Cambridge International AS & A Level · P5 · structured
Compute and draw two-axis intervals
A2 practical 8: transform the uncertainty as well as the value · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- demanding
- Marks
- 10
- Topics
- 4
- Answer
- Complete
Constructed readings are L=(0.500 ± 0.005) m and T=(1.42 ± 0.02) s. Calculate central values and endpoint bounds for lg(L/m) and lg(T/s); tabulate them beside the originals and plot the point with both uncertainty directions. Also find the fractional and percentage uncertainty of L. In a separate measurement, convert a 3.0% uncertainty of 2.00 V to an absolute uncertainty and write the voltage with its uncertainty. Finally state why ln(U/V) cannot be used if U=(0.02 ± 0.03) V.
- (a)
Calculate and tabulate log intervals.
5 marks - (b)
Draw two-axis error bars.
2 marks - (c)
Convert between absolute, fractional and percentage uncertainty, and assess the logarithm domain.
3 marks
Ready to self-mark?Reveal the detailed answer guide
(a)
Calculate and tabulate log intervals.
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
lg(L/m) approximately -0.3010 with[-0.3054,-0.2967]; lg(T/s) approximately 0.1523 with[0.1461, 0.1584]; preserve originals.
(b)
Draw two-axis error bars.
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
Correct horizontal L-log interval and vertical T-log interval at the central transformed point.
(c)
Convert between absolute, fractional and percentage uncertainty, and assess the logarithm domain.
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
L: fractional 0.010 and percentage 1.0%; the separate 2.00 V reading with 3.0% uncertainty is (2.00 ± 0.06) V. The stated U interval includes nonpositive values, so its logarithmic interval is undefined.
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.
- Original measurements and all uncertainty entries preserved in one table:1 mark.
- Correct central and endpoint log coordinates for both variables:4 marks.
- Plot both horizontal and vertical intervals at the same point:2 marks; inspect the drawing.
- Delta L/L=0.005/0.500=0.010 and percentage=1.0%: 1 mark. Separate voltage uncertainty=2.00x0.030=0.060 V, reported (2.00 ± 0.06) V: 1 mark.
- Identify U lower bound -0.01 V and invalid nonpositive log domain:1 mark.
Private on this device