Plot and interpret load-extension data
Choose labelled axes and use measured extension to interpret straight and curved portions.
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
- Calculate extension from two readings.
- Plot numerical pairs on consistent scales.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which pair should be plotted for 4 N producing extension 2 cm?
What you will learn
- Plot load vertically against extension horizontally.
- Read values and recognise when a straight proportional trend is no longer supported.
Make the axes describe the table
For the original illustrative spring table, extensions 0,0.5,1.0,1.5,2.0 cm pair with loads 0,1,2,3,4 N. Plot extension horizontally and load vertically, label both quantities and units, and select regular scales that use the available space. These ideal example points lie on a straight line through the origin.
Read a value using the axes rather than judging the drawn slope by eye. At extension 1.5 cm the load is 3 N in this example. Interpolating within the supported straight trend gives 2.5 N at 1.25 cm. Real scattered measurements usually call for an appropriate best-fit line rather than a zigzag between each point.
Keep conclusions inside the evidence
Equal extension increases accompany equal load increases in the straight portion. A curve means the same simple proportional pattern no longer describes that part of the data. Extended lessons later name its boundary and quantify spring stiffness; Core students should first explain what the graph shows.
A straight table ending at 4 N does not prove the spring continues to behave that way at 20 N. Additional approved measurements or a stated model would be needed. A plotted example is not a performed experiment, and a line of best fit does not erase systematic errors such as a moving ruler or a wrong unloaded reference.
Sources for this lesson
Pause and explain
The table is straight up to 4 N. Does it establish the extension at 20 N?
Worked example
Read the load at extension 1.5 cm from a line through (0,0) and (2.0 cm,4 N).
Show the worked solution
- The plotted line uses load vertically and extension horizontally.
- At 1.5 cm, the line reaches 3 N.
- The result is an interpolation within the supplied trend.
Answer 3 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.
Use the line from zero to (2.0 cm,4 N) to read load at 1.5 cm.
Give me a hint
Find the horizontal value and move to the line, then to the vertical axis.
Compare my reasoning
- Locate 1.5 cm extension.
- Its point lies at 3 N load.
- The reading stays inside the stated range.
3 N.
Look for these in your work
- Use labelled axes.
- Read an in-range value.
The same straight trend has 2 N at 1.0 cm and 3 N at 1.5 cm. Interpolate the load at 1.25 cm.
Give me a hint
The extension is halfway between the two observations.
Compare my reasoning
- 1.25 cm is the midpoint of 1.0 and 1.5 cm.
- The matching load is halfway between 2 and 3 N.
- Load = 2.5 N.
2.5 N.
Look for these in your work
- Interpolate between paired values.
- Give the force unit.
A student's graph is curved at larger loads but they draw a straight line through every point and predict all later readings. Explain the limitation.
Give me a hint
A chosen straight line cannot make a curved trend proportional.
Compare my reasoning
- The larger-load observations depart from a straight trend.
- One proportional model cannot describe all those data.
- Use a curve or appropriate range and avoid unsupported extrapolation.
The curved data do not support one straight proportional model over all loads.
Look for these in your work
- Identify the observed change of trend.
- Limit predictions to supported evidence.
Common mistakes
- Label which variable is vertical.
- A through-origin straight line supports a proportional trend.
- Do not extrapolate far beyond measured loads without justification.
What can you explain now?
On this line, what load corresponds to 1.25 cm extension?
Compare with the explanation
2.5 N.
It is halfway between the loads at 1.0 and 1.5 cm.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Draw axes for load against extension and explain interpolation versus unsupported extrapolation.
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.