Edexcel M2 Specimen — Question 4 9 marks

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
SessionSpecimen
Marks9
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMoments
TypeLadder on smooth wall and rough ground
DifficultyStandard +0.8 This is a standard M2 ladder equilibrium problem requiring resolution of forces, friction inequality, and taking moments about a strategic point. While it involves multiple steps (horizontal/vertical equilibrium, moment equation, friction condition), the approach is methodical and well-practiced. The man at the top simplifies the moment calculation compared to variable-position problems. Slightly above average due to the algebraic manipulation needed and the inequality direction, but follows a standard template taught in M2.
Spec3.03u Static equilibrium: on rough surfaces3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force

4. \section*{Figure 1}
\includegraphics[max width=\textwidth, alt={}]{0d3d35b1-e3c5-47ac-b05e-78cdf1eb3083-3_714_565_262_749}
A uniform ladder, of mass \(m\) and length \(2 a\), has one end on rough horizontal ground. The other end rests against a smooth vertical wall. A man of mass \(3 m\) stands at the top of the ladder and the ladder is in equilibrium. The coefficient of friction between the ladder and the ground is \(\frac { 1 } { 4 }\), and the ladder makes an angle \(\alpha\) with the vertical, as shown in Fig. 1. The ladder is in a vertical plane perpendicular to the wall. Show that \(\tan \alpha \leq \frac { 2 } { 7 }\).

4.

\section*{Figure 1}
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{0d3d35b1-e3c5-47ac-b05e-78cdf1eb3083-3_714_565_262_749}
\end{center}

A uniform ladder, of mass $m$ and length $2 a$, has one end on rough horizontal ground. The other end rests against a smooth vertical wall. A man of mass $3 m$ stands at the top of the ladder and the ladder is in equilibrium. The coefficient of friction between the ladder and the ground is $\frac { 1 } { 4 }$, and the ladder makes an angle $\alpha$ with the vertical, as shown in Fig. 1. The ladder is in a vertical plane perpendicular to the wall.

Show that $\tan \alpha \leq \frac { 2 } { 7 }$.\\

\hfill \mbox{\textit{Edexcel M2  Q4 [9]}}