| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Collision with vector velocities |
| Difficulty | Standard +0.3 This is a standard M2 oblique collision problem requiring conservation of momentum in vector form and impulse calculation. While it involves multiple steps and vector components, the techniques are routine for M2 students: apply momentum conservation to find B's final velocity, then calculate impulse from change in momentum. The vector arithmetic is straightforward with no geometric insight or novel problem-solving required. |
| Spec | 6.03c Momentum in 2D: vector form6.03d Conservation in 2D: vector momentum6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Impulse \(= 2m[(5\mathbf{i} + \mathbf{j}) - (3\mathbf{i} - \mathbf{j})] = 2m(2\mathbf{i} + 2\mathbf{j})\) | M1 A1 | |
| Magnitude \(= 4m\sqrt{2} \text{ Ns}\) or \(5.66m \text{ Ns}\) | M1 A1 | |
| (b) \(2m(3\mathbf{i} - \mathbf{j}) + 3m(4\mathbf{i} + \mathbf{j}) = 2m(5\mathbf{i} + \mathbf{j}) + 3m\mathbf{v}_B\) | M1 A1 | |
| \(3\mathbf{v}_B = 8\mathbf{i} - \mathbf{j}\) | M1 A1 | |
| \( | \mathbf{v}_B | = \frac{1}{3}\sqrt{65}\) |
**(a)** Impulse $= 2m[(5\mathbf{i} + \mathbf{j}) - (3\mathbf{i} - \mathbf{j})] = 2m(2\mathbf{i} + 2\mathbf{j})$ | M1 A1 |
Magnitude $= 4m\sqrt{2} \text{ Ns}$ or $5.66m \text{ Ns}$ | M1 A1 |
**(b)** $2m(3\mathbf{i} - \mathbf{j}) + 3m(4\mathbf{i} + \mathbf{j}) = 2m(5\mathbf{i} + \mathbf{j}) + 3m\mathbf{v}_B$ | M1 A1 |
$3\mathbf{v}_B = 8\mathbf{i} - \mathbf{j}$ | M1 A1 |
$|\mathbf{v}_B| = \frac{1}{3}\sqrt{65}$ | M1 A1 A1 | Speed of $B = 2.69 \text{ ms}^{-1}$
**Total: 9 marks**
---Two smooth spheres $A$ and $B$, of masses $2m$ and $3m$ respectively, are moving on a smooth horizontal table with velocities $(3\mathbf{i} - \mathbf{j})$ ms$^{-1}$ and $(4\mathbf{i} + \mathbf{j})$ ms$^{-1}$, where $\mathbf{i}$ and $\mathbf{j}$ are perpendicular unit vectors. They collide, after which $A$ has velocity $(5\mathbf{i} + \mathbf{j})$ ms$^{-1}$.
\begin{enumerate}[label=(\alph*)]
\item Find the magnitude of the impulse exerted on $B$ by $A$, stating the units of your answer. [4 marks]
\item Find the speed of $B$ immediately after the collision. [5 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 Q4 [9]}}