Question

At a smooth horizontal table there are two identical cubes each of mass m, connected by a spring of spring constant k. The length of spring in unstretched state is $l_0$. The right cube is linked to a load mass m at the end as shown. At some time, the system is released from rest when spring is unstretched. Find the maximum distance (in cm) between blocks during the motion of the system. [$l_0 = 1cm, m = 3kg, k = 1000N/m, g = 10m/s^2$]

Answer 1

2 cm

Answer 2

At maximum spring extension the blocks move with the same acceleration. Balancing the forces yields $T = 2k\delta$ and using the hanging mass dynamics, we get $\frac{3k\delta}{m} = g$. This gives $\delta = \frac{mg}{3k} = 1\,\text{cm}$. Adding the unstretched length $l_0 = 1\,\text{cm}$ gives the maximum distance as 2 cm.