| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2017 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Oblique and successive collisions |
| Type | Oblique collision, vector velocity form |
| Difficulty | Standard +0.3 This is a standard M4 oblique collision question requiring conservation of momentum in the j-direction, unchanged i-components (smooth spheres, line of centres parallel to j), Newton's restitution law, and solving simultaneous equations using the given kinetic energy condition. While it involves multiple steps and careful algebraic manipulation, it follows a well-established procedure that M4 students practice extensively, making it slightly easier than average. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03c Momentum in 2D: vector form6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact |
2.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{23e6a9ae-bf00-45a3-b462-e18760d9af45-04_912_988_260_470}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Two smooth uniform spheres $A$ and $B$ have masses $3 m \mathrm {~kg}$ and $m \mathrm {~kg}$ respectively and equal radii. The spheres are moving on a smooth horizontal surface. Initially, sphere $A$ has velocity $( 5 \mathbf { i } - 2 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }$ and sphere $B$ has velocity $( 3 \mathbf { i } + 4 \mathbf { j } ) \mathrm { ms } ^ { - 1 }$. When the spheres collide, the line joining their centres is parallel to $\mathbf { j }$, as shown in Figure 1.\\
The coefficient of restitution between the two spheres is $e$.\\
The kinetic energy of sphere $B$ immediately after the collision is $85 \%$ of its kinetic energy immediately before the collision.
Find
\begin{enumerate}[label=(\alph*)]
\item the velocity of each sphere immediately after the collision,
\item the value of $e$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M4 2017 Q2 [12]}}