4 \includegraphics[max width=\textwidth, alt={}, center]{b8e52188-f9a6-46fc-90bf-97965c6dd324-07_337_526_262_726} \includegraphics[max width=\textwidth, alt={}, center]{b8e52188-f9a6-46fc-90bf-97965c6dd324-07_111_116_486_1308} A particle \(P\) of mass 0.3 kg is attached to a fixed point \(A\) by a light elastic string of natural length 0.8 m and modulus of elasticity 16 N . The particle \(P\) moves in a horizontal circle which has centre \(O\). It is given that \(A O\) is vertical and that angle \(O A P\) is \(60 ^ { \circ }\) (see diagram). Calculate the speed of \(P\). [6]

## Question 4:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $T\cos 60 = 0.3g$ | M1 | Resolve vertically |
| $T = 6\text{ N}$ | A1 | |
| $T = \frac{16e}{0.8} (= 6)$ leads to $e = 0.3$ | M1 | Use $T = \frac{\lambda x}{L}$ |
| $r = (0.8 + 0.3)\sin 60 (= 1.1\sin 60)$ | A1 | |
| $T\sin 60 = \frac{0.3v^2}{1.1\sin 60}$ | M1 | Use N2L horizontally |
| $v = 4.06 \text{ m s}^{-1}$ | A1 | |
| | **6** | |

4\\
\includegraphics[max width=\textwidth, alt={}, center]{b8e52188-f9a6-46fc-90bf-97965c6dd324-07_337_526_262_726}\\
\includegraphics[max width=\textwidth, alt={}, center]{b8e52188-f9a6-46fc-90bf-97965c6dd324-07_111_116_486_1308}

A particle $P$ of mass 0.3 kg is attached to a fixed point $A$ by a light elastic string of natural length 0.8 m and modulus of elasticity 16 N . The particle $P$ moves in a horizontal circle which has centre $O$. It is given that $A O$ is vertical and that angle $O A P$ is $60 ^ { \circ }$ (see diagram). Calculate the speed of $P$. [6]\\

\hfill \mbox{\textit{CAIE M2 2019 Q4 [6]}}