| Exam Board | OCR |
|---|---|
| Module | FM1 AS (Further Mechanics 1 AS) |
| Year | 2021 |
| Session | June |
| Marks | 6 |
| Topic | Circular Motion 2 |
| Type | Vertical circle: complete revolution conditions |
| Difficulty | Standard +0.3 This is a standard vertical circle energy conservation problem with two straightforward parts: (a) applying conservation of energy at a given angle, and (b) checking if the bead reaches the top. Both require routine application of energy principles with no novel insight, making it slightly easier than average for Further Maths students who are expected to handle these mechanics problems fluently. |
| Spec | 6.02i Conservation of energy: mechanical energy principle6.05d Variable speed circles: energy methods |
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\includegraphics[max width=\textwidth, alt={}, center]{d6a0d7a6-4166-4c26-a461-39b2414c0412-02_494_390_251_255}
A smooth wire is shaped into a circle of radius 2.5 m which is fixed in a vertical plane with its centre at a point $O$. A small bead $B$ is threaded onto the wire. $B$ is held with $O B$ vertical and is then projected horizontally with an initial speed of $8.4 \mathrm {~ms} ^ { - 1 }$ (see diagram).
\begin{enumerate}[label=(\alph*)]
\item Find the speed of $B$ at the instant when $O B$ makes an angle of 0.8 radians with the downward vertical through $O$.
\item Determine whether $B$ has sufficient energy to reach the point on the wire vertically above $O$.
\end{enumerate}
\hfill \mbox{\textit{OCR FM1 AS 2021 Q1 [6]}}