Edexcel M2 2010 January — Question 6 7 marks

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2010
SessionJanuary
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMoments
TypeRod or block on rough surface in limiting equilibrium (no wall)
DifficultyStandard +0.3 This is a standard M2 statics problem requiring resolution of forces, friction at limiting equilibrium, and taking moments about a point. While it involves multiple steps (drawing a diagram, resolving horizontally and vertically, applying moment equation, using μ=0.5), these are routine techniques for M2 students with no novel insight required. The given tan α simplifies calculations. Slightly easier than average due to its straightforward application of standard methods.
Spec3.03v Motion on rough surface: including inclined planes3.04b Equilibrium: zero resultant moment and force6.04e Rigid body equilibrium: coplanar forces

\includegraphics{figure_2} A uniform rod \(AB\), of mass \(20\) kg and length \(4\) m, rests with one end \(A\) on rough horizontal ground. The rod is held in limiting equilibrium at an angle \(\alpha\) to the horizontal, where \(\tan \alpha = \frac{3}{4}\), by a force acting at \(B\), as shown in Figure 2. The line of action of this force lies in the vertical plane which contains the rod. The coefficient of friction between the ground and the rod is \(0.5\). Find the magnitude of the normal reaction of the ground on the rod at \(A\). [7]

AnswerMarks
\(m(B): R \times 4\cos\alpha = F \times 4\sin\alpha + 20g \times 2\cos\alpha\)M1 A2
Use of \(F = \frac{1}{2}R\)M1
Use of correct trig ratiosB1
\(R = 160\text{N or }157\text{N}\)DM1 A1
Total: [7]
$m(B): R \times 4\cos\alpha = F \times 4\sin\alpha + 20g \times 2\cos\alpha$ | M1 A2 |
Use of $F = \frac{1}{2}R$ | M1 |
Use of correct trig ratios | B1 |
$R = 160\text{N or }157\text{N}$ | DM1 A1 |

**Total: [7]**

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\includegraphics{figure_2}

A uniform rod $AB$, of mass $20$ kg and length $4$ m, rests with one end $A$ on rough horizontal ground. The rod is held in limiting equilibrium at an angle $\alpha$ to the horizontal, where $\tan \alpha = \frac{3}{4}$, by a force acting at $B$, as shown in Figure 2. The line of action of this force lies in the vertical plane which contains the rod. The coefficient of friction between the ground and the rod is $0.5$. Find the magnitude of the normal reaction of the ground on the rod at $A$.
[7]

\hfill \mbox{\textit{Edexcel M2 2010 Q6 [7]}}