| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Centre of Mass 1 |
| Type | Centre of mass with variable parameter |
| Difficulty | Standard +0.3 This is a straightforward centre of mass calculation requiring students to set up moments about a reference point and solve for the height, then use a given value to find a ratio. The geometry is simple (rectangular board with two supports), the calculation involves basic algebraic manipulation, and part (b) is a routine 'given the answer, find the parameter' question. Slightly easier than average due to the clear setup and standard technique. |
| Spec | 6.04b Find centre of mass: using symmetry6.04c Composite bodies: centre of mass |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(M(2.5) + 2m(1) = (M + 2m)\bar{x}\) | M1 A1 M1 A1 | |
| \(\bar{x} = \frac{5M + 4m}{2M + 4m}\) | ||
| (b) \(5M + 4m = 2.2(2M + 4m)\) | M1 A1 | |
| \(0.6M = 4.8m\) | ||
| \(M : m = 8 : 1\) | A1 A1 | 7 marks |
(a) $M(2.5) + 2m(1) = (M + 2m)\bar{x}$ | M1 A1 M1 A1 |
$\bar{x} = \frac{5M + 4m}{2M + 4m}$ | |
(b) $5M + 4m = 2.2(2M + 4m)$ | M1 A1 |
$0.6M = 4.8m$ | |
$M : m = 8 : 1$ | A1 A1 | 7 marks5.\\
\includegraphics[max width=\textwidth, alt={}, center]{9e1d8a2f-0c35-4398-98ff-083ec76653ec-1_367_529_2122_383}
A sign-board consists of a rectangular sheet of metal, of mass $M$, which is 3 metres wide and 1 metre high, attached to two thin metal supports, each of mass $m$ and length 2 metres. The board stands on horizontal ground.\\
(a) Calculate the height above the ground of the centre of mass of the sign-board, in terms of $M$ and $m$.
Given now that the centre of mass of the sign-board is $2 \cdot 2$ metres above the ground, (b) find the ratio $M : m$, in its simplest form.
\section*{MECHANICS 2 (A) TEST PAPER 9 Page 2}
\hfill \mbox{\textit{Edexcel M2 Q5 [7]}}