| Exam Board | SPS |
|---|---|
| Module | SPS FM Mechanics (SPS FM Mechanics) |
| Year | 2025 |
| Session | January |
| Marks | 11 |
| Topic | Advanced work-energy problems |
| Type | Elastic string vertical motion |
| Difficulty | Standard +0.3 This is a standard circular motion problem with an elastic string requiring resolution of forces and Hooke's law. Part (a) involves geometric reasoning with Pythagoras and elastic force equilibrium, while part (b) applies standard circular motion equations. The 'show that' format and straightforward setup make it slightly easier than average, though it requires competent handling of multiple mechanics concepts. |
| Spec | 6.02i Conservation of energy: mechanical energy principle6.05c Horizontal circles: conical pendulum, banked tracks |
2.
\begin{figure}[h]
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\includegraphics[alt={},max width=\textwidth]{7ecb33af-c165-4b72-98f2-7574fad3fdd5-04_506_613_246_671}
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\caption{Figure 2}
\end{center}
\end{figure}
A particle $P$ of mass $m$ is attached to one end of a light elastic string, of natural length $2 a$ and modulus of elasticity 6 mg . The other end of the string is attached to a fixed point $A$. The particle moves with constant speed $v$ in a horizontal circle with centre $O$, where $O$ is vertically below $A$ and $O A = 2 a$, as shown in Figure 2.
\begin{enumerate}[label=(\alph*)]
\item Show that the extension in the string is $\frac { 2 } { 5 } a$.
\item Find $v ^ { 2 }$ in terms of $a$ and $g$.\\[0pt]
[Question 2 Continued]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Mechanics 2025 Q2 [11]}}