| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2007 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Particle on table with string above |
| Difficulty | Moderate -0.3 This is a standard circular motion problem requiring resolution of forces and application of F=mv²/r. The setup is straightforward with given values, requiring vertical equilibrium (tension vs weight and normal reaction) and horizontal centripetal force equation. It's slightly easier than average as it involves only two equations with clear geometric setup and no complex problem-solving. |
| Spec | 3.03b Newton's first law: equilibrium3.03m Equilibrium: sum of resolved forces = 06.05c Horizontal circles: conical pendulum, banked tracks |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| M1 | For using \(a = \frac{v^2}{r}\) and Newton's second law horizontally | |
| \(T\sin 30° = 0.4 \times \frac{0.6^2}{0.08}\) | A1 | |
| Tension is 3.6N | A1 | [3 marks] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| M1 | For resolving forces vertically (3 terms) | |
| \(R + T\cos 30° = 0.4g\) | A1 | |
| Force is 0.882N | A1ft | [3 marks] ft \(\left[4 - \text{candidate's } Tx\cos 30°\right]\) (must be +ve) or \(T = 2.96\) from consistent sin/cos mix [Total: 6] |
## Question 2:
### Part (i)
| Answer/Working | Mark | Guidance |
|---|---|---|
| | M1 | For using $a = \frac{v^2}{r}$ and Newton's second law horizontally |
| $T\sin 30° = 0.4 \times \frac{0.6^2}{0.08}$ | A1 | |
| Tension is 3.6N | A1 | **[3 marks]** |
### Part (ii)
| Answer/Working | Mark | Guidance |
|---|---|---|
| | M1 | For resolving forces vertically (3 terms) |
| $R + T\cos 30° = 0.4g$ | A1 | |
| Force is 0.882N | A1ft | **[3 marks]** ft $\left[4 - \text{candidate's } Tx\cos 30°\right]$ (must be +ve) or $T = 2.96$ from consistent sin/cos mix **[Total: 6]** |
---2\\
\includegraphics[max width=\textwidth, alt={}, center]{b9080e9f-2c23-43ce-b171-bd68648dc56b-2_496_609_1535_769}
One end of a light inextensible string of length 0.16 m is attached to a fixed point $A$ which is above a smooth horizontal table. A particle $P$ of mass 0.4 kg is attached to the other end of the string. $P$ moves on the table in a horizontal circle, with the string taut and making an angle of $30 ^ { \circ }$ with the downward vertical through $A$ (see diagram). $P$ moves with constant speed $0.6 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. Find\\
(i) the tension in the string,\\
(ii) the force exerted by the table on $P$.
\hfill \mbox{\textit{CAIE M2 2007 Q2 [6]}}