Hooke’s law practical: force and extension
Measure spring extension, calculate spring constant and distinguish proportionality from elastic behaviour.
Practise the calculations · Print a classroom set
Apparatus and measurements
Clamp a spring securely beside a ruler. A pointer gives a consistent reading position. Record the unloaded length, then add known masses gradually and allow the spring to settle.
Larger apparatus diagram
Method and controls
- Measure the unloaded length before adding masses. Include the hanger mass when calculating the applied force. Convert mass to kg and calculate weight using the stated g.
- Subtract unloaded length from each loaded length to find extension. Read the ruler at eye level and use metres when calculating k.
- Plot force vertically against extension horizontally. Fit the linear region. Unload and check whether the spring returns to its original length; this is evidence about elastic behaviour.
Results to analyse
Original synthetic data for practice.
| Total hanging mass / kg | Loaded length / cm |
|---|---|
| 0 | 12.0 |
| 0.10 | 14.0 |
| 0.20 | 16.0 |
| 0.30 | 18.0 |
Questions
- Use g = 10 N kg⁻¹. Calculate force and extension for the 0.20 kg load.
- Find the spring constant from the linear data and energy stored at 0.30 kg.
- If the graph begins to curve at a larger load, does that prove the spring will remain stretched after unloading?
Show worked answers
- Force = 0.20 × 10 = 2.0 N. Extension = 16.0 − 12.0 = 4.0 cm = 0.040 m.
- k = 2.0/0.040 = 50 N m⁻¹. At 0.30 kg, x = 0.060 m, so E = ½ × 50 × 0.060² = 0.090 J.
- No. Curvature identifies loss of proportionality. Check the unloaded length to detect permanent deformation; the elastic limit is a separate boundary.
Evaluation
The gradient gives k only for force vertically against extension in metres horizontally. Reversing axes gives 1/k. Using cm changes the numerical gradient by a factor of 100.
Secure the stand and use a tray beneath the masses. Keep feet clear of falling masses and avoid stretching the spring beyond the teacher’s chosen range.
Specification links
AQA 8463: Required practical 6; 4.5.3. OCR Gateway J249: P2.3b–e; PAG P2 (selected). Selected skills only; no practical-completion assessment.
Continue with calculation practice · Graph skills · All six practical guides