Cambridge International AS & A Level · P3 · structured
Extract constants from your spring fit
AS practical 6: read the fitted line, not two measurements · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- demanding
- Marks
- 8
- Topics
- 6
- Answer
- Complete
The constructed data concern the loaded length L of a spring under force F; L0 is its unloaded length and k its spring constant, with L=L0+F/k in the linear range. Use your graph from the spring-table task, not just the first and last readings. If opening this task on its own, first draw and fit L against F from the supplied data on a readable grid with the L axis starting at 12 cm. Mark a gradient triangle longer than half your drawn line, obtain k and L0, and predict L at 1.75 N. Explain why predicting at 8 N would need extra evidence. Show the intercept calculation even though the vertical axis starts at 12 cm. Constructed illustrative data (not observed experimental evidence). Columns: F / N (constructed) | L / cm (constructed). Rows: 0.50 | 14.1; 1.00 | 15.4; 1.50 | 17.0; 2.00 | 18.5; 2.50 | 19.9; 3.00 | 21.6.
- (a)
Show a fit-line triangle and find k.
5 marks - (b)
Recover L0 algebraically.
1 mark - (c)
Predict L at 1.75 N and qualify the 8 N extrapolation.
2 marks
Ready to self-mark?Reveal the detailed answer guide
(a)
Show a fit-line triangle and find k.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
Large triangle on fitted line; reference m=3.00 cm N^-1 and k=33.3 N m^-1.
(b)
Recover L0 algebraically.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
L0=L-mF, reference 12.5 cm.
(c)
Predict L at 1.75 N and qualify the 8 N extrapolation.
Identify what the question is testing, organise the response into distinct mark-earning points, and make every conclusion traceable to a physical principle or to the evidence supplied.
- 1
About 17.8 cm; 8 N is outside tested elastic range.
Complete marking guidance
Use these worked steps alongside the part-by-part answers. They explain the method and mark allocation; they do not add extra marks.
- Inspect the drawing: two coordinates lie on the fit and triangle exceeds half the line span. Two marks.
- Correct slope and cm-to -m conversion: two marks.
- k=1/m after unit conversion: one mark.
- L0=L-mF using a fitted point: one mark.
- Interpolate about 17.8 cm: one mark.
- Identify extrapolation and possible breakdown of linear elastic response: one mark. Accept a range consistent with the learner's defensible fit.
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