Each of the blocks shown in figure has mass 1 kg. The rear block moves with a speed of 2 m/s towards the front block kept at rest. The spring attached to the front block is light and has a spring constant 50 N/m. find the maximum compression of the spring.

Explanation

EMaximum compression will take place when the blocks move with equal velocity. As no net external horizontal force acts on the system of the two blocks, the total linear momentum will remain constant. If V is the common speed at maximum compression, we have,
`(1kg) (2m//s)=(1kg)V+(1kg)V`
or, `V=1m//s.`
Initial kinetic energy `=(1)/(2)(1kg)(2m//s)^(2)=2J`.
Final kinetic energy
`=(1)/(2)(1kg)(1m//s)^(2)+(1)/(2)(1kg)(1m//s)^(2)=1J`
The kinetic energy lost is stored as the elastic energy in the spring.
Hence, `(1)/(2)(50N//m)x^(2)=2J-1J=1J`
or, x = 0.2 m.