(i)[4]
With $v = 2.5,$ determine $x$.
(ii)[5]
Now suppose instead that the kinetic energy of $P$ is twice the elastic potential energy stored in the string. Set up two simultaneous equations and hence determine $x$ and $v$.
Mathematics 9709 · AS & A Level · Probability
Probability — practice question
One end of a light elastic string of natural length $0.4\,\text{m}$ and modulus of elasticity $8\,\text{N}$ is fixed at a point $O$ on a smooth horizontal plane. Its other end is joined to a particle $P$ of mass $0.2\,\text{kg}$, which travels round the plane in a circular path centred at $O.$ The speed of $P$ is $v\,\text{m s}^{-1}$ and the string has extension $x\,\text{m}.$
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This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies Newton’s Second Law towards the centre: $T=0.2\times2.5^{2}/(0.4+e)$.” …
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