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

Classical Mechanics Level pending

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 $$m$$.

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

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