| Exam Board | SPS |
|---|---|
| Module | SPS FM Mechanics (SPS FM Mechanics) |
| Year | 2025 |
| Session | January |
| Marks | 9 |
| Topic | Oblique and successive collisions |
| Type | Oblique collision, direction deflected given angle |
| Difficulty | Challenging +1.2 This is a standard oblique collision problem requiring conservation of momentum along the line of centres, Newton's experimental law, and the principle that velocity perpendicular to the line of centres is unchanged. While it involves multiple steps and careful angle work, it follows a well-established method taught in Further Maths mechanics with no novel insight required. |
| Spec | 6.03k Newton's experimental law: direct impact6.03l Newton's law: oblique impacts |
1.
A smooth uniform sphere $A$, of mass $5 m$ and radius $r$, is at rest on a smooth horizontal plane. A second smooth uniform sphere $B$, of mass $3 m$ and radius $r$, is moving in a straight line on the plane with speed $u \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and strikes $A$. Immediately before the impact the direction of motion of $B$ makes an angle of $60 ^ { \circ }$ with the line of centres of the spheres. The direction of motion of $B$ is turned through an angle of $30 ^ { \circ }$ by the impact.
Find
\begin{enumerate}[label=(\alph*)]
\item the speed of $B$ immediately after the impact,
\item the coefficient of restitution between the spheres.
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Mechanics 2025 Q1 [9]}}