| Exam Board | SPS |
|---|---|
| Module | SPS FM Mechanics (SPS FM Mechanics) |
| Year | 2022 |
| Session | January |
| Marks | 9 |
| Topic | Impulse and momentum (advanced) |
| Type | Oblique collision of spheres |
| Difficulty | Challenging +1.3 This is a standard 2D collision problem requiring conservation of momentum (parallel and perpendicular to line of centres) and Newton's experimental law. While it involves multiple steps and vector decomposition, the techniques are routine for Further Maths mechanics students, with no novel insight required beyond applying standard formulae systematically. |
| Spec | 6.03k Newton's experimental law: direct impact6.03l Newton's law: oblique impacts |
\includegraphics{figure_4}
Two uniform smooth spheres A and B of equal radius are moving on a horizontal surface when they collide. A has mass 0.1 kg and B has mass 0.4 kg. Immediately before the collision A is moving with speed 2.8 ms$^{-1}$ along the line of centres, and B is moving with speed 1 ms$^{-1}$ at an angle $\theta$ to the line of centres, where $\cos \theta = 0.8$ (see diagram). Immediately after the collision A is stationary. Find:
\begin{enumerate}[label=(\roman*)]
\item the coefficient of restitution between A and B,
[5]
\item the angle turned through by the direction of motion of B as a result of the collision.
[4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Mechanics 2022 Q4 [9]}}