# Collisions in a System of Bodies

There are three blocks A,B and C, with B and C at rest connected by a light spring and A moving with a velocity v, all three lying on the same horizontal frictionless surface. After some time A collides elastically with B and we are required to find the maximum compression in the spring.

The problem is that in the solution they first consider the elastic collision of A and B separately and apply the momentum conservation with A and B as the system and form an equation using coefficient of restitution. Then using that velocity they do the further calculation.

I am unable to understand that how can conservation of momentum be used here as the instant A and B collide B will start accelerating and start compressing the spring therefore an external force i.e. the spring force will come into play. And can we use the coefficient of restitution as wouldn't there be change in the velocity of separation due to spring force.

Similarly when a third ball collides elastically with two balls in contact,all three of the same mass, then the ball at the extreme end gets all the velocity and in the justification the collisions are considered separately.

Conclusion: is it justified to use momentum conservation in the case of those three blocks? Can we consider the colliding bodies separately neglecting all the other bodies and their effect that they are in contact with? Can we use the coefficient of restitution to formulate equations without considering the effect of the rest of the bodies in the system?

• Spring force is non impulsive. Oct 5, 2019 at 14:16
• Can you please elaborate. Oct 5, 2019 at 14:30
• And if it is not impulsive, yet won't it start acting the moment it is compressed? And what about the balls? Oct 5, 2019 at 14:31
• Spring never reacts instantaneously Oct 5, 2019 at 14:53
• So can we use the analogy of springs in case of the collision between the balls? Oct 5, 2019 at 15:54