Hooke’s Law (Copy)
1. Core Principle
Hooke’s Law:
The extension of a spring is directly proportional to the force applied, provided the limit of proportionality is not exceeded.
Formula:
F = k × x
- F = force (N)
- k = spring constant (N/m)
- x = extension (m)
2. Objective of the Experiment
- To investigate the relationship between force and extension of a spring
- To verify Hooke’s Law using a linear graph
- To calculate the spring constant (k) from the graph
3. Apparatus Required
| Apparatus | Purpose |
|---|---|
| Clamp stand with boss and clamp | To hold the spring vertically |
| Spring | The object under investigation |
| Metre rule | To measure original and extended length |
| Weights / slotted masses | Apply force to the spring |
| Hanger (e.g. 50 g) | To hold masses |
| Pointer or paper strip | For accurate reading of extension |
| Balance (optional) | To verify mass values if required |
4. Step-by-Step Method
- Clamp a spring vertically using a stand and boss head.
- Attach a pointer or tape marker at the end of the spring.
- Position a metre rule behind the spring (aligned and vertical).
- Record the original length of the spring without any load.
- Add a known mass (e.g. 50 g = 0.50 N).
→ Use:F = m × g(g = 9.8 or 10 m/s²) - Record the new length, calculate extension = new length – original length.
- Repeat for several masses (e.g. 50 g to 300 g in 50 g intervals).
- Plot a graph of force (N) on the y-axis vs extension (m) on the x-axis.
- Determine the spring constant (k) from the gradient of the straight-line portion.
5. Sample Data Table
| Mass (g) | Force (N) | Length (cm) | Extension (cm) |
|---|---|---|---|
| 0 | 0.0 | 20.0 | 0.0 |
| 50 | 0.5 | 23.0 | 3.0 |
| 100 | 1.0 | 26.0 | 6.0 |
| 150 | 1.5 | 29.0 | 9.0 |
6. Graphical Analysis
- Plot:
→ Y-axis: Force (N)
→ X-axis: Extension (m or cm) - The straight line through origin confirms Hooke’s Law.
- Gradient = spring constant (k)
→k = F / x(from any linear section)
7. Limit of Proportionality
- The point where the graph curves (no longer linear)
- Beyond this point, the spring does not obey Hooke’s Law
- Do not include those values in your gradient calculation
8. Variables
| Type | Examples |
|---|---|
| Independent | Force applied (via mass) |
| Dependent | Extension of the spring |
| Controlled | Same spring, same measuring method, vertical alignment |
9. Common Errors and How to Avoid Them
| Error | Fix |
|---|---|
| Parallax error reading ruler | Always read at eye level |
| Spring not vertical | Use a clamp and align ruler behind |
| Spring bouncing during reading | Wait for spring to come to rest |
| Forgetting to subtract original length | Always calculate extension = stretched – original |
| Exceeding limit of proportionality | Stop adding weights once graph starts to curve |
| Wrong units | Convert cm to m if necessary (1 cm = 0.01 m) |
10. Alternate Variation: Two Springs in Parallel/Series
ATP may ask you:
- “How would extension change with two identical springs in parallel?”
→ Extension is halved - “What if springs are in series?”
→ Extension is doubled
✔️ Use diagram to explain setup and answer qualitatively if calculation is not required.
11. ATP-Style Question Types
| Question Type | Example |
|---|---|
| Design method | “Describe an experiment to verify Hooke’s Law.” |
| Data completion | Fill in force or extension in a results table |
| Graph plotting | “Plot a graph of force vs extension and find the spring constant” |
| Equation application | “Calculate extension when 1.2 N is applied and k = 40 N/m” → x = F/k = 0.03 m |
| Error suggestion | “Parallax error or uneven spring motion” |
| Limit of proportionality | “Identify where Hooke’s Law no longer applies” |
12. Exam Tips
- Always write:
→F = k × x
→ Substitution with correct units
→ Final answer with units (e.g. N/m) - Label graph axes as:
→Force / NandExtension / cmor/ m - Make sure graph covers at least 50% of space, uses a linear scale, and includes a best-fit line.
- State:
“Repeat readings and take average to improve reliability.”
“Avoid overloading to prevent permanent deformation of spring.”