Mathematics 9709 · AS & A Level · Energy, work and power

Energy, work and power — practice question

The diagram depicts a wire $ABCD$ made up of a straight section $AB$ with length $5\,\text{m}$ and a section $BCD$ formed as a semicircle of radius $6\,\text{m}$ with centre $O$. The diameter $BD$ of the semicircle lies horizontally, while $AB$ is vertical. A small ring is placed on the wire and can move along it. It is released from rest at $A$. The section $AB$ of the wire is rough, so the ring has constant acceleration of $2.5\,\text{m s}^{-2}$ from $A$ to $B$.
(i)[1]

Show that, on arriving at $B$, the ring's speed is $5\,\text{m s}^{-1}$.

(ii(a))[4]

Determine the ring’s speed at $C$, given that angle $BOC = 30^\circ$.

(ii(b))[2]

Determine the ring’s greatest speed.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Apply $v^2 = u^2 + 2as$, so that $v = \sqrt{2 \times 2.5 \times 5}$

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