The figure shows two blocks of mass m each, connected by an ideal unstretched spring and then placed on a frictionless floor. If the blocks are given velocities v 0 and 2 v 0 as shown, then the maximum extension in the spring is

Step-by-step solution

2 m v = m 2 v 0 - m v 0 v = v 0 2 w s = k f - k i - k 2 x 2 - 0 2 = 1 2 2 m v 2 - 1 2 m v 0 2 + 1 2 m 2 v 0 2 = m v 0 2 2 - 5 m v 0 2 2 ⇒         -   k x 2 2 = - 9 m v 0 2 4 x = 9 2 m v 0 2 k