| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Centre of Mass 1 |
| Type | Particle attached to lamina - find mass/position |
| Difficulty | Standard +0.3 This is a standard M2 centre of mass question involving a wire frame and an attached particle. Part (a) requires finding the centre of mass of a trapezium frame by treating each side as a uniform rod (routine application of moments). Part (b) involves using equilibrium conditions when suspended, which is a standard textbook exercise. The geometry is straightforward and the calculations are methodical rather than requiring insight. Slightly easier than average A-level due to clear setup and standard techniques. |
| Spec | 6.04b Find centre of mass: using symmetry6.04e Rigid body equilibrium: coplanar forces |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(1.24 \times 8\); \(\ 0.2g \times 8\); \(\ \frac{1}{2}0.2 \cdot 20^2\) or \(\frac{1}{2}0.2v^2\) | B1;B1;B1 | B1 for each term seen or implied: 9.92, 15.68, 40 or \(0.1v^2\) |
| \(1.24 \times 8 = \frac{1}{2}0.2 \cdot 20^2 - \frac{1}{2}0.2v^2 - 0.2g \times 8\) | M1 | Condone sign errors but all terms should be present |
| Correct equation | A1 | |
| \(v = 12\) | A1 | |
| Total | [6] |
## Question 2:
| Answer/Working | Marks | Guidance |
|---|---|---|
| $1.24 \times 8$; $\ 0.2g \times 8$; $\ \frac{1}{2}0.2 \cdot 20^2$ or $\frac{1}{2}0.2v^2$ | B1;B1;B1 | B1 for each term seen or implied: 9.92, 15.68, 40 or $0.1v^2$ |
| $1.24 \times 8 = \frac{1}{2}0.2 \cdot 20^2 - \frac{1}{2}0.2v^2 - 0.2g \times 8$ | M1 | Condone sign errors but all terms should be present |
| Correct equation | A1 | |
| $v = 12$ | A1 | |
| **Total** | **[6]** | |
---2.
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{173a2029-a0b8-437f-9339-5a1b6f30a8e3-004_378_652_294_630}
\end{center}
\end{figure}
A thin uniform wire, of total length 20 cm , is bent to form a frame. The frame is in the shape of a trapezium $A B C D$, where $A B = A D = 4 \mathrm {~cm} , C D = 5 \mathrm {~cm}$, and $A B$ is perpendicular to $B C$ and $A D$, as shown in Figure 1.
\begin{enumerate}[label=(\alph*)]
\item Find the distance of the centre of mass of the frame from $A B$.
The frame has mass $M$. A particle of mass $k M$ is attached to the frame at $C$. When the frame is freely suspended from the mid-point of $B C$, the frame hangs in equilibrium with $B C$ horizontal.
\item Find the value of $k$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 Q2}}