Edexcel M2 — Question 2 6 marks

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMoments
TypeLadder against wall
DifficultyStandard +0.3 This is a standard M2 statics problem requiring three equilibrium equations (horizontal forces, vertical forces, and moments) with straightforward friction inequality μR ≥ F. The setup is routine and the algebraic manipulation is minimal, making it slightly easier than average but still requiring proper method.
Spec3.03m Equilibrium: sum of resolved forces = 06.04e Rigid body equilibrium: coplanar forces
A stick of mass \(0.75\) kg is at rest with one end \(X\) on a rough horizontal floor and the other end \(Y\) leaning against a smooth vertical wall. The coefficient of friction between the stick and the floor is \(0.6\). Modelling the stick as a uniform rod, find the smallest angle that the stick can make with the floor before it starts to slip. \includegraphics{figure_2} [6 marks]
AnswerMarks Guidance
Reaction at \(X = R = 0.75g\)B1 B1
Friction \(= 0.6R = 0.45g\)B1
Reaction at \(Y = S = 0.45g\)B1
\(M(X): 0.75g(a\cos\alpha) = 0.45g(2a\sin\alpha)\)M1 A1 A1
\(\tan\alpha = 0.83\)
\(\alpha = 39.8°\)M1 A1 A1 Total: 6 marks 
Reaction at $X = R = 0.75g$ | B1 B1 |
Friction $= 0.6R = 0.45g$ | B1 |
Reaction at $Y = S = 0.45g$ | B1 |
$M(X): 0.75g(a\cos\alpha) = 0.45g(2a\sin\alpha)$ | M1 A1 A1 |
$\tan\alpha = 0.83$ | |
$\alpha = 39.8°$ | M1 A1 A1 | **Total: 6 marks**
A stick of mass $0.75$ kg is at rest with one end $X$ on a rough horizontal floor and the other end $Y$ leaning against a smooth vertical wall. The coefficient of friction between the stick and the floor is $0.6$. Modelling the stick as a uniform rod, find the smallest angle that the stick can make with the floor before it starts to slip.

\includegraphics{figure_2}

[6 marks]

\hfill \mbox{\textit{Edexcel M2  Q2 [6]}}
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