| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Topic | Moments |
| Type | Rod or block on rough surface in limiting equilibrium (no wall) |
| Difficulty | Standard +0.8 This is a multi-part statics problem requiring moments about a point, resolution of forces in two directions, and use of limiting equilibrium friction condition. While it involves several steps and careful geometric reasoning with the angles, it follows standard M2 mechanics procedures without requiring novel insight. The 14 total marks and need to coordinate multiple equations elevates it above average difficulty. |
| Spec | 3.03m Equilibrium: sum of resolved forces = 03.03n Equilibrium in 2D: particle under forces3.03t Coefficient of friction: F <= mu*R model3.04b Equilibrium: zero resultant moment and force |
\includegraphics{figure_3}
A straight log $AB$ has weight $W$ and length $2a$. A cable is attached to one end $B$ of the log. The cable lifts the end $B$ off the ground. The end $A$ remains in contact with the ground, which is rough and horizontal. The log is in limiting equilibrium. The log makes an angle $α$ to the horizontal, where $\tan α = \frac{4}{3}$. The cable makes an angle $β$ to the horizontal, as shown in Fig. 3. The coefficient of friction between the log and the ground is $\frac{1}{3}$. The log is modelled as a uniform rod and the cable as light.
\begin{enumerate}[label=(\alph*)]
\item Show that the normal reaction on the log at $A$ is $\frac{3}{4}W$.
[6]
\end{enumerate}
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the value of $β$.
[6]
\end{enumerate}
The tension in the cable is $kW$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find the value of $k$.
[2]
\end{enumerate}
END
\hfill \mbox{\textit{Edexcel M2 Q7 [14]}}