| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2015 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 2 |
| Type | Conical pendulum (horizontal circle) |
| Difficulty | Moderate -0.8 This is a standard conical pendulum problem requiring straightforward application of circular motion principles and resolving forces. Students need to find the angle from geometry (3-4-5 triangle), resolve tension vertically (T cos θ = mg) to get the given answer, then resolve horizontally (T sin θ = mv²/r) to find speed. It's a routine two-part question with clear setup and standard method, making it easier than average but not trivial since it requires correct force resolution and circular motion formula. |
| Spec | 6.05c Horizontal circles: conical pendulum, banked tracks |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| \(T\cos\theta = 0.2g\) | M1 | Weight = vertical component of tension |
| \(T \times \frac{0.4}{0.5} = 2\) | ||
| \(T = 2.5\) N | A1 AG | [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| \(2.5\sin\theta = \frac{0.2v^2}{r}\) | M1 | Horizontal component of tension and \(\text{accn} = v^2/r\) |
| \(2.5 \times \frac{0.3}{0.5} = \frac{0.2v^2}{0.3}\) | A1 | |
| \(v = 1.5 \text{ ms}^{-1}\) | A1 | [3] |
## Question 2(i):
| Working | Mark | Guidance |
|---------|------|----------|
| $T\cos\theta = 0.2g$ | M1 | Weight = vertical component of tension |
| $T \times \frac{0.4}{0.5} = 2$ | | |
| $T = 2.5$ N | A1 AG | **[2]** |
## Question 2(ii):
| Working | Mark | Guidance |
|---------|------|----------|
| $2.5\sin\theta = \frac{0.2v^2}{r}$ | M1 | Horizontal component of tension and $\text{accn} = v^2/r$ |
| $2.5 \times \frac{0.3}{0.5} = \frac{0.2v^2}{0.3}$ | A1 | |
| $v = 1.5 \text{ ms}^{-1}$ | A1 | **[3]** |
---2 One end of a light inextensible string of length 0.5 m is attached to a fixed point $A$. A particle $P$ of mass 0.2 kg is attached to the other end of the string. $P$ moves with constant speed in a horizontal circle with centre $O$ which is 0.4 m vertically below $A$.\\
(i) Show that the tension in the string is 2.5 N .\\
(ii) Find the speed of $P$.
\hfill \mbox{\textit{CAIE M2 2015 Q2 [5]}}