A-LevelMathematicsMechanics9709/52 · Oct/Nov 2018 · Q58 Marks

A particle P of mass 0.7 kg is attached to a fixed point O by a light elastic string of natural length 0.6 m and modulus of elasticity 15 N. The particle P is projected vertically downwards from the point A, 0.8 m vertically below O. The initial speed of P is 2 m s⁻¹.

(i)Find the distance below A of the point at which P comes to instantaneous rest.[4]
(ii)Find the greatest speed of P in the motion.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

[B1] 15(0.2 + x)²/(2 × 0.6) or 15 × 0.2²/(2 × 0.6)
[M1] Set up a 4 term energy equation
[A1] 15(0.2 + x)²/(2 × 0.6) = 15 × 0.2²/(2 × 0.6) + 0.7gx + (0.7 × 2²)/2
[A1] x = 0.424 m
[M1] Use T = λx/L
[A1] 0.7g = 15e/0.6
[A1] e = 0.28 m
[M1] Set up a 5 term energy equation
[A1] (0.7 × 2²)/2 + 0.7g(0.28 – 0.2) + (15 × 0.2²)/(2 × 0.6) = (0.7 × v²)/2 + (15 × 0.28²)/(2 × 0.6)
[A1] v = 2.06 m s⁻¹

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Topic: Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 8 marks.
Source: A-Level Mathematics, Oct/Nov 2018 Paper 5 Variant 2, question 5.

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