| Exam Board | SPS |
|---|---|
| Module | SPS FM Mechanics (SPS FM Mechanics) |
| Year | 2026 |
| Session | January |
| Marks | 8 |
| Topic | Hooke's law and elastic energy |
| Type | Particle at midpoint of string between two horizontal fixed points: horizontal surface motion |
| Difficulty | Challenging +1.2 This is a multi-step mechanics problem involving elastic strings, energy conservation, and forces. Part (a) requires setting up energy conservation with elastic potential energy in two configurations, which is moderately challenging but follows standard A-level FM mechanics methods. Part (b) requires resolving forces and using geometry to find acceleration components. While it involves several steps and careful bookkeeping of the elastic energy formula, the techniques are all standard for Further Maths mechanics with no novel insights required. |
| Spec | 6.02h Elastic PE: 1/2 k x^26.02i Conservation of energy: mechanical energy principle |
\includegraphics{figure_3}
A light elastic string has natural length $8a$ and modulus of elasticity $5mg$. A particle $P$ of mass $m$ is attached to the midpoint of the string. The ends of the string are attached to points $A$ and $B$ which are a distance $12a$ apart on a smooth horizontal table. The particle $P$ is held on the table so that $AP = BP = L$ (see diagram). The particle $P$ is released from rest. When $P$ is at the midpoint of $AB$ it has speed $\sqrt{80ag}$.
\begin{enumerate}[label=(\alph*)]
\item Find $L$ in terms of $a$. [5]
\item Find the initial acceleration of $P$ in terms of $g$. [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Mechanics 2026 Q3 [8]}}