| Exam Board | OCR |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2009 |
| Session | June |
| Marks | 11 |
| 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 strings problem requiring energy conservation and Hooke's law. While it involves multiple steps (finding extensions, applying energy equations, solving for unknowns), the techniques are routine for this module. The symmetry simplifies calculations, and the question guides students through the method ('by considering energy'). More challenging than basic mechanics but typical for M3 material. |
| Spec | 6.02h Elastic PE: 1/2 k x^26.02i Conservation of energy: mechanical energy principle6.02j Conservation with elastics: springs and strings |
\includegraphics{figure_5}
Each of two identical strings has natural length $1.5$ m and modulus of elasticity $18$ N. One end of one of the strings is attached to $A$ and one end of the other string is attached to $B$, where $A$ and $B$ are fixed points which are $3$ m apart and at the same horizontal level. $M$ is the mid-point of $AB$. A particle $P$ of mass $m$ kg is attached to the other end of each of the strings. $P$ is held at rest at the point $0.8$ m vertically above $M$, and then released. The lowest point reached by $P$ in the subsequent motion is $2$ m below $M$ (see diagram).
\begin{enumerate}[label=(\roman*)]
\item Find the maximum tension in each of the strings during $P$'s motion. [3]
\item By considering energy,
\begin{enumerate}[label=(\alph*)]
\item show that the value of $m$ is $0.42$, correct to 2 significant figures, [5]
\item find the speed of $P$ at $M$. [3]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{OCR M3 2009 Q5 [11]}}