Identify the limit of proportionality on a spring graph
Locate where the through-origin straight trend ends without claiming an unmeasured permanent change.
Mapped to the named 0654 section using teaching from the corresponding single-science course. A 0654-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Recognise a straight line through the origin.
- Use spring constant with consistent force and extension units.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What shape represents proportional load and extension?
What you will learn
- Define and identify the limit of proportionality.
- Explain why a previous constant spring relation may fail beyond it.
The boundary belongs to the proportional trend
The limit of proportionality is the boundary up to which load and extension are proportional. On a load-against-extension graph, locate the end of the straight line through the origin. The illustrative model is straight from zero to extension 3.0 cm and load 6.0 N, then curves through (4.0 cm,7.0 N) and (5.0 cm,7.5 N). Its stated limit is the point (3.0 cm,6.0 N).
Within that straight range, k = 6/0.030 = 200 N/m. At extension 4.0 cm, the observed model load is 7.0 N rather than the 8.0 N predicted by continuing F = 200x. The original constant model is therefore unsupported over the curved part.
Do not turn one boundary into another claim
The limit of proportionality concerns the load–extension relationship. The syllabus does not require an understanding of the elastic limit here. A curved loading graph alone does not establish a permanent extension after unloading; that is a separate observation, and the two ideas should not be treated as interchangeable.
With real scattered observations, identify the supported straight portion and its departure rather than claiming infinite precision from a sketch. In this exercise the boundary is stated by an original illustrative model, not inferred as a certified laboratory result. Further loading must remain within teacher-approved practical conditions.
Sources for this lesson
Pause and explain
The graph is straight through the origin to 6 N, then curves. What does 6 N mark?
Worked example
A model graph is proportional to (3.0 cm,6.0 N), then curves to (4.0 cm,7.0 N). State its limit and compare the later load with the old constant prediction.
Show the worked solution
- The through-origin straight portion ends at 3.0 cm and 6.0 N.
- Its k is 6/0.030 = 200 N/m.
- At 0.040 m, continuing that constant predicts 8.0 N, but the model gives 7.0 N.
Answer Limit: 3.0 cm at 6.0 N; old prediction 8.0 N versus model load 7.0 N.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Identify the limit on a graph straight to (3 cm,6 N), then curved beyond that point.
Give me a hint
Look for the end of the straight through-origin relationship.
Compare my reasoning
- The proportional portion ends at the supplied boundary.
- Its extension is 3 cm and load 6 N.
- Name both coordinates when locating the point.
3 cm extension at 6 N load.
Look for these in your work
- Identify the correct boundary.
- Use both axis quantities.
The proportional portion has k = 200 N/m, but the later curve gives 7 N at 4 cm. Compare the constant prediction and actual model value.
Give me a hint
Convert four centimetres before using the old linear equation.
Compare my reasoning
- 4 cm = 0.040 m.
- 200 × 0.040 = 8 N is the old prediction.
- The curve gives 7 N, so that constant is not valid across this later range.
Linear prediction 8 N; curve 7 N; the earlier constant does not describe this point.
Look for these in your work
- Convert extension correctly.
- Recognise the failed extension of the model.
A student labels the first curve departure as the point where permanent deformation is proved. Explain what their graph establishes and what additional observation would be needed.
Give me a hint
Separate a loading relationship from behaviour after unloading.
Compare my reasoning
- The graph establishes departure from proportional load and extension.
- It does not record the unloaded final length.
- A justified unloading observation would be needed for a permanent-change claim.
It shows non-proportional loading; a permanent-change claim needs unloading evidence.
Look for these in your work
- Name the demonstrated relationship.
- Avoid substituting a different boundary claim.
Common mistakes
- Identify the end of the proportional portion.
- Do not equate non-proportionality with proven permanent deformation.
- A point quotient beyond the limit does not validate the earlier constant model.
What can you explain now?
Does a curved loading graph alone prove a permanent extension after removing the load?
Compare with the explanation
No; unloading behaviour has not been measured.
A relationship during loading and a permanent change after unloading are different evidence claims.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Sketch a proportional region and its limit, then explain what a loading graph cannot establish about unloading.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.