| Exam Board | OCR |
|---|---|
| Module | Further Mechanics (Further Mechanics) |
| Year | 2021 |
| Session | June |
| Marks | 12 |
| Topic | Oblique and successive collisions |
| Type | Oblique collision, direction deflected given angle |
| Difficulty | Challenging +1.8 This is an oblique collision problem requiring resolution of velocities in two perpendicular directions, application of conservation of momentum along the line of centres, Newton's experimental law, and the perpendicularity condition to find unknowns. It demands careful vector decomposition, simultaneous equations, and energy calculations—significantly more sophisticated than standard direct impact questions, but follows established Further Mechanics techniques without requiring novel geometric insight. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03c Momentum in 2D: vector form6.03k Newton's experimental law: direct impact6.03l Newton's law: oblique impacts |
3 Two smooth circular discs $A$ and $B$ are moving on a horizontal plane. The masses of $A$ and $B$ are 3 kg and 4 kg respectively. At the instant before they collide
\begin{itemize}
\item the velocity of $A$ is $2 \mathrm {~ms} ^ { - 1 }$ at an angle of $60 ^ { \circ }$ to the line joining their centres,
\item the velocity of $B$ is $5 \mathrm {~ms} ^ { - 1 }$ towards $A$ along the line joining their centres (see Fig. 3).
\end{itemize}
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{d6bf2fa5-2f29-4632-b27d-ed8c5a0379cf-03_479_1025_1466_248}
\captionsetup{labelformat=empty}
\caption{Fig. 3}
\end{center}
\end{figure}
Given that the velocity of $A$ after the collision is perpendicular to the velocity of $A$ before the collision, find
\begin{enumerate}[label=(\alph*)]
\item the coefficient of restitution between $A$ and $B$,
\item the total loss of kinetic energy as a result of the collision.
\end{enumerate}
\hfill \mbox{\textit{OCR Further Mechanics 2021 Q3 [12]}}