| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2007 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Uniform beam on two supports |
| Difficulty | Moderate -0.3 This is a standard M1 moments question requiring taking moments about a point and solving linear equations. Part (a) is straightforward application of the moments principle with one unknown. Part (b) requires similar reasoning with an additional mass. Both parts are routine textbook exercises with no novel problem-solving 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) \(M(C) 8g \times (0.9 - 0.75) = mg(1.5 - 0.9)\) | M1 A1 | (4 marks) |
| Solving to \(m = 2\) ⭐ | cso DM1 A1 | |
| (b) \(M(D): 5g \times x = 8g \times (0.75 - x) + 2g(1.5 - x)\) | M1 A2(1, 0) | (5 marks) |
| Solving to \(x = 0.6\) \((AD = 0.6\) m\()\) | DM1 A1 | |
| [9] |
**(a)** $M(C) 8g \times (0.9 - 0.75) = mg(1.5 - 0.9)$ | M1 A1 | (4 marks)
Solving to $m = 2$ ⭐ | cso DM1 A1 |
**(b)** $M(D): 5g \times x = 8g \times (0.75 - x) + 2g(1.5 - x)$ | M1 A2(1, 0) | (5 marks)
Solving to $x = 0.6$ $(AD = 0.6$ m$)$ | DM1 A1 |
| | [9] |3.
\begin{figure}[h]
\begin{center}
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\caption{Figure 2}
\includegraphics[alt={},max width=\textwidth]{5b5d70b1-1eb6-461f-9277-5912b914f443-04_282_842_296_561}
\end{center}
\end{figure}
A uniform rod $A B$ has length 1.5 m and mass 8 kg . A particle of mass $m \mathrm {~kg}$ is attached to the rod at $B$. The rod is supported at the point $C$, where $A C = 0.9 \mathrm {~m}$, and the system is in equilibrium with $A B$ horizontal, as shown in Figure 2.
\begin{enumerate}[label=(\alph*)]
\item Show that $m = 2$.
A particle of mass 5 kg is now attached to the rod at $A$ and the support is moved from $C$ to a point $D$ of the rod. The system, including both particles, is again in equilibrium with $A B$ horizontal.
\item Find the distance $A D$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2007 Q3 [9]}}