| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2006 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Particle on table with string above |
| Difficulty | Standard +0.3 This is a standard conical pendulum problem with straightforward force resolution. Students resolve forces vertically (T cos θ = mg) and horizontally (T sin θ = ma), with geometry given. The two-part structure and clear setup make it slightly easier than average, though it requires competent handling of circular motion and trigonometry. |
| Spec | 3.03b Newton's first law: equilibrium3.03m Equilibrium: sum of resolved forces = 06.05b Circular motion: v=r*omega and a=v^2/r6.05c Horizontal circles: conical pendulum, banked tracks |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(T\cos\alpha = 0.24g\) where \(\sin\alpha = 0.35/1.25\) | M1 | For resolving forces vertically \((\alpha = 16.26)\) |
| Tension is \(2.5\)N | A1 (2) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| M1 | For using Newton's second law (3 terms required) | |
| \(R + T\sin\alpha = 0.24 \times 8\) | A1ft | ft for their \(T\) only |
| Force exerted is \(1.22\)N | A1 (3) |
## Question 3:
### Part (i)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $T\cos\alpha = 0.24g$ where $\sin\alpha = 0.35/1.25$ | M1 | For resolving forces vertically $(\alpha = 16.26)$ |
| Tension is $2.5$N | A1 (2) | |
### Part (ii)
| Answer/Working | Mark | Guidance |
|---|---|---|
| | M1 | For using Newton's second law (3 terms required) |
| $R + T\sin\alpha = 0.24 \times 8$ | A1ft | ft for their $T$ only |
| Force exerted is $1.22$N | A1 (3) | |
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\includegraphics[max width=\textwidth, alt={}, center]{0cb05368-9ddf-4564-8428-725c77193a1e-2_892_412_1217_865}
A hollow cylinder of radius 0.35 m has a smooth inner surface. The cylinder is fixed with its axis vertical. One end of a light inextensible string of length 1.25 m is attached to a fixed point $O$ on the axis of the cylinder. A particle $P$ of mass 0.24 kg is attached to the other end of the string. $P$ moves with constant speed in a horizontal circle, in contact with the inner surface of the cylinder, and with the string taut (see diagram).\\
(i) Find the tension in the string.\\
(ii) Given that the magnitude of the acceleration of $P$ is $8 \mathrm {~m} \mathrm {~s} ^ { - 2 }$, find the force exerted on $P$ by the cylinder.
\hfill \mbox{\textit{CAIE M2 2006 Q3 [5]}}