| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2008 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Non-uniform beam on supports |
| Difficulty | Standard +0.3 This is a standard M1 moments question with two parts: (a) requires taking moments about a point with uniform rod assumption (routine calculation), and (b) extends to non-uniform rod requiring algebraic manipulation with two equations. While multi-step, it follows a predictable template with no novel insight required, 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) \(M(A): 8g \times 0.8 + 12g \times 1.2 = X \times 2.4\) giving \(X \approx 85 \text{ (N)}\) | M1 A1 DM1 A1 | (4) Accept 84.9, \(\frac{26g}{3}\) |
| (b) \(R(\uparrow): (X + 10) + X = 8g + 12g\) giving \((X = 93)\) | M1 B1 A1 | |
| \(M(A): 8g \times 0.8 + 12g \times x = X \times 2.4\) giving \(x = 1.4 \text{ (m)}\) | M1 A1 | (6) [10] Accept 1.36 |
**(a)** $M(A): 8g \times 0.8 + 12g \times 1.2 = X \times 2.4$ giving $X \approx 85 \text{ (N)}$ | M1 A1 DM1 A1 | (4) Accept 84.9, $\frac{26g}{3}$
**(b)** $R(\uparrow): (X + 10) + X = 8g + 12g$ giving $(X = 93)$ | M1 B1 A1 |
$M(A): 8g \times 0.8 + 12g \times x = X \times 2.4$ giving $x = 1.4 \text{ (m)}$ | M1 A1 | (6) [10] Accept 1.36
---6.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{9dbbbc01-fb66-460d-a42e-2c37ec8b451a-08_392_678_260_614}
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\caption{Figure 2}
\end{center}
\end{figure}
A plank $A B$ has mass 12 kg and length 2.4 m . A load of mass 8 kg is attached to the plank at the point $C$, where $A C = 0.8 \mathrm {~m}$. The loaded plank is held in equilibrium, with $A B$ horizontal, by two vertical ropes, one attached at $A$ and the other attached at $B$, as shown in Figure 2. The plank is modelled as a uniform rod, the load as a particle and the ropes as light inextensible strings.
\begin{enumerate}[label=(\alph*)]
\item Find the tension in the rope attached at $B$.
The plank is now modelled as a non-uniform rod. With the new model, the tension in the rope attached at $A$ is 10 N greater than the tension in the rope attached at $B$.
\item Find the distance of the centre of mass of the plank from $A$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2008 Q6 [10]}}