| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2010 |
| Session | June |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Rod hinged to wall with string support |
| Difficulty | Standard +0.3 This is a standard M2 moments equilibrium problem requiring taking moments about the hinge and resolving forces. Part (a) involves straightforward geometry to find the string angle and moment calculations with given masses. Part (b) extends this to find a limiting mass value. While it requires careful setup and multiple steps (8 marks total), the techniques are routine for M2 students and the problem structure is typical of textbook exercises. |
| Spec | 3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force |
\includegraphics{figure_2}
Figure 2 shows a uniform rod $AB$ of mass $m$ and length $4a$. The end $A$ of the rod is freely hinged to a point on a vertical wall. A particle of mass $m$ is attached to the rod at $B$. One end of a light inextensible string is attached to the rod at $C$, where $AC = 3a$. The other end of the string is attached to the wall at $D$, where $AD = 2a$ and $D$ is vertically above $A$. The rod rests horizontally in equilibrium in a vertical plane perpendicular to the wall and the tension in the string is $T$.
\begin{enumerate}[label=(\alph*)]
\item Show that $T = mg\sqrt{13}$.
(5)
\end{enumerate}
The particle of mass $m$ at $B$ is removed from the rod and replaced by a particle of mass $M$ which is attached to the rod at $B$. The string breaks if the tension exceeds $2mg\sqrt{13}$. Given that the string does not break,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item show that $M \leq \frac{5}{2}m$.
(3)
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2010 Q6}}