A 2-kg block slides on a frictionless horizontal surface and is connected on one side to a spring (k=40 N/m) as shown in the figure. The other side is connected via a massless rope to a 4-kg block that hangs vertically. The system starts from rest with the spring unextended. What is the maximum extension of the spring? What is the speed of the 4-kg block when the extension is 50 cm?
Let's make the following denotations:
M1 = 2kg - first block mass M2 = 4kg - second& block mass E - extension of a spring
Let's find the extension of a spring at the state of equilibrium: g*M2 = k*E ==> E = g*M2/k = 9.8*4/40 = 0.98 m. So, the maximum extension of the spring is 98 cm.