| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2005 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Two-sphere oblique collision |
| Difficulty | Standard +0.8 This M4 oblique collision problem requires understanding that impulse acts along the line of centres, vector manipulation to find the unit vector, and conservation of momentum. While methodical, it demands careful vector work and conceptual understanding of collision mechanics beyond standard A-level, making it moderately challenging for Further Maths students. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors1.10b Vectors in 3D: i,j,k notation6.03a Linear momentum: p = mv6.03b Conservation of momentum: 1D two particles6.03c Momentum in 2D: vector form6.03d Conservation in 2D: vector momentum6.03e Impulse: by a force6.03f Impulse-momentum: relation6.03g Impulse in 2D: vector form |
[In this question $\mathbf{i}$ and $\mathbf{j}$ are horizontal perpendicular unit vectors.]
Two smooth uniform spheres $A$ and $B$ have equal radius but masses $m$ and $5m$ respectively. The spheres are moving on a smooth horizontal plane when they collide. Immediately before the collision, the velocities of $A$ and $B$ are $(\mathbf{i} + 2\mathbf{j})$ m s$^{-1}$ and $(-\mathbf{i} + 3\mathbf{j})$ m s$^{-1}$ respectively. Immediately after the collision, the velocity of $A$ is $(-2\mathbf{i} + 5\mathbf{j})$ m s$^{-1}$.
\begin{enumerate}[label=(\alph*)]
\item By considering the impulse on $A$, find a unit vector parallel to the line joining the centres of the spheres when they collide. [4]
\item Find the velocity of $B$ immediately after the collision. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M4 2005 Q1 [7]}}