Mathematics 9709 · AS & A Level · Representation of data

Representation of data — practice question

A light elastic string, with natural length $3\,\text{m}$ and modulus of elasticity $45\,\text{N}$, has a particle $P$ of mass $0.6\,\text{kg}$ fixed at its mid-point. Its two ends are fastened to points $A$ and $B$ on the line of greatest slope of a smooth plane inclined at $30^\circ$ to the horizontal. The separation $AB$ is $4\,\text{m}$, and $A$ is above $B$.
(i)[3]

Calculate the distance $AP$ for the case when $P$ is in equilibrium on the slope.

(ii)[4]

$P$ is released from rest at the point between $A$ and $B$ where $AP = 2.5\,\text{m}$. Find the maximum speed of $P$.

(iii)[2]

Show that $P$ is at rest when $AP = 1.6\,\text{m}$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Use the tension relation $T = \frac{45e}{1.5}$.

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