Mathematics 9709 · AS & A Level · Momentum

Momentum — practice question

Two small smooth spheres $A$ and $B$, with equal radii and masses $km\ \text{kg}$ and $m\ \text{kg}$ respectively, where $k > 1$, are able to move freely on a smooth horizontal plane. $A$ moves towards $B$ at speed $6\ \text{m s}^{-1}$, and $B$ moves towards $A$ at speed $2\ \text{m s}^{-1}$. Following the collision, $A$ and $B$ coalesce and then travel with speed $4\ \text{m s}^{-1}$.
(a)[3]

Find the value of $k$.

(b)[2]

Find, in terms of $m$, the loss of kinetic energy caused by the collision.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: An attempt to apply conservation of momentum, with all four terms implied

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