| Exam Board | OCR |
|---|---|
| Module | FM1 AS (Further Mechanics 1 AS) |
| Year | 2018 |
| Session | March |
| Marks | 7 |
| Topic | Circular Motion 1 |
| Type | Conical pendulum – particle on horizontal surface |
| Difficulty | Easy -1.2 This is a straightforward application of circular motion formulas with a horizontal conical pendulum setup. Part (i) uses F=ma directly with given values, part (ii) applies v²=ar, and part (iii) uses distance/speed. All steps are routine calculations requiring only basic recall of standard circular motion equations with no problem-solving insight needed. |
| Spec | 6.05a Angular velocity: definitions6.05b Circular motion: v=r*omega and a=v^2/r |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(21 = 2.4a\) and \(8.75 \text{ m s}^{-2}\) | M1, A1 [2] | Use of Newton II |
| Towards \(O\) | B1 [1] | |
| \(8.75 = \frac{v^2}{1.4}\) and \(3.5 \text{ m s}^{-1}\) | M1, A1 [2] | Equating \(\frac{v^2}{r}\) to their value from (i) |
| \(\frac{2\pi \times 1.4}{3.5}\) and \(2.51 \text{ s}\) | M1, A1 [2] | \(2\pi r\) divided by their value from (ii) |
| Answer | Marks | Guidance |
|--------|-------|----------|
| $21 = 2.4a$ and $8.75 \text{ m s}^{-2}$ | M1, A1 [2] | Use of Newton II |
| Towards $O$ | B1 [1] | |
| $8.75 = \frac{v^2}{1.4}$ and $3.5 \text{ m s}^{-1}$ | M1, A1 [2] | Equating $\frac{v^2}{r}$ to their value from (i) |
| $\frac{2\pi \times 1.4}{3.5}$ and $2.51 \text{ s}$ | M1, A1 [2] | $2\pi r$ divided by their value from (ii) |1 A particle $P$ of mass 2.4 kg is attached to one end of a light inextensible string of length 1.4 m . The other end of the string is attached to a fixed point $O$ on a smooth horizontal table. $P$ moves on the table at constant speed along a circular path with $O$ at its centre. The magnitude of the tension in the string is 21 N .
\begin{enumerate}[label=(\roman*)]
\item (a) Find the magnitude of the acceleration of $P$.\\
(b) State the direction of the acceleration of $P$.
\item Find the speed of $P$.
\item Find the time taken for $P$ to complete a single revolution.
\end{enumerate}
\hfill \mbox{\textit{OCR FM1 AS 2018 Q1 [7]}}