OCR MEI Further Mechanics B AS 2019 June — Question 4

Exam BoardOCR MEI
ModuleFurther Mechanics B AS (Further Mechanics B AS)
Year2019
SessionJune
TopicMomentum and Collisions 2

4 Two uniform discs, A of mass 0.2 kg and B of mass 0.5 kg , collide with smooth contact while moving on a smooth horizontal surface.
Immediately before the collision, A is moving with speed \(0.5 \mathrm {~ms} ^ { - 1 }\) at an angle \(\alpha\) with the line of centres, where \(\sin \alpha = 0.6\), and B is moving with speed \(0.3 \mathrm {~ms} ^ { - 1 }\) at right angles to the line of centres. A straight smooth vertical wall is situated to the right of B , perpendicular to the line of centres, as shown in Fig. 4. The coefficient of restitution between A and B is 0.75 . \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4acb019b-e630-4766-9d7f-39bc0e174ba1-3_725_1131_1361_242} \captionsetup{labelformat=empty} \caption{Fig. 4}
\end{figure}
  1. Find the speeds of A and B immediately after the collision.
  2. Explain why there could be a second collision between A and B if B rebounds from the wall with sufficient speed.
  3. Find the range of values of the coefficient of restitution between B and the wall for which there will be a second collision between A and B .
  4. How does your answer to part (b) change if the contact between B and the wall is not smooth?