| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Beam on point of tilting |
| Difficulty | Standard +0.3 This is a standard M1 moments question requiring taking moments about a pivot point. Part (a) involves a single equation with one unknown. Part (b) requires setting up a similar equation with a different configuration. The modelling assumptions part (c) is routine recall. While it requires careful setup and arithmetic, it follows a well-practiced textbook method with no novel insight needed, making it slightly easier than average. |
| Spec | 3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Taking moments about C: \(M(C): 40g \cdot 1.6 = Mg \cdot 0.4 + 25g \cdot 2.4\) \(\Rightarrow M = 10 \text{ kg}\) | M1 A1, A1 | 3 marks |
| (b) Taking moments about C: \(M(C): 25g \cdot x + 10g(x - 2) = 40g(4 - x)\) \(\Rightarrow 75x = 180\) \(\Rightarrow x = 2.4 \text{ m}\) | M1 A1 A1, M1 A1 | 5 marks |
| Answer | Marks | Guidance |
|---|---|---|
| - (i) Weight acts at centre of plank | B1 | |
| - (ii) Plank remains straight | B1 | |
| - (iii) Weights act at the ends of the plank | B1 | 3 marks (total 11 marks) |
**(a)** Taking moments about C: $M(C): 40g \cdot 1.6 = Mg \cdot 0.4 + 25g \cdot 2.4$ $\Rightarrow M = 10 \text{ kg}$ | M1 A1, A1 | 3 marks
**(b)** Taking moments about C: $M(C): 25g \cdot x + 10g(x - 2) = 40g(4 - x)$ $\Rightarrow 75x = 180$ $\Rightarrow x = 2.4 \text{ m}$ | M1 A1 A1, M1 A1 | 5 marks
**(c)**
- (i) Weight acts at centre of plank | B1
- (ii) Plank remains straight | B1
- (iii) Weights act at the ends of the plank | B1 | 3 marks (total 11 marks)
---\includegraphics{figure_2}
A plank $AB$ has length $4$ m. It lies on a horizontal platform, with the end $A$ lying on the platform and the end $B$ projecting over the edge, as shown in Fig. 2. The edge of the platform is at the point $C$.
Jack and Jill are experimenting with the plank. Jack has mass $40$ kg and Jill has mass $25$ kg. They discover that, if Jack stands at $B$ and Jill stands at $A$ and $BC = 1.6$ m, the plank is in equilibrium and on the point of tilting about $C$. By modelling the plank as a uniform rod, and Jack and Jill as particles,
\begin{enumerate}[label=(\alph*)]
\item find the mass of the plank. [3]
\end{enumerate}
They now alter the position of the plank in relation to the platform so that, when Jill stands at $B$ and Jack stands at $A$, the plank is again in equilibrium and on the point of tilting about $C$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the distance $BC$ in this position. [5]
\item State how you have used the modelling assumptions that
\begin{enumerate}[label=(\roman*)]
\item the plank is uniform,
\item the plank is a rod,
\item Jack and Jill are particles.
\end{enumerate}
[3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q4 [11]}}