Two blocks A and B of masses m and 2m, respectively are connected by a spring of force constant k. The masses are moving to the right with uniform velocity v each, the heavier mass leading the lighter one. The spring is in the natural length during this motion. Block B collides head on with a third block C of mass m, at rest, the collision being completely inelastic. Calculate the maximum compression of the spring.

Two blocks A and B of masses m and 2m, respectively are connected by a

1.	Two blocks A and B of masses m and 2m, respectively are connected by a spring of force constant k. The masses are moving to the right with uniform velocity v each, the heavier mass leading the lighter one. The spring is in the natural length during this motion. Block B collides head on with a third block C of mass m, at rest, the collision being completely inelastic. Calculate the maximum compression of the spring.
Answer» Solution :First considering an inelastic collision between `B` and `C`. `2mv(m+2m)v_(B)` `v_(B)=2/3v` VELOCITY of (`B` and `C`) Then velocity of centre of MASS during MAXIMUM compression `v_(CM)=(3MV)/(4m)=3/4v` `1/2mv_(4)^(2)+1/23mv_((b+c))^(2)=1/24mv_(CM)^(2)+1/2kx^(2)` Then substituting the value `x=sqrt((MV^(2))/(12k))`