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 .
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\caption{Fig. 4}
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- Find the speeds of A and B immediately after the collision.
- Explain why there could be a second collision between A and B if B rebounds from the wall with sufficient speed.
- 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 .
- How does your answer to part (b) change if the contact between B and the wall is not smooth?