| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2013 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Centre of Mass 1 |
| Type | Particles at coordinate positions |
| Difficulty | Moderate -0.3 This is a straightforward application of the centre of mass formula with two unknowns. Students must set up and solve two linear equations using the standard formula (sum of mass×position)/(total mass) = centre of mass coordinate. While it requires careful algebraic manipulation across two parts, it's a routine textbook exercise with no conceptual challenges beyond direct formula application, making it slightly easier than average. |
| Spec | 6.04b Find centre of mass: using symmetry |
| Answer | Marks | Guidance |
|---|---|---|
| \(6 - 3 + 4m = (m+5) \times 2\) | M1 | Moments equation for y coordinate. Terms of correct structure but condone sign slips |
| \(7 = 2m\) | A2 | -1 each error |
| \(m = 3.5\) | A1(4) |
| Answer | Marks | Guidance |
|---|---|---|
| \(2a + 9 - 2m = 0 (x(m+5))\) | M1 | Moments equation for x coordinate. Terms of correct structure but condone sign slips |
| A1 | ||
| \(2a + 9 - 7 = 0\) | M1 | Substitute their m and solve for a |
| use their \(m\) | ||
| \(a = -1\) | A1(4) | |
| [8] |
**(a)**
| $6 - 3 + 4m = (m+5) \times 2$ | M1 | Moments equation for y coordinate. Terms of correct structure but condone sign slips |
| $7 = 2m$ | A2 | -1 each error |
| $m = 3.5$ | A1(4) | |
**(b)**
| $2a + 9 - 2m = 0 (x(m+5))$ | M1 | Moments equation for x coordinate. Terms of correct structure but condone sign slips |
| | A1 | |
| $2a + 9 - 7 = 0$ | M1 | Substitute their m and solve for a |
| use their $m$ | | |
| $a = -1$ | A1(4) | |
| | [8] | |Three particles of masses 2 kg, 3 kg and $m$ kg are positioned at the points with coordinates $(a, 3)$, $(3, -1)$ and $(-2, 4)$ respectively. Given that the centre of mass of the particles is at the point with coordinates $(0, 2)$, find
\begin{enumerate}[label=(\alph*)]
\item the value of $m$, [4]
\item the value of $a$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2013 Q1 [8]}}