Successive impactsEdexcel International A Level Further Maths: Mind map

Exam questions on Successive impacts

1. A particle of mass $0.4$ kg moves with speed $12$ m s$^{-1}$ along smooth horizontal ground directly towards a fixed smooth vertical wall, hitting the wall at right angles. The coefficient of restitution between the particle and the wall is $\frac23$.
   Find the magnitude of the impulse exerted by the wall on the particle.2 marks
2. Particles $A$ and $B$ have masses $2$ kg and $1$ kg. They lie on smooth horizontal ground in a straight line perpendicular to a fixed smooth vertical wall, with $B$ between $A$ and the wall. Particle $A$ is projected towards $B$ with speed $6$ m s$^{-1}$. The coefficient of restitution between $A$ and $B$ is $\frac12$, and between $B$ and the wall is $\frac13$.
   Explain why there must be a second collision between $A$ and $B$.2 marks
3. Three particles $A$, $B$ and $C$, of masses $4$ kg, $2$ kg and $3$ kg, lie at rest in a straight line on smooth horizontal ground, with $B$ between $A$ and $C$. Particle $A$ is projected towards $B$ with speed $6$ m s$^{-1}$. The coefficient of restitution between any two of the particles is $\frac12$.
   Show that, immediately after the first collision, $A$ has speed $3$ m s$^{-1}$ and $B$ has speed $6$ m s$^{-1}$.3 marks