OCR A Level: Mechanics 2 - Coefficient Of Restitution [June 2009 Q6]

Two uniform spheres, $A$ and $B$ , have the same radius. The mass of $A$ is $0.4 \text{kg}$ and the mass of $B$ is $0.2 \text{kg}$ . The spheres $A$ and $B$ are travelling in the same direction in a straight line on a smooth horizontal surface, $A$ with speed $5 \text{ms}^{-1}$ , and $B$ with speed $V \text{ms}^{-1}$ , where $V < 5$ . A collides directly with $B$ and the impulse between them has magnitude $0.9 \text{Ns}$ . Immediately after the collision, the speed of $B$ is $6 \text{ms}^{-1}$ .

$(\text{i})$ Calculate $V$ .

$B$ subsequently collides directly with a stationary sphere $C$ of mass $0.1 \text{kg}$ and the same radius as $A$ and $B$ . The coefficient of restitution between $B$ and $C$ is $0.6$ .

$(\text{ii})$ Determine whether there will be a further collision between $A$ and $B$ .

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Input $V$ if a further collision takes place, otherwise input $2V$ , to three significant figures.

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There are 3 marks available for part (i) and 10 marks for part (ii).

In total, this question is worth 18.1% of all available marks in the paper.

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This is part of the set OCR A Level Problems .