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

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

1. Two smooth spheres $A$ and $B$ of equal radii, with masses $2$ kg and $3$ kg, move towards each other along the same straight line on a smooth horizontal surface. $A$ has speed $5$ m s$^{-1}$ and $B$ has speed $2$ m s$^{-1}$. They collide directly. The coefficient of restitution between the spheres is $0.5$.
   Hence find the velocity of $B$ after the collision, stating its direction.2 marks
2. A smooth ball of mass $0.3$ kg strikes a fixed smooth vertical wall at right angles with speed $8$ m s$^{-1}$. The coefficient of restitution between the ball and the wall is $0.5$.
   Find the kinetic energy lost by the ball in the impact.2 marks
3. Two smooth spheres $A$ and $B$ of equal radii have masses $m$ and $3m$. They lie on a smooth horizontal surface. $A$ moves with speed $6$ m s$^{-1}$ and collides directly with $B$, which is at rest. The coefficient of restitution between the spheres is $\frac12$.
   Find the speed of $A$ and the speed of $B$ immediately after the collision.3 marks