Cambridge International AS & A Level · P5 · structured
Construct and interpret a common-log fit
A2 practical 6: determine a power law with dimensionless logarithms · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- demanding
- Marks
- 10
- Topics
- 4
- Answer
- Complete
A pendulum is modelled by T/s=A(L/m)^n, where A is a dimensionless numerical prefactor and n is the exponent. Using the constructed pendulum table, complete both log columns and draw lg(T/s) against lg(L/m). Obtain n and A from your fitted line. Explain the units of both axes and justify logarithmic decimal places for 0.600 m. State which notation is explicitly used for common logs in the2028-2030 syllabus. Constructed illustrative data (not observed experimental evidence). Columns: L / m (constructed) | T / s (constructed) | lg(L/m) | lg(T/s). Rows: 0.400 | 1.27 | -0.3979 | 0.1038; 0.500 | 1.42 | calculate | calculate; 0.600 | 1.55 | calculate | calculate; 0.700 | 1.68 | calculate | calculate; 0.800 | 1.79 | calculate | calculate; 1.00 | 2.01 | calculate | calculate.
- (a)
Complete the transformed table and draw the graph.
6 marks - (b)
Find exponent and prefactor.
2 marks - (c)
Explain units, precision and edition notation.
2 marks
Ready to self-mark?Reveal the detailed answer guide
(a)
Complete the transformed table and draw the graph.
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
Six correct logarithmic pairs and a correctly scaled all-point best fit.
(b)
Find exponent and prefactor.
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
n approximately 0.500; A=10^intercept approximately 2.01.
(c)
Explain units, precision and edition notation.
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
Dimensionless quantity/unit ratios; 3 or4 decimal places for 3 sf raw values; lg explicitly means common logarithm in 2028-2030.
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.
- Correct transformed table with quantity/unit ratios and suitable decimal places:3 marks.
- Candidate graph follows P3 layout/point conventions and fits all transformed points:3 marks.
- Gradient about 0.500 and inverse-log intercept A about 2.01:2 marks.
- Dimensionless ratios/axes and dp-versus -sf explanation:1 mark.
- lg explicitly identifies base 10 in the future edition:1 mark. Assess the drawing rather than awarding graph marks solely for the reference numbers.
Private on this device