Question

A light spring of spring constant k is kept compressed between two blocks of masses m and M on a smooth horizontal surface. When released, the blocks acquire velocities in opposite directions. The spring loses contact with the blocks when it acquires natural length. The spring was initially compressed through a distance d find the final speeds of the two blocks.

Answer 1

As net external force acting on the system is zero `("net" F_(ext)=0)`
`therefore`Applying conservation of momentum in horizontal direction

`P_(f)=P_(i)`
`MV_(2)-mv_(1)=0`…(i)
applying conservation of mechanical energy (as no work is done)
`(1)/(2)kx^(2)=(1)/(2)mv_(1)^(2)+(1)/(2)MV_(2)^(2)`.....(ii)
`v_(1)=sqrt((MK)/(m(m+M))),v_(2)=sqrt((mK)/(M(m+M)))`