Standard +0.3 This is a standard M2 statics problem involving a ladder in limiting equilibrium. Students must resolve forces horizontally and vertically, take moments about a point, and apply F=μR. The setup is straightforward with clearly given information (centre of mass position, angle), requiring systematic application of three equilibrium equations but no novel insight or complex geometry.
A non-uniform ladder \(AB\), of length \(3a\), has its centre of mass at \(G\), where \(AG = 2a\). The ladder rests in limiting equilibrium with the end \(B\) against a smooth vertical wall and the end \(A\) resting on rough horizontal ground. The angle between \(AB\) and the horizontal in this position is \(\alpha\), where \(\tan \alpha = \frac{14}{9}\).
\includegraphics{figure_3}
Calculate the coefficient of friction between the ladder and the ground. [7 marks]
A non-uniform ladder $AB$, of length $3a$, has its centre of mass at $G$, where $AG = 2a$. The ladder rests in limiting equilibrium with the end $B$ against a smooth vertical wall and the end $A$ resting on rough horizontal ground. The angle between $AB$ and the horizontal in this position is $\alpha$, where $\tan \alpha = \frac{14}{9}$.
\includegraphics{figure_3}
Calculate the coefficient of friction between the ladder and the ground. [7 marks]
\hfill \mbox{\textit{Edexcel M2 Q3 [7]}}