| Exam Board | OCR |
|---|---|
| Module | M3 (Mechanics 3) |
| Session | Specimen |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Oblique and successive collisions |
| Type | Oblique collision, direction deflected given angle |
| Difficulty | Challenging +1.2 This is a standard M3 oblique collision problem requiring resolution of velocities, conservation of momentum in two directions, and Newton's experimental law. While it involves multiple equations and some algebraic manipulation, the setup is conventional and the techniques are well-practiced at this level. The perpendicular motion condition and equal speeds constraint make it more structured than open-ended, though it requires careful systematic work across both parts. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03c Momentum in 2D: vector form6.03i Coefficient of restitution: e6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact |
2\\
\includegraphics[max width=\textwidth, alt={}, center]{bfa6d51d-0992-4f43-adab-77ce893c1ca9-2_296_798_461_694}
A sphere $A$ of mass $m$, moving on a horizontal surface, collides with another sphere $B$ of mass $2 m$, which is at rest on the surface. The spheres are smooth and uniform, and have equal radius. Immediately before the collision, $A$ has velocity $u$ at an angle $\theta ^ { \circ }$ to the line of centres of the spheres (see diagram). Immediately after the collision, the spheres move in directions that are perpendicular to each other.\\
(i) Find the coefficient of restitution between the spheres.\\
(ii) Given that the spheres have equal speeds after the collision, find $\theta$.
\hfill \mbox{\textit{OCR M3 Q2 [7]}}