| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Session | Specimen |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Ladder on smooth wall and rough ground |
| Difficulty | Standard +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. |
| Spec | 3.03u Static equilibrium: on rough surfaces3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force |
4.
\section*{Figure 1}
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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]}}