| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2018 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Oblique and successive collisions |
| Type | Oblique collision, vector velocity form |
| Difficulty | Standard +0.8 This M4 oblique collision question requires multiple sophisticated steps: applying conservation of momentum in 2D, using the geometric constraint that impulse acts along the line of centres, and applying Newton's law of restitution in the correct direction. While the calculations are manageable, the conceptual understanding of oblique collisions (that momentum perpendicular to line of centres is conserved for each sphere individually) elevates this above standard mechanics questions. It's harder than typical A-level but not exceptionally so for M4 material. |
| Spec | 6.03c Momentum in 2D: vector form6.03d Conservation in 2D: vector momentum6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact |
7. Two smooth uniform spheres $A$ and $B$, of mass 2 kg and 3 kg respectively, and of equal radius, are moving on a smooth horizontal plane when they collide. Immediately before the collision the velocity of $A$ is $( 3 \mathbf { i } + \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }$ and the velocity of $B$ is $( - \mathbf { i } + 2 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }$. Immediately after the collision the velocity of $A$ is $( \mathbf { i } + 3 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }$.
\begin{enumerate}[label=(\alph*)]
\item Show that, at the instant when $A$ and $B$ collide, their line of centres is parallel to $- \mathbf { i } + \mathbf { j }$.
\item Find the velocity of $B$ immediately after the collision.
\item Find the coefficient of restitution between $A$ and $B$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M4 2018 Q7 [13]}}