The shape of the lesson
By the end of the lesson, learners can
- Load it up, watch it stretch: Add loads one at a time and watch the extension grow in equal steps, the signature of a proportional relationship.
- Straight, then curved.
- Hooke's law: extension proportional to load, F = kx, up to the limit of proportionality.
- Spring constant: k = F ÷ x (the gradient of the straight-line region).
- Name it right: the point where the line stops being straight is the limit of proportionality.
One picture every idea returns to
Up to the limit of proportionality, the extension of a spring is directly proportional to the load: F = kx, where k is the spring constant in N/m. Beyond that limit, extension is no longer proportional to load and the graph curves.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, A spring keeps its promise, up to a point.. Hang a load on a spring and it stretches. Put the figure on the board: it is the one picture every idea in the lesson returns to. | Whole class, then pairs |
| 5 to 17 min | Teach and check: Load it up, watch it stretch | Add loads one at a time and watch the extension grow in equal steps, the signature of a proportional relationship. Project tab 4 of the lab (Hooke's law) and let a student drive it while the class predicts. | Whole class, then pairs |
| 17 to 30 min | Teach and check: Straight, then curved | Straight, then curved. Model the worked example Worked example on the board, one line at a time. | Round Table |
| 30 to 36 min | Check | The four Stage 1 questions from the student lesson, answered on mini whiteboards or by show of fingers. Re-teach the one most get wrong. | Individual, then whole class |
| 36 to 43 min | Plenary | The exam-style questions from Stage 2, one at a time: thirty seconds alone, then a random call. The feedback lines in the key give the examiner's wording. | Individual, random call |
| 43 to 45 min | Exit and homework | Set the worksheet below (6 questions, 14 marks). Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in Straight, then curved, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Round Table
One sheet travels round the team. Each student adds one line of working or one idea and passes it on, so the solution is built four hands at a time and every contribution is visible.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| The point where the straight line ends is the limit of proportionality. | Avoid writing elastic limit, which is a different point on the graph and is not the term the syllabus wants here. When a load-extension graph stops being a straight line, the quantity you name is the limit of proportionality. |
Hooke’s law: worksheet
6 questions, 14 marks. Written in the style of the papers; no past paper question is reproduced.
State Hooke's law.
Describe the shape of the load-extension graph for a spring that is loaded beyond the point where Hooke's law stops holding. Name that point.
Within the proportional region, a load of 6.0 N produces an extension of 0.040 m. Calculate the spring constant.
A spring has a spring constant of 25 N/m. Calculate the load needed to produce an extension of 0.20 m, assuming it stays within the proportional region.
On a load-extension graph, a student labels the end of the straight-line section the "elastic limit." State the term the syllabus expects here, and note whether the two are the same point.
A spring has an original length of 12.0 cm. With a 1.5 N load it stretches to 15.0 cm, within the proportional region.
(a)Calculate the extension. (b)Calculate the spring constant in N/m.Answer key and marking notes
- The extension of a spring is directly proportional to the load applied. ✓
- This holds up to the limit of proportionality. ✓
- A straight line through the origin at first (extension proportional to load). ✓
- After the limit of proportionality the line curves (extension increases more rapidly per unit load). ✓
- The point named is the limit of proportionality. ✓
- k = F ÷ x = 6.0 ÷ 0.040
k = 150 N/m
- F = k x = 25 × 0.20
F = 5.0 N
- The expected term is the limit of proportionality. ✓
- It is not the same as the elastic limit; they are different points on the graph. ✓
(a) extension = 15.0 − 12.0 = 3.0 cm = 0.030 m ✓
(b) k = F ÷ x = 1.5 ÷ 0.030
k = 50 N/m
2 multiple-choice questions on this lesson
From the topic question bank. Assign them in the app for a marked score in your gradebook, or run the topic as a class game.
The load-extension graph for a spring is shown. Beyond which point does the spring stop obeying Hooke's law?
- Aat the origin
- Bat point P, where the line stops being straight
- Cat the highest load shown
- Dthe spring always obeys Hooke's law
A spring obeys Hooke's law. It extends by 4.0 cm when a 2.0 N load is hung from it. What load produces an extension of 10 cm?
- A0.80 N
- B5.0 N
- C8.0 N
- D20 N
Quiz key
Up to P the graph is a straight line through the origin, so load and extension are proportional. Beyond P the line curves, so proportionality is lost: P is the limit of proportionality.
The extension grows by a factor of 10 ÷ 4 = 2.5, so the load = 2.0 × 2.5 = 5.0 N. Option C wrongly uses a factor of 4; D multiplies load and extension.
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.