AQA AS Level Physics Paper 2, June 2022: Question 1
10 marks · Medium difficulty · Practical Techniques & Data Analysis
Analyze a free-fall experiment to determine the acceleration due to gravity, including error bars, maximum and minimum gradients, percentage uncertainty, and the effect of a systematic delay.
Practise this questionQuestion
Question text
01 Figure 1 shows apparatus used to determine the acceleration g due to gravity by
a free-fall method.
Figure 1
When the switch is opened a timer starts and a steel ball is released from rest.
The ball falls vertically onto an impact switch and this stops the timer.
The timer displays the time t for the ball to fall through the vertical distance4 s shown
in Figure 1.
A student obtains values of t for different values of s.
The student plots the graph of 2s against t2 shown in Figure 2.
Figure 2
01.1 The student has used an absolute uncertainty in s to draw the vertical error bars
in Figure 2.
Deduce the student’s absolute uncertainty in s.
[1 mark]
absolute uncertainty in s = m
01.2 Determine
• the maximum gradient Gmax of a straight line that passes through all the error bars
• the minimum gradient Gmin of a straight line that passes through all the error bars.
[3 marks]
Gmax =
6 Gmin =
01.3 It can be shown that 2s = gt2.
Determine a value for g using Gmax and Gmin.
[2 marks]
g = m s−2
01.4 Determine the percentage uncertainty in your value for g.
[2 marks]
percentage uncertainty = %
A fault develops in the apparatus.
When the switch is opened there is now a 30 ms delay before the ball is released.
01.5 State the type of error produced by this fault.
[1 mark]
01.6 A graph of 2s against t2 is produced using results from the faulty apparatus.
Describe how this graph is different from the graph in Figure 2.
[1 mark]
Mark scheme
Show the mark scheme
Question Answers Additional Comments/Guidance Mark AO
01.1 (±) 0.04 (m) Correct answer only 1 AO3
– SICS – – JUNE 2022
1 requires at least one line to be well-drawn i.e.
01.2 Gmax line ruled through bottom of first error bar and through top 3 3 ×
thin, single, continuous
of fifth error bar OR Gmin line ruled through top of first error bar AO2
For 2 expect a 3 sf value. Accept 2 sf value only if
and through bottom of sixth error bar 1 it comes from expected range. Condone 4 sf value.
Gmax between 10.7 and 10.9 2 For 3 accept 2 or 3 sf values only
For at least one Δt2 step 0.08 (s2) (i.e. half
G between 8.7 and 8.9 23
min 3
width of grid)
Ignore any unit given with Gmax or Gmin
– SICS – – JUNE 2022
01.3 Gmax + Gmin If no other mark given, allow 1 mark for a value of 2 2 ×
uses g = with their values from 01.2 1 −2
29.7 (m s ) from a well-drawn best-fit line. AO3
evaluates mean of their Gmax and Gmin to 2 sf 2 Give no credit for an unsupported answer.
Treat “10” as a 2 sf answer.
– SICS – – JUNE 2022
01.4 absolute uncertainty in g 1 Mark each point independently. If no other mark 2 1 x AO3
given, allow 1 mark for a percentage uncertainty (1 1 x AO2
or 2 sf) based on the full range (rather than half the
range).
For 1 must use their Gmax AND/OR their Gmin e.g.
G - G OR Gmax – their g
g = max min
OR their g – Gmin
May be seen in working for percentage uncertainty
e.g.
Gmax - g OR g - Gmin
100 100
g g
OR Gmax - Gmin
Gmax + Gmin
their g
8 percentage uncertainty in g = 100 2
their g For 2 allow 1 or 2 sf
– SICS – – JUNE 2022
01.5 systematic (error) 'zero error' is neutral 1 AO1
01.6 points/line displaced to right owtte Must refer to a property of the graph; comments 1 AO3
about error bars are neutral; ignore (new)
OR calculated values of t2.
Accept ‘gradient is decreased’ / ‘graph (or line)
line moves down becomes a curve of decreasing gradient’ owtte.
No credit for ‘points move down’ / ‘t2 values are
OR increased’.
