| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2011 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Uniform beam on two supports |
| Difficulty | Moderate -0.8 This is a straightforward M1 moments question requiring standard application of equilibrium conditions (sum of moments = 0, sum of forces = 0) with clearly defined geometry. Part (a) involves taking moments about one point to find reactions, while part (b) requires setting two reactions equal and solving for a distance. No novel insight or complex problem-solving is needed—just routine application of textbook methods. |
| Spec | 3.04b Equilibrium: zero resultant moment and force |
| Answer | Marks | Guidance |
|---|---|---|
| Part | Answer/Working | Marks |
| (a) | Taking moments about B: \(5 \times R_C = 20g \times 3\) → \(R_C = 12g\) or \(60g/5\) or \(118\) or \(120\) | M1 A1 A1 |
| Resolving vertically: \(R_C + R_B = 20g\) → \(R_B = 8g\) or \(78.4\) or \(78\) | M1 A1 | (5 marks) |
| (b) | Resolving vertically: \(50g = R + R\) | B1 |
| Taking moments about B: \(5 \times 25g = 3 \times 20g + (6-x) \times 30g\) | M1 A1 A1 | |
| \(30x = 115\) → \(x = 3.8\) or better or \(23/6\) oe | A1 | (5 marks) |
| [10 marks total] |
| **Part** | **Answer/Working** | **Marks** | **Guidance** |
|----------|-------------------|----------|-------------|
| (a) | Taking moments about B: $5 \times R_C = 20g \times 3$ → $R_C = 12g$ or $60g/5$ or $118$ or $120$ | M1 A1 A1 | |
| | Resolving vertically: $R_C + R_B = 20g$ → $R_B = 8g$ or $78.4$ or $78$ | M1 A1 | (5 marks) |
| (b) | Resolving vertically: $50g = R + R$ | B1 | |
| | Taking moments about B: $5 \times 25g = 3 \times 20g + (6-x) \times 30g$ | M1 A1 A1 | |
| | $30x = 115$ → $x = 3.8$ or better or $23/6$ oe | A1 | (5 marks) |
| | | | **[10 marks total]** |3.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{4878b6c2-0c62-4398-8a8f-913139bc8a14-04_245_860_260_543}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
A uniform beam $A B$ has mass 20 kg and length 6 m . The beam rests in equilibrium in a horizontal position on two smooth supports. One support is at $C$, where $A C = 1 \mathrm {~m}$, and the other is at the end $B$, as shown in Figure 1. The beam is modelled as a rod.
\begin{enumerate}[label=(\alph*)]
\item Find the magnitudes of the reactions on the beam at $B$ and at $C$.
A boy of mass 30 kg stands on the beam at the point $D$. The beam remains in equilibrium. The magnitudes of the reactions on the beam at $B$ and at $C$ are now equal. The boy is modelled as a particle.
\item Find the distance $A D$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2011 Q3 [10]}}