Two identical blocks A and B each of mass 2 kg move with velocities v _(1) = 10 m//sand v _(2) = 5m//salong a smooth horizontal plane. The block B has a spring, attached to its rear end of spring constant k = 500 N/m. Find the maximum compression undergone by the spring.

Two identical blocks A and B each of mass 2 kg move with velocities v

1.	Two identical blocks A and B each of mass 2 kg move with velocities v _(1) = 10 m//sand v _(2) = 5m//salong a smooth horizontal plane. The block B has a spring, attached to its rear end of spring constant k = 500 N/m. Find the maximum compression undergone by the spring.
Answer» Solution :At the instant of maximum compression, the velocities of the two vlocks are EQUAL. LET their common velocity be v. Since no FORCE acts o the system horizontally, by the principle of conservation of momentum along hte horizontal direction. `m (10) + m (5) = mv + mv,` where m is the mass of each block` implies v = 7.5 m//s.` By conservation of total mechanical energy, INITIAL K.E.= Final K.E. + elastic P.E. of the spring. `1.2m (10) ^(2) + 1/2 m (5) ^(2) = 1/2 (m+m) v ^(2) + 1/2 kx _(0) ^(2) , 1/2 (2) (10) ^(2) + 1/2 (2) (5) ^(2) = 1/2 xx2 xx (7.5) ^(2) xx 2 + 1/2 xx 500 xx _(0) ^(2)` Solving for `x _(0),` we get `x_(0) = 0.22 m`