A block of mass 2.0 kg is moving on a frictionless horizontal surface with a velocity of 1.0 m/s (figure 9-E12) towards another block of equal mass kept at rest. The spring constant of the spring fixed at one end is 100 N/m. Find the maximum compression of the spring.


Mass of each block M1 and M2 is 2 kg,


Velocity of the first block v1= 1 m/s,


Velocity of the second block v2= 0 m/s,


Spring constant of the spring is 100 N/m.


Then, block first strikes spring with velocity 1 m/s


After collision velocity starts to decrease continuously and at instant whole system i.e., block 1 and block 2 starts moving together with common velocity.


Let the velocity be v


Using law of conservation energy




______ (1)


As there is no external force in horizontal direction, the momentum should be conserved.





___________ (2)


Putting in equation (1)








So, the maximum compression of the spring will be 10 cm.


1