AQA AS Level Physics Paper 1, June 2025: Question 4
9 marks · Medium difficulty · Short Answer
State the principle of moments, calculate an unknown reaction force on a loaded trolley in equilibrium, and analyze how the forces change when tilted on a step.
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Question text
04.1 State the principle of moments.
[2 marks]
04.2 Figure 4 shows a trolley at rest on a horizontal surface. A load is fixed to the base of
the trolley.
Figure 4
Assume that the forces in Figure 4 are coplanar.
The distance between the centre of the front wheels and the centre of the
back wheels is 85 cm.
The total reaction force at the front wheels is 97 N and the total reaction force at the
back wheels is R.
The trolley and load have a total weight W.
The perpendicular distance between the lines of action of the forces W and R
is 12 cm.
Calculate R.
[3 marks]
R = N
Figure 5 shows the trolley after its back wheels have been lifted onto a step.
The trolley is stationary.
Figure 5
04.3 When the back wheels are on the step, the moment of W about the centre of the
back wheels is less than that in Figure 4.
Explain why.
[1 mark]
04.4 Deduce how the magnitude of R1 in Figure 5 compares with the value of 97 N
in Figure 4.
[3 marks]
Mark scheme
Show the mark scheme
Question Answers Additional Comments/Guidance Mark AO
04.1 The clockwise moment(s) equals the anticlockwise moment(s) 2 AO1
Includes all the following
• (system must be) in equilibrium
• moments about the same point
• sum of the clockwise moments equals the sum of the
anticlockwise moments.
Use of principle of moments 1
04.2 Expect to see one of the following 3 1 × AO1
• 97 × 73 = R ×12 1 2 2 × AO2
• W × 73 = R × 85 1 2
• 97 × 85 = W × 12 1
Condone one error in MP1
• 97 × a distance = R × 12
• 97 × a distance = W × 12
• W × a distance= R × 85
• 97 × 85 = W × a distance
determines perpendicular distance between 97 N and weight’s MP2 (option 1)
line of action = 85 – 12 = 73 (cm) Accept:
18 • 73 (cm) seen in Figure 4
OR • 73 × 97 seen
• 73 × W seen
R = W – 97 2 MP2 (option 2)
Accept W = R + 97
(R = ) 590 (N) 3 Calculator value 590.0833333
04.3 (The moment of the weight about the back wheel decreases Condone: idea that perpendicular component 1 AO1
because) perpendicular distance between (line of action of) of weight has decreased.
weight and (centre of back) wheel decreases
04.4 idea that (still in rotational equilibrium therefore) clockwise Must state that magnitude remains the same 3 1 × AO2
moment (about back wheel) equals anticlockwise moment for maximum of 3 marks.
2 × AO3
(about the back wheel)
MP1: Accept that R1’s moment must decrease
OR because weight’s moment decreases.
Idea that W = R1 + R2
the perpendicular distance between (the line of action of) R1
and the point (around which moments are taken) decreases MP2:
Expect to see point declared as back wheel.
perpendicular distances (for W and R ) decrease by the same MP3:
Allow perpendicular distance for R1 and R2
factor and therefore the magnitudes are the same. decrease by the same amount where go on to
state that sum of these equals W
Total 9
How to answer it
Moments, Equilibrium & Tilting Forces on a Trolley
- Principle of Moments: Precise formal definition including the necessary equilibrium conditions.
- Rotational Equilibrium Calculations: Choosing a smart pivot point, calculating lever arms (perpendicular distances), and solving for unknown contact forces.
- Geometry of Tilted Systems: Understanding how tilting alters lines of action and perpendicular lever arms.
- Deductive Reasoning: Analyzing how scaling of perpendicular distances preserves force magnitudes under rotational equilibrium.
State the principle of moments
Foundational Definition
✅ Model Answer
For a system in equilibrium, the sum of the clockwise moments about any point is equal to the sum of the anticlockwise moments about the same point.
