AQA AS Level Physics Paper 2, June 2023: Question 2
10 marks · Medium difficulty · Practical Techniques & Data Analysis
Investigate projectile motion and rolling motion of a ball using tracks, rulers, and graphs to determine horizontal distance, height, gradient, and minimum time.
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Question text
02 Figure 4 shows an arrangement used to investigate projectile motion of a ball.
Figure 4
The ball is placed on the track at the release point.
The ball is released from rest from a vertical distance h above the table.
When the ball reaches the end of the track, it is a vertical distance H above the
horizontal floor.
The ball leaves the track horizontally and lands on the floor at a horizontal distance x
from the end of the track.
02.1 To measure x a student must locate a point P on the floor vertically below the end
of the track.
Describe a procedure to locate P.
You may add detail to Figure 4 to illustrate your answer.
[1 mark]
02.2 A ruler, graduated in mm, is used to determine x.
The student places the ruler on the floor with the zero graduation aligned with P.
The student determines x when the ball is released six times at a particular value of h.
He makes marks on the floor where the ball lands.
Figure 5 shows circles that indicate these marks.
Figure 5
Determine x for this value of h.
[3 marks]
9 x = mm
02.3 The student obtains values of x corresponding to other values of h.
Figure 6 shows his results.
Figure 6
x2 20
It can be shown that = h
H 7
Determine H.
[3 marks]
H = m
In a different arrangement, the ball is released from rest and then continues to roll at a
constant velocity across a horizontal table, as shown in Figure 7.
Figure 7
The bottom of the track is fixed to the table at point Q.
The angle between the straight part of the track and the table is α.
A marker is placed at R, a point midway between Q and the edge of the table.
The student uses a stopwatch to measure the time t for the ball to roll from Q to R.
02.4 Explain why increasing the distance QR will reduce the percentage uncertainty in t.
[1 mark]
02.5 Figure 8 shows values of t for different values of α.
Figure 8
At a particular value of α the ball rolls from Q to R at its maximum velocity.
Explain how the student should use Figure 8 to determine this value of α.
Go on to suggest what further readings should be taken to reduce the uncertainty in
this value of α.
[2 marks]
END OF SECTION A
Section B
Answer all questions in this section.
Mark scheme
Show the mark scheme
Question Answers Additional Comments/Guidance Mark AO
02.1 identifies appropriate equipment and makes a relevant Use of plumb line (accept ‘mass / weight on string’) 1 AO1
comment about how it is used OR
use of a metre ruler made vertical with a set-square
in contact with the floor
OR
using a (long) spirit level.
Comments that the string of the plumb line / edge of
metre ruler / edge of spirit level should be in contact
with the projecting end of the track.
Give credit for suitable annotation to Figure 4
02.2 rejects anomalous mark (at 607) 1 3 AO1
For 2 expect to see readings of 581, 583, 583,
calculates mean from readings of marks 2 586, 588 (and 607) for centres of circles. Allow
readings from left edge or from right edge, but not a
mix. Reject readings given to a precision greater
than 0.5 mm. Allow an arithmetic error. Expect to
see 2921 or 3528.
For 3 allow 588 (mm)
584 (mm) 3
For 3 3 sf answer only.
02.3 ruled best-fit line passing below 3rd plot and above 2nd and 4th Withhold if line is poorly marked. 3 AO1
plots 1
For 2 condone one read-off error. Gradient from h
finds gradient and multiplies by 7 2 step 0.10 m. Expect gradient in range 2.20 –
20 2.37. Allow any appropriate use of 7 .
h / m x2 / m2
0.12 0.285
0.16 0.360
0.20 0.470
0.24 0.535
0.28 0.655
For 3 2 sf only.
H in result in range 0.78 to 0.83 3
Allow 1 2×3 = 2 MAX for H in range obtained
using co-ordinates of a point on the line.
Allow 1×2×3 = 1 MAX for H in range obtained
using a plotted point if no best-fit line is drawn.
02.4 idea that absolute uncertainty is the same but value of t is Allow sample calculation or reference to equation. 1 AO1
larger Condone ‘uncertainty’ for ‘absolute uncertainty’.
