| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2002 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Elastic string equilibrium |
| Difficulty | Standard +0.3 This is a standard M3 equilibrium problem requiring moments about a point and resolving forces, followed by straightforward application of Hooke's law. The geometry is given (tan α = 3/4, perpendicular strings), making it easier than if students had to derive these relationships. Part (a) tests conceptual understanding, parts (b-c) are routine multi-step calculations typical of mechanics modules. |
| Spec | 3.04b Equilibrium: zero resultant moment and force6.02g Hooke's law: T = k*x or T = lambda*x/l6.04e Rigid body equilibrium: coplanar forces |
\includegraphics{figure_1}
A rod $AB$, of mass $2m$ and length $2a$, is suspended from a fixed point $C$ by two light strings $AC$ and $BC$. The rod rests horizontally in equilibrium with $AC$ making an angle $\alpha$ with the rod, where $\tan \alpha = \frac{3}{4}$, and with $AC$ perpendicular to $BC$, as shown in Fig. 1.
\begin{enumerate}[label=(\alph*)]
\item Give a reason why the rod cannot be uniform. [1]
\item Show that the tension in $BC$ is $\frac{4}{5}mg$ and find the tension in $AC$. [5]
\end{enumerate}
The string $BC$ is elastic, with natural length $a$ and modulus of elasticity $kmg$, where $k$ is constant.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find the value of $k$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M3 2002 Q3 [10]}}