• [1 mark]: Clockwise moment(s) equal anticlockwise moment(s).
• [1 mark]: Must include all key conditions: system is in equilibrium, moments taken about the same point, and the word sum (or total).
❌ Common Errors & Pitfalls
- Forgetting to state "in equilibrium" (vital condition).
- Omitting the word "sum" or "total" (many forces can contribute to either side).
- Failing to mention that moments must be taken "about the same pivot/point".
- Confusing the principle of moments with Newton's First or Third Law.
Calculate the reaction force R at the back wheels
Equilibrium on a Horizontal Surface
📐 Step-by-Step Calculation
Pivot choice: Take moments about the line of action of weight W to directly relate the front reaction (97 N) and rear reaction (R).
- Find perpendicular distance from front wheel to W:
Total span = 85 cm.
Distance from W to back wheel = 12 cm.
Distance from front wheel to W = 85 cm − 12 cm = 73 cm (or 0.73 m). - Apply the principle of moments about the centre of mass (W):
Clockwise moment = Anticlockwise moment
97 N × 73 cm = R × 12 cm - Solve for R:
R = (97 × 73) / 12 = 7081 / 12 = 590.08 N
R = 590 N (to 2 or 3 s.f.)
🧠 Exam Technique & Insight
- Unit conversion shortcut: Because distances appear on both sides of the moment equation ( force × distance = force × distance ), converting cm to m is optional as long as the same unit is used throughout.
- Sensible check: The load W is located much closer to the back wheels (12 cm) than the front wheels (73 cm). Therefore, the rear reaction R must be significantly larger than 97 N. 590 N makes intuitive sense.
- Significant figures: Data in the question is given to 2 s.f. (97 N, 85 cm, 12 cm). An answer of 590 N is ideal.
Explain why the moment of W about the back wheels is less in Figure 5
Effect of Tilting on Lever Arm
✅ Model Answer
The perpendicular distance from the centre of the back wheel to the vertical line of action of the weight W has decreased (due to the tilt angle, dnew = 12 × cos θ ).
💡 Key Knowledge
- Moment is defined strictly as: Moment = Force × perpendicular distance to pivot .
- The weight W always acts purely vertically downwards due to gravity.
- When the trolley is tilted through angle θ, the perpendicular lever arm from the back wheel axis reduces from d to d cos θ . Because cos θ < 1 for any non-zero angle, the moment decreases.
Deduce how the magnitude of R₁ compares with the value of 97 N
Rotational Equilibrium Under Tilt
✅ Model Answer
- Equilibrium condition: The trolley is stationary (rotational equilibrium), so the total clockwise moment about the back wheel equals the total anticlockwise moment about the back wheel ( R₁ × d₁ = W × dW ).
- Geometric effect: Tilting causes the perpendicular distance from the back wheel to the line of action of R₁ to decrease by a factor of cos θ , and the perpendicular distance to the line of action of W also decreases by the exact same factor ( cos θ ).
- Conclusion: Because both perpendicular distances decrease in the same proportion, the ratio remains unchanged; therefore, the magnitude of R₁ remains the same (97 N).
• MP1: Equating moments about back wheel OR stating R₁ 's moment must decrease because weight's moment decreases.
• MP2: Stating that the perpendicular distance for R₁ decreases.
• MP3: Both perpendicular distances decrease by the same factor, so R₁ = 97 N (magnitude remains the same).
❌ Common Misconceptions
- The "obvious guess" trap: Many students guess that because the back wheel is raised, more weight shifts to the front, so R₁ increases. This is false! R₁ acts vertically and the wheels remain parallel along the trolley frame.
- Failing to state the pivot: Always declare the pivot explicitly (e.g., "taking moments about the back wheel").
- Missing the conclusion: The question asks you to deduce how the magnitude compares—you must explicitly state that it remains equal to 97 N to access full marks.
Topics
Physics · 3.4 Mechanics and materials
Question and mark scheme from the AQA AS Level Physics examination, Paper 1, June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.