Completely inelastic collision with object attached to spring

[jayjay5531]

Homework Statement

In Fig. 9-64, block 2
(mass 1.0 kg) is at rest on a
frictionless surface and touch-
ing the end of an unstretched
spring of spring constant 200
N/m. The other end of the spring is fixed to a wall. Block 1 (mass 2.0 kg), traveling at speed v₁ = 4.0 m/s, collides with block 2, and the two blocks stick together. When the blocks momentarily stop, by what distance is the spring compressed?

Homework Equations

m₁v₁+m₂v₂=MV where M is the mass of the system and V is the velocity of the system

Hooke's Law: F = kx

The Attempt at a Solution

I was able to find the final velocity of the system:

V = (m₁v₁)/(m₁+m₂) = 2.974

How do I get from there to the distance that the spring is compressed?

 

[ehild]

Does conservation of energy hold after the collision?

ehild