02.5 draw a best-fit curve/line and read-off (α) where value of t is a For 1 ‘draw a line’ is not enough. 2 AO2
minimum 1 Accept read off at ‘bottom of curve’ / ‘where the
gradient is zero’ / ‘at the turning point’.
Annotations to Figure 8 can earn MP1; any line of
best-fit drawn does not need to be neat.
take more readings around α when t has minimum value, or
words to that effect (owtte) 2 For reject bland ‘repeat readings’.
Total 10
How to answer it
Projectile Motion & Experimental Physics Study Guide
What this question tests
This exam question tests your practical skills, graphical analysis, and understanding of projectile motion kinematics. You will be assessed on experimental design (plumb lines), handling experimental anomalies, calculating physical constants from graphical gradients, understanding fractional/percentage uncertainties, and optimising data collection techniques.
Locating Point P Vertically Below the Track
✅ Correct Answer
Use a plumb line (mass/weight on a string) suspended from the projecting end of the track, or a vertical metre rule with a set-square/spirit level, ensuring it touches the floor directly below the track edge where point P is located.
💡 Key Knowledge
To align a point precisely in the vertical axis relative to an elevated object, gravity must be used as a reference line. A plumb line relies entirely on the pull of gravity to define a true vertical line.
❌ Common Errors
Guessing visually by eye from a distance, or holding a standard ruler loosely without checking if it is perpendicular to the floor.
Determining Horizontal Distance x
✅ Correct Answer
Reject the anomalous reading of 607 mm . Calculate the mean of the remaining valid readings (581, 583, 583, 586, 588 mm).
Final Answer: 584 mm
📐 Step-by-Step Calculation
- Identify and discard the outlier: 607 mm is significantly higher than the clustered group around 580–590 mm.
- Sum the remaining values: 581 + 583 + 583 + 586 + 588 = 2921 mm .
- Divide by the number of valid trials (5): 2921 / 5 = 584.2 mm .
- Round to appropriate significant figures matching the instrument precision: 584 mm .
❌ Common Errors
Failing to remove the anomalous point before calculating the mean, or mixing up measurements taken from the left edge versus the right edge of the landing marks.
Determining H from Graphical Analysis
✅ Correct Answer
Draw a best-fit line passing correctly through the data points, find its gradient, and use the given relation to calculate H .
Final Answer Range: H = 0.78 to 0.83 m
📐 Step-by-Step Calculation
- From the given equation x² / H = (20/7) h , rearrange to get x² = (20 H / 7) h .
- Recognise that the gradient of the graph of x² against h equals 20 H / 7 .
- Calculate gradient from your line: e.g., gradient ≈ 2.28 to 2.37 .
- Rearrange for H: H = 7 × gradient / 20 .
- Evaluate: 7 × 2.30 / 20 = 0.805 m (falling within the accepted 0.78 to 0.83 range).
🧠 Exam Technique
Ensure your line is a true line of best fit with a balanced spread of points above and below it. When calculating the gradient, choose large points far apart on your line rather than using small data coordinate triangles.
Reducing Percentage Uncertainty in t
✅ Correct Answer
Increasing the distance QR increases the time value t while keeping the absolute uncertainty (human reaction time error of the stopwatch) constant, which decreases the overall percentage uncertainty.
💡 Key Knowledge
Percentage uncertainty is calculated as: (Absolute Uncertainty / Measured Value) × 100% . Making the measured quantity larger reduces its relative fractional impact.
Finding Maximum Velocity via Minimum Time
✅ Correct Answer
- Draw a smooth best-fit curve on Figure 8 and read off the angle α corresponding to the lowest point (minimum value) of t .
- Take more readings of t at smaller angle increments around this turning point to pinpoint the minimum more accurately.
🧠 Exam Technique
Examiners heavily penalise vague answers like "repeat readings". You must specify where and why you are taking additional readings—specifically around the turning point (minimum value) where the curve is flattest.
❌ Common Errors
Treating the graph as a straight-line relationship and attempting to draw a straight line of best fit instead of a smooth curve, or failing to explain how extra data refines the minimum coordinate.
Topics
Physics · Practical skills · 3.4 Mechanics and materials · Experimental design · Data analysis · Uncertainty and evaluation
Question and mark scheme from the AQA AS Level Physics examination, Paper 2, June 2023. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.