| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Year | 2006 |
| Session | June |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Impulse and momentum (advanced) |
| Type | Oblique collision of spheres |
| Difficulty | Challenging +1.2 This is a standard M4 oblique collision problem requiring resolution of velocities along/perpendicular to the line of centres, application of conservation of momentum and Newton's restitution law, followed by projectile motion to the wall. While multi-step with 14 marks total, it follows a well-established procedure taught explicitly in M4 with no novel insight required—just careful bookkeeping of the geometry and standard formulae application. |
| Spec | 3.02i Projectile motion: constant acceleration model6.03k Newton's experimental law: direct impact6.03l Newton's law: oblique impacts |
\includegraphics{figure_2}
Two small smooth spheres $A$ and $B$, of equal size and of mass $m$ and $2m$ respectively, are moving initially with the same speed $U$ on a smooth horizontal floor. The spheres collide when their centres are on a line $L$. Before the collision the spheres are moving towards each other, with their directions of motion perpendicular to each other and each inclined at an angle of $45°$ to the line $L$, as shown in Figure 2. The coefficient of restitution between the spheres is $\frac{1}{2}$.
\begin{enumerate}[label=(\alph*)]
\item Find the magnitude of the impulse which acts on $A$ in the collision.
[9]
\end{enumerate}
\includegraphics{figure_3}
The line $L$ is parallel to and a distance $d$ from a smooth vertical wall, as shown in Figure 3.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find, in terms of $d$, the distance between the points at which the spheres first strike the wall.
[5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M4 2006 Q6 [14]}}