| Exam Board | OCR |
|---|---|
| Module | FM1 AS (Further Mechanics 1 AS) |
| Year | 2021 |
| Session | June |
| Marks | 6 |
| Topic | Work done and energy |
| Type | Particle on smooth curved surface |
| Difficulty | Standard +0.8 This is a standard energy conservation problem in circular motion with a rod, typical of FM1. Part (a) requires applying conservation of energy to find speed at a given angle (routine 4-mark calculation). Part (b) asks for the angle at instantaneous rest (straightforward 2-mark application). While it involves Further Maths content (making it harder than pure maths on an absolute scale), it's a textbook exercise requiring no novel insight—just direct application of mechanical energy principles. |
| Spec | 6.02i Conservation of energy: mechanical energy principle |
A particle $P$ of mass 5.6 kg is attached to one end of a light rod of length 2.1 m. The other end of the rod is freely hinged to a fixed point $O$.
The particle is initially at rest directly below $O$. It is then projected horizontally with speed $5 \text{ ms}^{-1}$. In the subsequent motion, the angle between the rod and the downward vertical at $O$ is denoted by $\theta$ radians, as shown in the diagram.
\includegraphics{figure_2}
\begin{enumerate}[label=(\alph*)]
\item Find the speed of $P$ when $\theta = \frac{1}{4}\pi$. [4]
\item Find the value of $\theta$ when $P$ first comes to instantaneous rest. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR FM1 AS 2021 Q2 [6]}}