A-LevelMathematicsMechanics9709/42 · May/June 2023 · Q24 Marks

Two particles A and B, of masses 3.2kg and 2.4kg respectively, lie on a smooth horizontal table. A moves towards B with a speed of vms¯¹ and collides with B, which is moving towards A with a speed of 6 ms¯¹. In the collision the two particles come to rest.

Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

2(a)
[3.2v+2.4×(-6)]=0
[M1] Attempt at conservation of momentum; 2 non-zero terms; allow sign errors.
v = 4.5
[A1] M1A0 for use of mgv. v = -4.5 is A0.
2(b)
KE =±½×3.2×(their 4.5)² OR ±½×2.4×6²
[M1] Attempt at either KE term, using their v. Do not allow ½×3.2×(their 4.5±6)², or ½×2.4×(their 4.5±6)², or ½×(3.2+2.4)×(their 4.5±6)², or ½×3.2×(their 4.5-0)², or ½×2.4×(6-0)².
KEloss = 75.6 J
[A1] Allow -75.6. Note ½×(3.2+2.4)×6² or ½×(3.2+2.4)×(their 4.5)² is M1A0.

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Topic: Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source: A-Level Mathematics, May/June 2023 Paper 4 Variant 2, question 2.

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