| Exam Board | OCR |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2007 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Two strings, two fixed points |
| Difficulty | Standard +0.3 This is a standard M2 circular motion problem with two strings at different angles. It requires resolving forces horizontally and vertically, applying F=mrω², and calculating kinetic energy - all routine techniques for this topic. The geometry is straightforward and the multi-part structure is typical, making it slightly easier than average overall. |
| Spec | 6.02e Calculate KE and PE: using formulae6.05c Horizontal circles: conical pendulum, banked tracks |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(5\cos30° = 0.3\times9.8 + S\cos60°\) | M1 | res. vertically (3 parts with comps) |
| A1 | ||
| \(2.78\) N | A1 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(r = 0.4\sin30° = 0.2\) | B1 | may be on diagram |
| \(5\sin30° + S\sin60° = 0.3 \times 0.2 \times \omega^2\) | M1 | res. horizontally (3 parts with comps) |
| \(9.04\ \text{rads}^{-1}\) | A1 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(v = 0.2 \times 9.04\) | M1 | or previous \(v\) via \(\frac{mv^2}{r}\) |
| \(KE = \frac{1}{2} \times 0.3 \times (0.2 \times 9.04)^2\) | M1 | |
| \(0.491\) J or \(0.49\) | A1\(\checkmark\) 3 | \(\checkmark\) their \(\omega^2 \times 0.006\) |
## Question 6(i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $5\cos30° = 0.3\times9.8 + S\cos60°$ | M1 | res. vertically (3 parts with comps) |
| | A1 | |
| $2.78$ N | A1 **3** | |
## Question 6(ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $r = 0.4\sin30° = 0.2$ | B1 | may be on diagram |
| $5\sin30° + S\sin60° = 0.3 \times 0.2 \times \omega^2$ | M1 | res. horizontally (3 parts with comps) |
| $9.04\ \text{rads}^{-1}$ | A1 **3** | |
## Question 6(iii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $v = 0.2 \times 9.04$ | M1 | **or** previous $v$ via $\frac{mv^2}{r}$ |
| $KE = \frac{1}{2} \times 0.3 \times (0.2 \times 9.04)^2$ | M1 | |
| $0.491$ J or $0.49$ | A1$\checkmark$ **3** | $\checkmark$ their $\omega^2 \times 0.006$ |
---6\\
\includegraphics[max width=\textwidth, alt={}, center]{9951c978-37e6-4d89-9fe3-c1e5e28b221e-3_670_613_274_767}
A particle $P$ of mass 0.3 kg is attached to one end of each of two light inextensible strings. The other end of the longer string is attached to a fixed point $A$ and the other end of the shorter string is attached to a fixed point $B$, which is vertically below $A$. $A P$ makes an angle of $30 ^ { \circ }$ with the vertical and is 0.4 m long. $P B$ makes an angle of $60 ^ { \circ }$ with the vertical. The particle moves in a horizontal circle with constant angular speed and with both strings taut (see diagram). The tension in the string $A P$ is 5 N .
Calculate\\
(i) the tension in the string $P B$,\\
(ii) the angular speed of $P$,\\
(iii) the kinetic energy of $P$.
\hfill \mbox{\textit{OCR M2 2007 Q6 [9]}}