Two small smooth spheres $A$ and $B$, with equal radii and masses of $4\,\text{kg}$ and $2\,\text{kg}$ respectively, are on a smooth horizontal plane. At the beginning, $B$ is at rest, while $A$ is travelling towards $B$ at $10\,\text{m s}^{-1}$. After they collide, $A$ keeps moving in the same direction, but at half the speed of $B$.
(a)[2]
Find $B$'s speed immediately after the collision.
(b)[3]
A third small smooth sphere $C$, of mass $1\,\text{kg}$ and with the same radius as $A$ and $B$, is initially at rest on the plane. $B$ then collides directly with $C$. After this collision, $B$ continues to move in the same direction, but at one third of the speed of $C$. Show that there is another collision between $A$ and $B$.
(c)[5]
$A$ and $B$ coalesce during this collision. Determine the total loss of kinetic energy in the system caused by the three collisions.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Momentum relation written as $4\times10[+0]=4\times0.5v+2v$” …