(vertical) intercept is decreased / now has negative intercept Allow answers in form of their own diagram or on
Figure 2.
Total 10
How to answer it
Determining Acceleration Due to Gravity ($g$) from Free-Fall Data
This question assesses your practical physics and data analysis skills based on determining the acceleration due to gravity ($g$) using a free-fall drop apparatus. Key skills include interpreting error bars, calculating maximum and minimum gradients (uncertainty bounds), determining physical constants from graphical equations, finding percentage uncertainties, and distinguishing between types of experimental errors (random vs. systematic).
Part 01.1: Deducing Absolute Uncertainty in $s$
✅ Correct Answer
± 0.04 m
🧠 Exam Technique
Examine the vertical error bars on Figure 2. The total length of an error bar represents twice the absolute uncertainty ( 2 × Δs ). Measure the total height of a bar using the grid scale and divide by 2, or inspect the span from the plotted data point to either extreme end.
❌ Common Errors
Students often quote the full length of the error bar instead of halving it to find the ± absolute uncertainty, or forget to include the units ( m ).
Part 01.2: Determining Maximum and Minimum Gradients
✅ Correct Answers
Gmax: Between 10.7 and 10.9
Gmin: Between 8.7 and 8.9
🧠 Exam Technique
Use a sharp pencil and a transparent ruler. Draw a steepest viable line ( Gmax ) passing from the bottom of the first error bar to the top of the last error bar. Draw the shallowest viable line ( Gmin ) from the top of the first error bar to the bottom of the last error bar. Ensure lines pass through all error bars.
❌ Common Errors
Drawing "best-fit" lines of the wrong steepness that miss extreme error bars, or failing to make the gradient triangle large enough (Δt² step must span at least half the width of the grid).
Part 01.3: Calculating $g$ from Gradients
✅ Correct Answer
A value derived from g = (Gmax + Gmin) / 2 , yielding around 9.7 to 9.9 m s⁻² (depending on drawn lines).
📐 Calculation Steps
- Step 1: Relate the equation 2s = gt² to the linear equation y = mx , where y = 2s , x = t² , and gradient m = g . Thus, gradient equals $g$.
- Step 2: Find the mean of your extreme gradients: g = (Gmax + Gmin) / 2 .
- Step 3: Round your final answer to 2 or 3 significant figures and attach standard units ( m s⁻² ).
Part 01.4: Percentage Uncertainty in $g$
✅ Correct Answer
Calculated percentage uncertainty using (Δg / g) × 100 (typically between 5% and 11% based on drawn lines).
💡 Key Knowledge
The uncertainty in a gradient-derived value is found using half the range of the extreme gradients: Δg = (Gmax - Gmin) / 2 .
❌ Common Errors
Forgetting to multiply the final ratio by 100 to convert into a percentage, or using the entire range instead of half-range when calculating absolute uncertainty in $g$.
Part 01.5: Identifying the Type of Experimental Error
✅ Correct Answer
Systematic error (Note: "zero error" is accepted as neutral/synonymous here).
💡 Key Knowledge
A constant time delay occurring every time the switch is opened introduces a consistent offset across all measurements rather than random scatter. This shifts all results systematically.
Part 01.6: Describing Graph Alterations from Faults
✅ Correct Answers (Any valid descriptor)
- Points or line are displaced to the right.
- The line moves down.
- The vertical intercept is decreased / now has a negative intercept.
🧠 Exam Technique
Think about the equation 2s = g(t + tdelay)² or how a time delay affects measured $t$ for a given distance $s$. Because recorded times are systematically too large for every distance, plotted points shift horizontally or vertically in a predictable direction. Always anchor your description to a property of the graph (e.g., intercept or shift).
❌ Common Errors
Vague statements like "points move down" without specifying graph axes/intercept properties, or discussing error bar sizes (which are unaffected by a systematic time shift).
Topics
Physics · Practical skills · Required Practicals · 3.1 Measurements and their errors · 3.4 Mechanics and materials · Uncertainty and evaluation · Data analysis · AS practicals (1–6)
Question and mark scheme from the AQA AS Level Physics examination, Paper 2, June 2022. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.