OCR A Level: Mechanics 2 - Coefficient Of Restitution [January 2011 Q7]

Three small smooth spheres $A$ , $B$ and $C$ of masses $0.2 \text{kg}$ , $0.7 \text{kg}$ and $m \text{kg}$ respectively are free to move in a straight line on a smooth horizontal table. Initially $B$ and $C$ are stationary and $A$ is moving with velocity $1.8 \text{ms} ^{-1}$ directly towards $B$ . The coefficient of restitution for the collision between $A$ and $B$ is $e$ . Immediately after this collision the speed of $A$ is greater than the speed of $B$ .

$(\text{i})$ Calculate the set of possible values of $e$ .

It is now given that the speed of $B$ immediately after the collision with $A$ is $0.75 \text{ms} ^{-1}$ . $B$ continues its motion and strikes $C$ directly in a perfectly elastic collision. $B$ has speed $0.25 \text{ms} ^{-1}$ immediately after its collision with $C$ .

$(\text{ii})$ Calculate the two possible values of $m$ .

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Input the sum of the two possible values of $m$ as your answer.

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There are 9 marks available for part (i) and 6 marks for part (ii).

In total, this question is worth 20.8% of all available marks in the paper.

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This is part of the set OCR A Level Problems .