Required Practical: Force and Extension

This lesson covers the required practical investigation into the relationship between force and extension for a spring, as required by the AQA GCSE Physics specification (4.5.4). This practical demonstrates Hooke's law and is one of the most frequently tested required practicals in the GCSE Physics exam. You must know the method, equipment, variables, results analysis, and safety precautions in detail.

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Hooke's Law

Hooke's law states that the extension of an elastic object (such as a spring) is directly proportional to the force applied to it, provided the limit of proportionality is not exceeded.

The equation for Hooke's law is:

F = k x e

Where:

• F = force applied (N)
• k = spring constant (N/m)
• e = extension (m)

The spring constant (k) tells you how stiff the spring is. A larger spring constant means the spring is stiffer and harder to stretch.

Spring	Spring Constant (N/m)	Meaning
Soft spring	10	Easy to stretch
Medium spring	50	Moderate stiffness
Stiff spring	200	Hard to stretch

Exam Tip: The equation F = k x e is on the AQA equation sheet, but you MUST be able to rearrange it. To find extension: e = F / k. To find the spring constant: k = F / e. Practise rearranging this equation until it is automatic.

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Key Terminology

Term	Definition
Extension	The increase in length of the spring from its natural (unstretched) length
Natural length	The original length of the spring when no force is applied
Elastic deformation	The spring returns to its original shape when the force is removed
Inelastic (plastic) deformation	The spring is permanently stretched and does not return to its original length
Limit of proportionality	The point beyond which the extension is no longer proportional to the force
Elastic limit	The point beyond which the spring will not return to its original shape

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Equipment List

You will need the following equipment for this practical:

• Spring (helical spring)
• Clamp stand, boss, and clamp (to hold the spring vertically)
• Ruler (metre rule, measuring in mm)
• Set of known masses (e.g. 100 g masses, known weight = mass x g)
• Pointer (attached to the bottom of the spring to help read the ruler accurately)
• Safety goggles (to protect eyes in case the spring snaps)
• Soft landing surface (e.g. a cushion or sand tray below the spring)

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Method

Follow these steps carefully:

1. Set up the equipment. Clamp the spring securely at the top using the clamp stand, boss, and clamp. Attach a pointer to the bottom of the spring. Place a ruler vertically beside the spring.

2. Measure the natural length. Record the position of the pointer on the ruler with no masses attached. This is the natural (unstretched) length of the spring.

3. Add the first mass. Hang a 100 g mass (weight = 1.0 N, using g = 10 N/kg) from the bottom of the spring. Allow the spring to come to rest (stop oscillating).

4. Record the new length. Read the position of the pointer on the ruler. Calculate the extension by subtracting the natural length from the new length.

5. Repeat with additional masses. Add masses one at a time (100 g increments), recording the new length and calculating the extension each time. Continue up to at least 6 or 7 different masses.

6. Record results in a table.

7. Repeat the entire experiment at least 3 times and calculate a mean extension for each force value.

8. Plot a graph of force (y-axis) against extension (x-axis).

graph TD
    A["Clamp stand"] --> B["Clamp and boss"]
    B --> C["Spring (attached at top)"]
    C --> D["Pointer"]
    D --> E["Hanging masses"]
    F["Ruler (alongside spring)"] -.-> D

    style A fill:#2c3e50,color:#fff
    style C fill:#2980b9,color:#fff
    style E fill:#e74c3c,color:#fff
    style F fill:#27ae60,color:#fff

Exam Tip: In the exam, you may be asked to describe how to improve the accuracy of this experiment. Key answers include: use a pointer attached to the spring to reduce parallax error; take the reading at eye level; allow the spring to stop oscillating before reading; and repeat measurements to calculate a mean.

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Variables

Variable Type	Variable	Details
Independent variable	Force applied (weight of masses)	Changed by adding masses in equal increments
Dependent variable	Extension of the spring	Measured using a ruler
Control variables	Same spring, same starting position, same ruler, temperature	Must remain constant throughout the experiment

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Recording Results

Your results table should look like this:

Mass (g)	Weight / Force (N)	Length (mm)	Extension (mm)	Extension Trial 1 (mm)	Extension Trial 2 (mm)	Extension Trial 3 (mm)	Mean Extension (mm)
0	0.0	250	0	0	0	0	0
100	1.0	270	20	20	21	19	20
200	2.0	290	40	40	39	41	40
300	3.0	310	60	60	61	59	60
400	4.0	330	80	81	79	80	80
500	5.0	350	100	99	101	100	100
600	6.0	375	125	124	126	125	125

Exam Tip: Notice that the extension at 600 g (125 mm) is greater than expected if proportionality continued (it should be 120 mm). This suggests the spring may have passed the limit of proportionality. In the exam, you may be asked to identify this point from a graph or data table.

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Analysing the Graph

When you plot force (y-axis) against extension (x-axis):

• The graph is a straight line through the origin in the region where Hooke's law is obeyed.
• The gradient of the straight-line section equals the spring constant (k).
• The point where the graph starts to curve is the limit of proportionality.
• Beyond the limit of proportionality, the spring extends more for each additional unit of force.

graph LR
    subgraph "Force vs Extension Graph"
        A["Origin (0,0)"] -->|"Straight line: Hooke’s law obeyed"| B["Limit of proportionality"]
        B -->|"Curve: Hooke’s law no longer obeyed"| C["Spring permanently deformed"]
    end

    style A fill:#27ae60,color:#fff
    style B fill:#e67e22,color:#fff
    style C fill:#e74c3c,color:#fff

Calculating the Spring Constant from the Graph

The spring constant is the gradient of the straight-line section:

k = F / e

For example, if a force of 4.0 N produces an extension of 0.08 m:

k = 4.0 / 0.08 = 50 N/m

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Elastic and Inelastic Deformation