| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2006 |
| 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 | Moderate -0.3 This is a standard conical pendulum problem requiring resolution of forces (tension and weight) and application of circular motion equations (v = rω). It involves straightforward trigonometry and algebraic manipulation with all necessary information provided, making it slightly easier than average but still requiring proper method and multiple steps. |
| Spec | 6.05a Angular velocity: definitions6.05c Horizontal circles: conical pendulum, banked tracks |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(T \cos 35° = mg\) | B1, M1 | For using Newton's second law and \(a = r\omega^2\) |
| Answer | Marks |
|---|---|
| \(L = 2.52\) | A1, A1, 4 |
| Answer | Marks | Guidance |
|---|---|---|
| Speed is 3.18 m s\(^{-1}\) | M1, A1 ⊞ | 2 |
**(i)** $T \cos 35° = mg$ | B1, M1 | For using Newton's second law and $a = r\omega^2$
$T \sin 35° = m(L \sin 35°) \times 2^2$
$L = 2.52$ | A1, A1, 4 |
$v = 2.2(2.52\sin 35°)$
Speed is 3.18 m s$^{-1}$ | M1, A1 ⊞ | 2 | For using $v = \omega r$
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\includegraphics[max width=\textwidth, alt={}, center]{ece63d46-5e56-4668-939a-9dbbcfc1a77a-3_437_567_269_788}
A particle $P$ of mass $m \mathrm {~kg}$ is attached to one end of a light inextensible string of length $L \mathrm {~m}$. The other end of the string is attached to a fixed point $O$. The particle $P$ moves with constant speed in a horizontal circle, with the string taut and inclined at $35 ^ { \circ }$ to the vertical. $O P$ rotates with angular speed $2.2 \mathrm { rad } \mathrm { s } ^ { - 1 }$ about the vertical axis through $O$ (see diagram). Find\\
(i) the value of $L$,\\
(ii) the speed of $P$ in $\mathrm { m } \mathrm { s } ^ { - 1 }$.
\hfill \mbox{\textit{CAIE M2 2006 Q3 [6]}}