| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2005 |
| Session | June |
| Marks | 8 |
| 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 particle attachment. Part (a) requires dividing the trapezium into segments and using the standard formula for composite bodies. Part (b) involves taking moments about the suspension point with BC horizontal. Both parts follow routine procedures taught in M2 with no novel insight required, making it slightly easier than average. |
| Spec | 6.04b Find centre of mass: using symmetry6.04c Composite bodies: centre of mass6.04e Rigid body equilibrium: coplanar forces |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Notes |
| \(M(AB): 7 \times 3.5 + 5 \times 5.5 + 4 \times 2 = 20 \times \bar{x}\) | M1 A2,1,0 | |
| \(\Rightarrow 20\bar{x} = 24.5 + 27.5 + 8 = 60 \Rightarrow \bar{x} = 3 \text{ cm}\) | dep M1 A1 | |
| (5) |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Notes |
| \(M(XY): M \times (3.5 - 3) = kM \times 3.5\) | M1 A1 | \(\checkmark\) |
| \(\Rightarrow k = \frac{1}{7}\) | A1 | |
| (3) |
## Question 2:
### Part (a):
| Working | Marks | Notes |
|---------|-------|-------|
| $M(AB): 7 \times 3.5 + 5 \times 5.5 + 4 \times 2 = 20 \times \bar{x}$ | M1 A2,1,0 | |
| $\Rightarrow 20\bar{x} = 24.5 + 27.5 + 8 = 60 \Rightarrow \bar{x} = 3 \text{ cm}$ | dep M1 A1 | |
| | **(5)** | |
### Part (b):
| Working | Marks | Notes |
|---------|-------|-------|
| $M(XY): M \times (3.5 - 3) = kM \times 3.5$ | M1 A1 | $\checkmark$ |
| $\Rightarrow k = \frac{1}{7}$ | A1 | |
| | **(3)** | |
---2.
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{3847deb8-d86e-4254-828f-5d62f20c186f-03_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 2005 Q2 [8]}}