| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2010 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Conical pendulum – horizontal circle in free space (no surface) |
| Difficulty | Standard +0.3 This is a standard conical pendulum problem requiring resolution of forces (vertical equilibrium and horizontal centripetal force) and application of circular motion formulas. The question guides students through the solution with clear parts and standard techniques, making it slightly easier than average for A-level mechanics. |
| Spec | 6.05a Angular velocity: definitions6.05b Circular motion: v=r*omega and a=v^2/r6.05c Horizontal circles: conical pendulum, banked tracks |
| Answer | Marks | Guidance |
|---|---|---|
| \(mg = T\cos\theta\) \(ma = T\sin\theta\) \(\tan\theta = a/g = 0.75\) \(T = 0.24 \times 10/\cos\theta = 3\) | B1 B1 B1 B1 [4] | SR B1 not B2 for \(\tan\theta = \sqrt{3}/gr\) or \(a/g\) used. AG For using \(T\cos\theta = mg\) to find \(T\) |
| Answer | Marks | Guidance |
|---|---|---|
| \([v^2 = 7.5 \times 2\sin\theta]\) Speed is 3ms\(^{-1}\) | M1 A1 [2] | For using \(v^2 = ar\) to find \(v\) |
## (i)
$mg = T\cos\theta$ $ma = T\sin\theta$ $\tan\theta = a/g = 0.75$ $T = 0.24 \times 10/\cos\theta = 3$ | B1 B1 B1 B1 [4] | SR B1 not B2 for $\tan\theta = \sqrt{3}/gr$ or $a/g$ used. AG For using $T\cos\theta = mg$ to find $T$
## (ii)
$[v^2 = 7.5 \times 2\sin\theta]$ Speed is 3ms$^{-1}$ | M1 A1 [2] | For using $v^2 = ar$ to find $v$
---\includegraphics{figure_3}
A particle of mass 0.24 kg is attached to one end of a light inextensible string of length 2 m. The other end of the string is attached to a fixed point. The particle moves with constant speed in a horizontal circle. The string makes an angle $\theta$ with the vertical (see diagram), and the tension in the string is $T$ N. The acceleration of the particle has magnitude $7.5 \text{ m s}^{-2}$.
\begin{enumerate}[label=(\roman*)]
\item Show that $\tan \theta = 0.75$ and find the value of $T$. [4]
\item Find the speed of the particle. [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2010 Q3 [6]}}