| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2011 |
| Session | November |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Multiple particles on string |
| Difficulty | Standard +0.8 This is a multi-particle circular motion problem requiring systematic application of Newton's second law to three connected particles, with careful bookkeeping of tensions and radii. While the individual steps are standard (F=mrω²), the three-part structure with interdependent calculations and the need to track multiple tensions and masses makes this more challenging than typical single-particle circular motion questions. |
| Spec | 6.05b Circular motion: v=r*omega and a=v^2/r6.05c Horizontal circles: conical pendulum, banked tracks |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(0.2\omega^2 \times 1.2 = 6\) | M1 | Uses radial acceleration on \(R\), 1 force |
| \(\omega = 5\) | A1 | [2] |
| (ii) \(m\omega^2 \times 2 \times 0.4 = 10 - 6\) | M1 | Uses radial acceleration on \(Q\), 2 forces |
| \(m = 0.2 \text{ kg}\) | A1 | A1 [3] |
| (iii) \(0.2 \times (5 \times 1.2)^2/2 = M(5 \times 0.4)^2/2\) | M1 | |
| \(M = 1.8 \text{ kg}\) | A1 | |
| \(1.8 \times 5^2 \times 0.4 = T - 10\) | DM1 | |
| \(T = 28 \text{ N}\) | A1 | [4] |
**(i)** $0.2\omega^2 \times 1.2 = 6$ | M1 | Uses radial acceleration on $R$, 1 force
$\omega = 5$ | A1 | [2]
**(ii)** $m\omega^2 \times 2 \times 0.4 = 10 - 6$ | M1 | Uses radial acceleration on $Q$, 2 forces
$m = 0.2 \text{ kg}$ | A1 | A1 [3]
**(iii)** $0.2 \times (5 \times 1.2)^2/2 = M(5 \times 0.4)^2/2$ | M1 |
$M = 1.8 \text{ kg}$ | A1 |
$1.8 \times 5^2 \times 0.4 = T - 10$ | DM1 |
$T = 28 \text{ N}$ | A1 | [4]5\\
\includegraphics[max width=\textwidth, alt={}, center]{a093cbad-3ba0-45ce-a617-d4ecc8cb1ec9-3_927_1022_689_559}
One end of a light inextensible string of length 1.2 m is attached to a fixed point $O$ on a smooth horizontal surface. Particles $P , Q$ and $R$ are attached to the string so that $O P = P Q = Q R = 0.4 \mathrm {~m}$. The particles rotate in horizontal circles about $O$ with constant angular speed $\omega \operatorname { rads } ^ { - 1 }$ and with $O , P$, $Q$ and $R$ in a straight line (see diagram). $R$ has mass 0.2 kg , and the tensions in the parts of the string attached to $Q$ are 6 N and 10 N .\\
(i) Show that $\omega = 5$.\\
(ii) Calculate the mass of $Q$.\\
(iii) Given that the kinetic energy of $P$ is equal to the kinetic energy of $R$, calculate the tension in the part of the string attached to $O$.
\hfill \mbox{\textit{CAIE M2 2011 Q5 [9]}}