Required Practical: Density

This lesson covers the Required Practical for determining the density of regular and irregular solid objects and liquids, as specified in the AQA GCSE Physics specification (4.3.1). This is one of the required practicals that you must understand in detail for the exam — you may be asked about the method, equipment, variables, sources of error, and how to improve accuracy.

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Overview of the Required Practical

The aim of this practical is to use appropriate apparatus to measure the density of:

1. A regular solid (e.g. a rectangular block or cylinder)
2. An irregular solid (e.g. a pebble or a key)
3. A liquid (e.g. water, salt solution, or oil)

The fundamental equation used throughout is:

density = mass / volume

p = m / V

Exam Tip: This is one of the eight required practicals for AQA GCSE Physics. You will not necessarily carry out this practical in the exam, but you MUST be able to describe the method, identify variables, evaluate sources of error, and suggest improvements. Questions on required practicals are worth significant marks.

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Part 1: Measuring the Density of a Regular Solid

A regular solid has a shape that allows its volume to be calculated using a mathematical formula (e.g. a cuboid, cylinder, or sphere).

Equipment Needed

Equipment	Purpose
Balance (resolution 0.1 g or better)	To measure the mass of the solid
Ruler or vernier callipers	To measure the dimensions of the solid
Calculator	To calculate volume and density

Method

1. Place the regular solid on the balance and record its mass in grams (g).
2. Use a ruler (or vernier callipers for greater precision) to measure the dimensions of the solid.
   • For a cuboid: measure length (l), width (w), and height (h).
   • For a cylinder: measure the diameter (d) and height (h). Calculate the radius as r = d / 2.
3. Calculate the volume using the appropriate formula:
   • Cuboid: V = l x w x h
   • Cylinder: V = pi x r2 x h
4. Calculate the density using p = m / V.
5. Repeat the measurements at least three times and calculate a mean to improve accuracy.

Volume Formulae for Regular Shapes

Shape	Volume Formula
Cuboid	V = length x width x height
Cylinder	V = pi x r2 x h
Sphere	V = (4/3) x pi x r3

Exam Tip: When measuring the dimensions of a regular solid, take measurements at different positions along the object (e.g. measure the length at the top, middle, and bottom) and calculate the mean. This accounts for any irregularities in the shape and improves the reliability of your result.

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Part 2: Measuring the Density of an Irregular Solid

An irregular solid does not have a regular geometric shape, so its volume cannot be calculated using a formula. Instead, you use the displacement method (also called the eureka can method).

Equipment Needed

Equipment	Purpose
Balance (resolution 0.1 g or better)	To measure the mass of the solid
Eureka can (displacement can)	To measure the volume by water displacement
Measuring cylinder (appropriate size)	To collect and measure the displaced water
Water	The displacement fluid

Method

1. Place the irregular solid on the balance and record its mass in grams.
2. Fill the eureka can with water until it overflows from the spout. Wait until the water stops dripping.
3. Place an empty measuring cylinder under the spout of the eureka can.
4. Gently lower the irregular solid into the eureka can using a piece of string or thread (to avoid splashing).
5. The solid displaces its own volume of water, which flows out of the spout into the measuring cylinder.
6. Read the volume of displaced water from the measuring cylinder — this equals the volume of the solid.
7. Calculate the density using p = m / V.
8. Repeat at least three times and calculate a mean.

Alternative: Using a Measuring Cylinder Directly

If the object is small enough to fit inside a measuring cylinder:

1. Fill a measuring cylinder with a known volume of water. Record this as V1.
2. Carefully lower the object into the water.
3. Record the new water level as V2.
4. The volume of the object = V2 - V1.

graph TD
    A["Fill measuring cylinder<br/>Record initial level V1"] --> B["Lower object into water"]
    B --> C["Record new level V2"]
    C --> D["Volume of object = V2 - V1"]
    D --> E["Calculate density = mass / volume"]

    style A fill:#2c3e50,color:#fff
    style B fill:#2980b9,color:#fff
    style C fill:#e67e22,color:#fff
    style D fill:#27ae60,color:#fff
    style E fill:#8e44ad,color:#fff

Exam Tip: When reading the water level in a measuring cylinder, always read from the bottom of the meniscus (the curved surface of the water) at eye level. Reading from above or below introduces a parallax error. This is a very common exam question point.

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Part 3: Measuring the Density of a Liquid

Equipment Needed

Equipment	Purpose
Balance (resolution 0.1 g or better)	To measure the mass of the liquid
Measuring cylinder (appropriate size)	To measure the volume of the liquid

Method

1. Place an empty measuring cylinder on the balance and record its mass. This is m1.
2. Pour a known volume of the liquid into the measuring cylinder. Record the volume (V) in cm3.
3. Place the measuring cylinder (with liquid) on the balance and record the total mass. This is m2.
4. Calculate the mass of the liquid: m = m2 - m1.
5. Calculate the density using p = m / V.
6. Repeat with different volumes of the same liquid and calculate a mean density.

Worked Example

An empty measuring cylinder has a mass of 85.0 g. When 50.0 cm3 of oil is added, the total mass is 131.0 g.

Step 1: Mass of oil = 131.0 - 85.0 = 46.0 g

Step 2: Volume of oil = 50.0 cm3

Step 3: Density = mass / volume = 46.0 / 50.0 = 0.92 g/cm3

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Variables in the Required Practical

Variable Type	Variable	Details
Independent	Type of material / object	Different solids or liquids are tested
Dependent	Density	Calculated from mass and volume
Control	Temperature	Must remain constant throughout
Control	Method of measurement	Must use the same technique consistently

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Sources of Error and Improvements