AQA M2 2015 June — Question 2 4 marks

Exam BoardAQA
ModuleM2 (Mechanics 2)
Year2015
SessionJune
Marks4
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Mark schemeDownload PDF ↗
TopicCentre of Mass 1
TypeParticles at coordinate positions
DifficultyModerate -0.8 This is a straightforward centre of mass calculation requiring only the application of the standard formula (sum of moments = total mass × distance to COM). With clearly defined masses and positions, it involves basic algebraic manipulation to solve for one unknown distance. The 4-mark allocation reflects routine working rather than conceptual challenge.
Spec6.04c Composite bodies: centre of mass
2 A uniform rod \(A B\), of mass 4 kg and length 6 metres, has three masses attached to it. A 3 kg mass is attached at the end \(A\) and a 5 kg mass is attached at the end \(B\). An 8 kg mass is attached at a point \(C\) on the rod. Find the distance \(A C\) if the centre of mass of the system is 4.3 m from point \(A\).
[0pt] [4 marks]
Question 2:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
Total mass \(= 3 + 4 + 5 + 8 = 20\) kgB1 Correct total mass
Taking moments about \(A\): \(20 \times 4.3 = 3\times 0 + 4\times 3 + 8\times AC + 5\times 6\)M1 A1 Moments equation; rod centre of mass at 3 m from A
\(86 = 0 + 12 + 8\cdot AC + 30\)
\(8\cdot AC = 86 - 42 = 44\)DM1 Solve for \(AC\)
\(AC = 5.5\) mA1 
# Question 2:

| Answer/Working | Marks | Guidance |
|---|---|---|
| Total mass $= 3 + 4 + 5 + 8 = 20$ kg | B1 | Correct total mass |
| Taking moments about $A$: $20 \times 4.3 = 3\times 0 + 4\times 3 + 8\times AC + 5\times 6$ | M1 A1 | Moments equation; rod centre of mass at 3 m from A |
| $86 = 0 + 12 + 8\cdot AC + 30$ | | |
| $8\cdot AC = 86 - 42 = 44$ | DM1 | Solve for $AC$ |
| $AC = 5.5$ m | A1 | |

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2 A uniform rod $A B$, of mass 4 kg and length 6 metres, has three masses attached to it. A 3 kg mass is attached at the end $A$ and a 5 kg mass is attached at the end $B$. An 8 kg mass is attached at a point $C$ on the rod.

Find the distance $A C$ if the centre of mass of the system is 4.3 m from point $A$.\\[0pt]
[4 marks]

\hfill \mbox{\textit{AQA M2 2015 Q2 [4]}}
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Q1 10 Q2 4 Q3 9 Q4 10 Q5 6 Q6 9 Q7 9 Q8 10 Q9 8