| Exam Board | CAIE |
|---|---|
| Module | Further Paper 3 (Further Paper 3) |
| Year | 2020 |
| Session | Specimen |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Oblique collision of spheres |
| Difficulty | Challenging +1.2 This is a standard oblique collision problem requiring resolution of velocities along/perpendicular to the line of centres, conservation of momentum, and Newton's restitution law. While it involves multiple steps and careful component work, the techniques are routine for Further Maths mechanics students. The 'show that' part provides a target to verify, reducing problem-solving demand. Part (b) is straightforward energy calculation once velocities are found. |
| Spec | 6.02j Conservation with elastics: springs and strings6.03k Newton's experimental law: direct impact |
\includegraphics{figure_4}
Two uniform smooth spheres $A$ and $B$ of equal radii have masses $m$ and $2m$ respectively. Sphere $B$ is at rest on a smooth horizontal surface. Sphere $A$ is moving on the surface with speed $u$ at an angle of $30°$ to the line of centres of $A$ and $B$ when it collides with $B$ (see diagram). The coefficient of restitution between the spheres is $e$.
\begin{enumerate}[label=(\alph*)]
\item Show that the speed of $B$ after the collision is $\frac{\sqrt{3}}{6}u(1 + e)$ and find the speed of $A$ after the collision. [6]
\item Given that $e = \frac{1}{2}$, find the loss of kinetic energy as a result of the collision. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE Further Paper 3 2020 Q4 [9]}}