| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2019 |
| Session | January |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hooke's law and elastic energy |
| Type | Particle at midpoint of string between two horizontal fixed points: vertical motion |
| Difficulty | Challenging +1.2 This is a standard M3 elastic string problem requiring equilibrium analysis using Hooke's law and energy conservation. Part (a) involves resolving forces with symmetry and basic trigonometry. Part (b) uses energy methods to show the particle stops before reaching AB. While it requires multiple steps and careful setup, the techniques are routine for M3 students and the 'show that' format provides clear targets, making it moderately above average difficulty. |
| Spec | 6.02g Hooke's law: T = k*x or T = lambda*x/l6.02h Elastic PE: 1/2 k x^26.02i Conservation of energy: mechanical energy principle |
4.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{ae189c40-0071-4a6b-91eb-8ffebe082a04-12_364_718_278_612}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}
The ends of a light elastic string, of natural length $4 l$ and modulus of elasticity $\lambda$, are attached to two fixed points $A$ and $B$, where $A B$ is horizontal and $A B = 4 l$. A particle $P$ of mass $2 m$ is attached to the midpoint of the string. The particle hangs freely in equilibrium at a distance $\frac { 3 } { 2 } l$ vertically below the midpoint of $A B$, as shown in Figure 2.
\begin{enumerate}[label=(\alph*)]
\item Show that $\lambda = \frac { 20 } { 3 } m g$.
The particle is pulled vertically downwards from its equilibrium position until the total length of the string is 6l. The particle is then released from rest.
\item Show that $P$ comes to instantaneous rest before reaching the line $A B$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M3 2019 Q4 [13]}}