Cambridge International AS & A Level · P5 · structured
Construct and check the worst acceptable fit
A2 practical 9: a worst acceptable line must pass every interval · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- demanding
- Marks
- 13
- Topics
- 5
- Answer
- Complete
Within its linear range, a spring follows L=L0+F/k, where L is loaded length, L0 is unloaded length and k is spring constant. Plot the five constructed spring observations with± 0.25 cm vertical bars and negligible horizontal uncertainty for this exercise. Draw your best fit and a labelled worst acceptable line. Show that the selected extreme passes every interval, determine slope/intercept uncertainties, and report k and L0 with units and uncertainty, justifying the reported precision and decimal-place alignment. Explain why half the range of extreme gradients is not the required rule. Submit the graph for assessment. Constructed pairs (F/N, L/cm): (1.00, 3.05),(2.00, 4.90),(3.00, 7.00),(4.00, 9.10),(5.00, 10.95). Each L has absolute uncertainty 0.25 cm.
- (a)
Draw data, bars and two labelled fits.
4 marks - (b)
Check every interval and obtain line parameters.
4 marks - (c)
Report parameter uncertainties and physical results, explaining the precision used.
4 marks - (d)
State the uncertainty rule and qualify the conclusion.
1 mark
Ready to self-mark?Reveal the detailed answer guide
(a)
Draw data, bars and two labelled fits.
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
Accurate points/bars; best and worst lines distinct.
(b)
Check every interval and obtain line parameters.
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
Every bar passed; large fitted-line triangles; reference Mbest2.00, Mworst1.85, Cbest1.00, Cworst1.45.
(c)
Report parameter uncertainties and physical results, explaining the precision used.
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
Delta M=0.15, Delta C=0.45; k=(50 ± 4) N m^-1, L0=(1.00 ± 0.45) cm. Use one or two sf for the uncertainty and align the value's decimal place.
(d)
State the uncertainty rule and qualify the conclusion.
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
Best-minus-worst magnitude, not half extreme range; conclusion applies to tested range and stated uncertainty model.
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.
- Plot all points and bars accurately:2 marks.
- Defensible all-point best fit and clearly distinguished worst line:2 marks.
- Verify all five intervals rather than endpoints only:2 marks.
- Use large triangles on fitted lines and determine slope/intercept:2 marks.
- Delta M=|2.00-1.85|=0.15 and Delta C=|1.00-1.45|=0.45:2 marks.
- k=100/2.00=50 N m^-1 and uncertainty about 4 N m^-1, with the value rounded to the same decimal place as its 1-sf uncertainty; L0=(1.00 ± 0.45) cm uses aligned decimal places with a 2-sf uncertainty: 2 marks for correct physical results and explicit precision justification.
- Explicit best-minus-worst rule and qualified tested-range conclusion:1 mark. Accept consistent values from a defensible independently drawn fit; graph marks require the graph.
Private on this device