| Exam Board | OCR |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2009 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Impulse and momentum (advanced) |
| Type | Oblique collision of spheres |
| Difficulty | Standard +0.8 This is a 2D oblique collision problem requiring resolution of velocities parallel and perpendicular to the line of centres, application of conservation of momentum in the direction of the line of centres, and use of Newton's experimental law. The constraint that A moves perpendicular to the line of centres after collision provides a key condition that makes the problem tractable but requires careful geometric reasoning. While the techniques are standard M3 content, the multi-step nature, coordinate resolution, and the need to work backwards from the given constraint make this moderately challenging. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03d Conservation in 2D: vector momentum6.03i Coefficient of restitution: e6.03k Newton's experimental law: direct impact |
\includegraphics{figure_3}
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 $3 \text{ m s}^{-1}$. The spheres are moving in opposite directions, each at $60°$ to the line of centres (see diagram). After the collision $A$ moves in a direction perpendicular to the line of centres.
\begin{enumerate}[label=(\roman*)]
\item 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. [8]
\item Find the coefficient of restitution between the spheres. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR M3 2009 Q3 [10]}}