A-LevelMathematicsMechanics9709/51 · Oct/Nov 2018 · Q37 Marks
A particle P of mass 0.4 kg is attached to a fixed point O by a light elastic string of natural length 0.5 m and modulus of elasticity 20 N. The particle P is released from rest at O.
- (i)Find the greatest speed of P in the subsequent motion.[4]
- (ii)Find the distance below O of the point at which P comes to instantaneous rest.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.
- [M1] 20e/0.5 = 0.4g (Use T = λx/L)
- [A1] e = 0.1
- [M1] 0.4v²/2 = 0.4g(0.5 + 0.1) – 20×0.1²/(2×0.5) (Attempt to set up a 3 term energy equation)
- [A1] v = √11 = 3.32
- [M1] 0.4g(5 + x) = 20x²/(2×0.5) (Attempt to set up a 2 term energy equation)
- [M1] [0 = 20x² − 4x − 2] [ x = 0.432] (Attempt to solve a 3 term quadratic equation)
- [A1] Distance below O = (0.5 + 0.432) = 0.932 m
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