| Exam Board | Edexcel |
|---|---|
| Module | M4 (Mechanics 4) |
| Session | Specimen |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Impulse and momentum (advanced) |
| Type | Oblique collision of spheres |
| Difficulty | Challenging +1.2 This is an oblique collision problem requiring conservation of momentum in two perpendicular directions and Newton's experimental law. While it involves multiple steps and vector components, the approach is standard for M4: decompose velocities, apply conservation perpendicular to line of centers (unchanged components), use momentum parallel to line of centers, and apply restitution. The 'right angle deflection' constraint provides the key relationship but is a straightforward geometric condition. More challenging than basic mechanics but follows established M4 collision methodology. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03k Newton's experimental law: direct impact |
\includegraphics{figure_2}
Two smooth uniform spheres $A$ and $B$, of equal radius, are moving on a smooth horizontal plane. Sphere $A$ has mass 3 kg and velocity (2$\mathbf{i}$ + $\mathbf{j}$) m s$^{-1}$, and sphere $B$ has mass 5 kg and velocity ($-\mathbf{i}$ + $\mathbf{j}$) m s$^{-1}$. When the spheres collide the line joining their centres is parallel to $\mathbf{i}$, as shown in Fig. 2.
Given that the direction of $A$ is deflected through a right angle by the collision, find
\begin{enumerate}[label=(\alph*)]
\item the velocity of $A$ after the collision,
[5]
\item the coefficient of restitution between the spheres.
[6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M4 Q4 [11]}}