Mathematics 9709 · AS & A Level · Probability

Probability — practice question

The diagram depicts a smooth, narrow tube bent into a fixed vertical circle with centre $O$ and radius $0.9\,\text{m}$. One end of a light elastic string, whose modulus of elasticity is $8\,\text{N}$ and natural length is $1.2\,\text{m}$, is fastened to the top point $A$ on the inside of the tube. The opposite end is attached to a particle $P$ of mass $0.2\,\text{kg}$. The particle is released from rest at the lowest point on the inside of the tube. Using energy, calculate
(i)[4]

the speed of $P$ when it is at the same horizontal height as $O$.

(ii)[3]

the speed of $P$ at the instant when the string turns slack.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Writes the elastic energy as $EE = 8(0.9\pi-1.2)^2/(2\times1.2)

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