Mathematics 9709 · AS & A Level · Newton's laws of motion

Newton's laws of motion — practice question

The diagram gives the vertical cross-section $OAB$ of a slide. The straight section $AB$ is tangent to the curve $OA$ at $A$. The line $AB$ makes an angle $\alpha$ with the horizontal, where $\sin \alpha = 0.28$. Point $O$ is $10\,\text{m}$ above $B$, and $AB$ is $10\,\text{m}$ long (see diagram). The section of the slide containing the curve $OA$ is smooth, whereas the section containing $AB$ is rough. A particle $P$ of mass $2\,\text{kg}$ is released from rest at $O$ and slides down the slide.
(i)[3]

Find the speed of $P$ at $A$.

(ii)[3]

Find the acceleration of $P$ as it travels from $A$ to $B$, given that the coefficient of friction between $P$ and the section of the slide containing $AB$ is $\frac{1}{12}$.

(iii)[2]

Find the speed of $P$ as it reaches $B$.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Loss of PE $= 2g(10 - 10 \times 0.28)$

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