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

Classical Mechanics Level pending

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 $$B$$.

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

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