AQA AS Level Physics Paper 2, June 2023: Question 3
10 marks · Hard difficulty · Extended Answer
Analyze the principles of moments using a measuring spoon apparatus, including balancing conditions, deriving mass relationships, interpreting a graph of mass against distance, and evaluating scale uncertainty.
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Question text
03 Figure 9 shows a spoon used to measure the mass of food.
The empty spoon balances when a pivot is placed under a point P halfway along the
spoon.
Figure 9
The spoon tilts when food of mass M is placed in the bowl. The spoon is rebalanced
by moving the pivot a distance x to the right of P. The new position of the pivot is
under point Q in Figure 10.
Figure 10
The total length of the spoon is 32.0 cm. The weight of the food acts through a line at
a distance of 4.0 cm from the right-hand edge of the spoon.
03.1 Explain why the spoon in Figure 10 is balanced when the pivot is at Q.
[2 marks]
03.2 The empty spoon has mass m.
Show that, for the arrangement in Figure 10,
m (12.0 − x)
=
M x
*12* [2 marks]
03.3 Figure 11 shows how x varies with M.
Figure 11
Determine, using Figure 11, the weight of the empty spoon.
[3 marks]
14 weight = N
03.4 A scale, in grams, is marked on the spoon between P and the bowl. Figure 11 is
used to calibrate this scale in intervals of 25 g.
M can be measured by balancing the spoon. The value is read from the point of the
scale directly above the pivot.
State and explain how the uncertainty in the value read from the scale changes
as M increases.
[3 marks]
Mark scheme
Show the mark scheme
Question Answers Additional Comments/Guidance Mark AO
03.1 idea that moments are balanced or that there is no resultant Answer must relate to the context e.g. reference to 2 AO1
moment Q or weight of food/spoon
Allow ‘force × distance’ or ‘F × d’ for ‘moment’.
(because)
(overall) centre of mass is now beneath/at Q ‘Anticlockwise moment of weight of spoon about Q
OR = clockwise moment of weight of M about Q’ gains
line of action of (overall) weight is through Q both marks.
03.2 For 1 mark: condone absent g if credible evidence 2 AO2
statement of balanced moments seen e.g. mgx = Mg(16 – 4 –
for ’12 – x’ presented e.g. mx = M(16 – 4 – x)
x), leading to required formula
or mx = M(28 – 16 – x)
OR
condone lack of evidence for ‘12 – x‘ if g is shown
e.g. mgx = Mg(12 – x).
Need to see g and evidence for ‘12 – x‘ for both
marks. Evidence for ‘12 – x‘ need not be in an
expression of a moment.
Allow 9.81 or 9.8 instead of g.
max two from: Allow correct conversion of M to kg and/or x to m
03.3 3 AO1
for read offs or in the substitution. 13
• reads off a pair of values (e.g. 115 g, 5.0 cm)
Expect to see 160 g for mass of spoon.
• substitutes into formula
Allow credit for an algebraic solution to get m:
• multiplies their m by g
m (12 – x)
e.g. when m = M, = =1
M x
So, 12 = 2x, x = 6.0 cm. Reads off M at 6.0 cm to
answer that rounds to 1.5 or 1.6 (N) get 160 g.
03.4 (absolute) uncertainty in M increases as M increases MP1 only awarded supported by some relevant 3 AO3
explanation. Treat ‘percentage’ uncertainty as
neutral.
(because) as M increases:
marks on the scale get closer OR range of values of M for a Allow MP2 and MP3 for quantitative evidence given
fixed range of x increases (or vice versa) using Figure 11 e.g. from 0 g to 25 g, Δx ~ 1.5 cm;
from 175 g to 200 g, Δx ~ 0.4 cm OR calculates
gradients at low and high M.
the gradient (in Figure 11) increases so the scale markings are
unequal owtte
Total 10
How to answer it
Study Guide: Moments, Equilibrium and Calibration
What this question tests
This question assesses the principle of moments, conditions for static equilibrium, algebraic modelling of physical setups, interpreting non-linear graphical data, and analysing uncertainties in graduated scales.
Explaining Equilibrium under a New Pivot Point
✅ Correct Answer
The spoon is balanced because moments are balanced (no resultant moment), and the line of action of the overall weight passes directly through the new pivot Q (or the overall centre of mass is vertically beneath Q ).
💡 Key Knowledge
- First condition for equilibrium: Net force = 0.
- Second condition for equilibrium: Net moment = 0 about any point.
Deriving the Equilibrium Formula
✅ Correct Answer
Equating clockwise and anticlockwise moments about pivot Q :
Anticlockwise moment of spoon = mg × (12.0 - x)
Clockwise moment of food = Mg × x
Equating them: mg(12.0 - x) = Mgx
Rearranging gives: m / M = (12.0 - x) / x
🧠 Exam Technique
Carefully determine distance lever arms relative to point Q using total length and offsets given in the diagram. Total length is 32.0 cm, pivot P is halfway (16.0 cm), and the bowl center is 4.0 cm from the edge.
❌ Common Errors
Forgetting to include acceleration due to gravity ( g ) initially in the moment equations, or making arithmetic slip-ups when expressing the distance of the spoon's centre of mass from Q .
Determining the Weight of the Empty Spoon
📐 Step-by-Step Calculation
- Select a clear coordinate pair from the curve on Figure 11 (e.g., x = 5.0 cm , M = 115 g ). Alternatively, use the algebraic intercept where m = M giving x = 6.0 cm .
- Substitute values into the derived formula:
m / M = (12.0 - 5.0) / 5.0
m / 115 = 7.0 / 5.0 = 1.4
m = 1.4 × 115 = 161 g (approx 160 g). - Convert mass to weight in Newtons:
Weight = mg = 0.160 kg × 9.81 m s⁻² = 1.57 N (rounds to 1.6 N or 1.5 N depending on coordinate choice).
❌ Common Calculation Traps
Failing to convert mass in grams ( g ) to kilograms ( kg ) before multiplying by g (9.81 or 9.8) to find weight in Newtons!
Uncertainty Analysis of the Calibration Scale
✅ Correct Answer
The absolute uncertainty in the value read for M increases as M increases.
💡 Explanation & Reasoning
- The scale divisions on the spoon are fixed/evenly spaced (intervals of 25 g).
- Due to the non-linear (exponential/quadratic-like) curve on Figure 11, equal changes in mass ( ΔM ) correspond to smaller and smaller shifts in pivot position ( Δx ) at higher masses.
- Alternatively, for a fixed scale resolution of x , a constant interval step on the physical scale represents a much wider range of mass values at the upper end of the calibration curve because the gradient increases significantly.
Topics
Physics · Practical skills · 3.4 Mechanics and materials · 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.