| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2006 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Rod on smooth peg or cylinder |
| Difficulty | Standard +0.3 This is a standard M2 moments equilibrium problem requiring taking moments about a point, resolving forces, and applying friction conditions. The geometry is straightforward (3-4-5 triangle), and the method is routine: moments about C to find reaction, then resolve forces and apply limiting friction. While it requires multiple steps and careful algebra, it follows a standard textbook approach with no novel insight needed. |
| Spec | 3.03u Static equilibrium: on rough surfaces3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force |
Figure 2
\includegraphics{figure_2}
A wooden plank $AB$ has mass $4m$ and length $4a$. The end $A$ of the plank lies on rough horizontal ground. A small stone of mass $m$ is attached to the plank at $B$. The plank is resting on a small smooth horizontal peg $C$, where $BC = a$, as shown in Figure 2. The plank is in equilibrium making an angle $\alpha$ with the horizontal, where $\tan \alpha = \frac{3}{4}$. The coefficient of friction between the plank and the ground is $\mu$. The plank is modelled as a uniform rod lying in a vertical plane perpendicular to the peg, and the stone as a particle. Show that
\begin{enumerate}[label=(\alph*)]
\item the reaction of the peg on the plank has magnitude $\frac{16}{5}mg$,
[3]
\end{enumerate}
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item $\mu \geq \frac{48}{61}$.
[6]
\end{enumerate}
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item State how you have used the information that the peg is smooth.
[1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2006 Q6 [10]}}