Direct impact and Newton's law of restitutionEdexcel International A Level Further Maths: Mind map

Exam questions on Direct impact and Newton's law of restitution

1. Particle $A$ of mass $2$ kg moves with speed $5$ m s$^{-1}$ along a straight line on a smooth horizontal surface and collides directly with particle $B$ of mass $3$ kg, which is at rest. The coefficient of restitution between the particles is $0.5$.
   Find the magnitude of the impulse exerted by $A$ on $B$ in the collision.2 marks
2. Particles $P$ and $Q$, of mass $3$ kg and $5$ kg, move towards each other along the same straight line on a smooth horizontal surface with speeds $4$ m s$^{-1}$ and $2$ m s$^{-1}$ respectively. They collide directly. After the collision the direction of motion of $P$ is reversed and its speed is $1$ m s$^{-1}$.
   Find the total kinetic energy lost in the collision.2 marks
3. Two smooth spheres $A$ and $B$ of equal radii and masses $m$ and $3m$ lie on a smooth horizontal table. Sphere $A$ is projected with speed $u$ directly towards $B$, which is at rest. The coefficient of restitution between the spheres is $e$.
   Show that the speed of $B$ immediately after the collision is $\frac{(1+e)u}{4}$.3 marks