| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2016 |
| Session | October |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Centre of Mass 1 |
| Type | Particles at coordinate positions |
| Difficulty | Moderate -0.8 This is a straightforward application of the centre of mass formula for particles in 2D. Students substitute coordinates into the standard formula, use the y-coordinate equation to find k, then use the x-coordinate equation to find c. It requires only direct formula application with basic algebra, making it easier than average but not trivial since it involves two unknowns and coordinate manipulation. |
| Spec | 6.04b Find centre of mass: using symmetry6.04c Composite bodies: centre of mass |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Notes |
| Take moments about the \(x\)-axis | M1 | All terms needed and no extras. Must be dimensionally correct. Condone sign errors |
| \(m \times 2 + 4m \times 3 - km \times 4 = 0\) | A1 | Correct unsimplified equation |
| \(4k = 14\), \(k = 3.5\) | A1 | Or equivalent |
| (3 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Notes |
| Take moments about the \(y\)-axis: \(m \times -3 + 4m \times 4 + km \times 6 = (5+k)m \times c\) | M1 | Allow when seen. All terms needed. Must be dimensionally correct. Condone sign errors |
| \(-3 + 16 + 21(6k) = 8.5c\) | A1ft | ft their \(k\) |
| \(c = 4\) | A1 | |
| (3 marks) |
# Question 1:
## Part 1a:
| Working | Mark | Notes |
|---------|------|-------|
| Take moments about the $x$-axis | M1 | All terms needed and no extras. Must be dimensionally correct. Condone sign errors |
| $m \times 2 + 4m \times 3 - km \times 4 = 0$ | A1 | Correct unsimplified equation |
| $4k = 14$, $k = 3.5$ | A1 | Or equivalent |
| **(3 marks)** | | |
## Part 1b:
| Working | Mark | Notes |
|---------|------|-------|
| Take moments about the $y$-axis: $m \times -3 + 4m \times 4 + km \times 6 = (5+k)m \times c$ | M1 | Allow when seen. All terms needed. Must be dimensionally correct. Condone sign errors |
| $-3 + 16 + 21(6k) = 8.5c$ | A1ft | ft their $k$ |
| $c = 4$ | A1 | |
| **(3 marks)** | | |
---\begin{enumerate}
\item Three particles of masses $m , 4 m$ and $k m$ are placed at the points whose coordinates are $( - 3,2 ) , ( 4,3 )$ and $( 6 , - 4 )$ respectively. The centre of mass of the three particles is at the point with coordinates $( c , 0 )$.
\end{enumerate}
Find\\
(a) the value of $k$,\\
(b) the value of $c$.\\
\hfill \mbox{\textit{Edexcel M2 2016 Q1 [6]}}