 m
  50 cm = 0.5 m
• Using the mass and volume, determine the density using the formula: Density = Mass / Volume
  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 objective is to determine the densities of irregular objects using a displacement technique.
Variables:

• Independent variable: Varied irregular shapes or masses of objects being tested.
• Dependent variable: Volume of water displaced by the irregular objects.

Method:

1. Place the irregular object on a digital balance and record its mass.
2. Fill the eureka can with water just below the spout level.
3. Position an empty measuring cylinder under the spout of the eureka can.
4. Gently submerge the object into the water in the eureka can.
5. Measure the volume of water displaced in the measuring cylinder.
6. Repeat the above steps, calculate the average, and then determine the density of the object.

Another approach involves placing the object in a graduated cylinder filled with a known volume of liquid, and subsequently measuring the change in volume.

• Once the mass and volume of an object are determined, its density can be calculated.
• A sample table of results could appear as follows:
  

Analysis of Results

• The displaced water volume equals the volume of the object. 
• After determining the mass and volume of the shape, density can be calculated using:
  

Experiment 3: Measuring Density of Liquids

The objective of this experiment is to calculate the density of a liquid based on the variation in its mass.

Variables:

• Independent variable: The volume of water added.
• Dependent variable: The mass of the cylinder.

Method:

1. Place an empty measuring cylinder on a digital balance and record the mass.
2. Fill the cylinder with the liquid and note the volume.
3. Record the new reading on the digital balance.
4. Repeat these steps, calculate the average, and then determine the density.

An example of a results table:

Analysis of Results

• Calculate the mass of the liquid by subtracting the final reading from the initial reading.
• Mass of liquid = Mass of cylinder with water - mass of cylinder.

Remember:

• Convert between grams (g) and kilograms (kg) by dividing by 1000.
• 1 kilogram (kg) = 1000 grams (g).

Mass and Density Calculations

• 1 gram is equivalent to 0.001 kilograms.
• 78 grams is equal to 0.078 kilograms.

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

Evaluating the ExperimentsL

Systematic Errors:

• Always ensure that the digital balance is calibrated to zero before measuring mass.
• When determining the density of a liquid, remove the measuring cylinder and zero the balance before adding the liquid.

Random Errors:

• Length measurements represent a significant potential source of error in this experiment.
  • To mitigate this, ensure to take repeated measurements and calculate an average.
• When placing the irregular object into the displacement can, exercise caution to prevent water splashing. Dropping the object from a height can lead to inaccurate volume readings.

Safety Considerations

• Exercise care when handling the glassware utilized in this experiment.
• Avoid pouring water into the measuring cylinder while it's on the electric balance to prevent the risk of electric shock.
• Maintain a standing position throughout the experiment to promptly address any spills.