Momentum of blocks compressing spring

[Mugen Prospec]

Homework Statement

In the figure below, block 1 (mass 1.6 kg) is moving rightward at 8 m/s and block 2 (mass 4.2 kg) is moving rightward at 2.8 m/s. The surface is frictionless, and a spring with spring constant of 1120 N/m is fixed to block 2. When the blocks collide, the compression of the spring is maximum at the instant the blocks have the same velocity. Find the maximum compression.

Homework Equations

mv+mv=mv
not sure what spring equation is needed.

The Attempt at a Solution

Tried taking the velocity of the system them puting that into kinetic energy = spring energy but that was not right.

 

[Andrew Mason]

What is the change in velocity of each block when they are both moving at the same speed? What is that speed?

Your approach is right but not all the energy is in the spring - just the lost energy. Assume that the energy that is lost by the blocks is stored in the spring. (hint: The energy of the spring is .5kx^2 where k is the spring constant and x is the displacement from equilibrium).

AM

 

[Mugen Prospec]

Oh ok so the total kinetic energy plus the spring energy equals the original energy of the system. I might not have said the right but I understand what your saying. I was just having a hard time figuring out where the energy went but then, like you showed, it wasnt a perfectly elastic collision.
Thank you Andrew