How Do You Calculate Maximum Spring Compression in an Inelastic Collision?

[darklich21]

Homework Statement

A 10500kg freight car rests against a spring bumper at the end of a raildroad track. The spring has constant k = 3.4 x 10^N/m. The car is hit by a second car of 9400 kg mass moving at 7.5 m/s, and the two cars couple together.

a) what is the maximum compression of the spring?
b) what is the speed of the two cars together when the rebound from the spring?

Homework Equations

The Attempt at a Solution

For starters, I know this is an elastic collision problem since the 2 cars stick together. Perhaps the equation m1v1=V(m1+m2) has some relevance. I also know the initial energy of the first car is 0 since it's at rest. But I'm not sure how to factor the spring here. What equation or equations can I use to solve this problem?

 

[darklich21]

Ok correction, I solved part b. I did use m1v1+ m2v2=v(m1+m2), and I got 3.5 m/s, which is correct. But how do I solve part a? What equation should I use