| Exam Board | SPS |
|---|---|
| Module | SPS FM Mechanics (SPS FM Mechanics) |
| Year | 2024 |
| Session | January |
| Marks | 10 |
| Topic | Oblique and successive collisions |
| Type | Oblique collision, direction deflected given angle |
| Difficulty | Challenging +1.2 This is an oblique collision problem requiring conservation of momentum parallel and perpendicular to the line of centres, plus Newton's experimental law. While it involves multiple steps and careful component resolution, the structure is standard for Further Maths mechanics: given information leads directly to showing B's speed is unchanged, then finding the angle and coefficient of restitution follows systematically. The 'show that' part provides scaffolding, making this a moderately challenging but routine FM mechanics question. |
| Spec | 6.03c Momentum in 2D: vector form6.03d Conservation in 2D: vector momentum6.03k Newton's experimental law: direct impact6.03l Newton's law: oblique impacts |
3.\\
\includegraphics[max width=\textwidth, alt={}, center]{5f9a87c6-2255-4178-ab04-441bb0cc4ce0-06_397_878_159_571}
Two uniform smooth spheres $A$ and $B$, of equal radius, have masses 4 kg and 2 kg respectively. They are moving on a horizontal surface when they collide. Immediately before the collision both spheres have speed $3 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The spheres are moving in opposite directions, each at $60 ^ { \circ }$ to the line of centres (see diagram). After the collision $A$ moves in a direction perpendicular to the line of centres.\\
(i) Show that the speed of $B$ is unchanged as a result of the collision, and find the angle that the new direction of motion of $B$ makes with the line of centres.\\
(ii) Find the coefficient of restitution between the spheres.\\[0pt]
[Question 3 Continued]\\
\hfill \mbox{\textit{SPS SPS FM Mechanics 2024 Q3 [10]}}