Maximizing Spring Compression in Colliding Carts

[port31]

Homework Statement

A 2kg cart has a spring with k=5000N/m attached to its
front parallel to the ground. This cart rolls at 4m/s toward a stationary
1kg cart.
What is the maximum compression of the spring during the collision

The Attempt at a Solution

I think the spring will stop compressing when the 2 carts are moving
at the same speed. And there will be a point where the potential energy in the spring
plus the KE of the 2 carts will equal the original energy of moving cart.
so I think I should start with
kx^2+m_2v^2+m_1v^2=m_2{v_0}^2
now I need another equation because I have 2 unknowns in my one equation

 

[Doc Al]

What else is conserved in every collision?

 

[port31]

ok thanks momentum. ok i got it figured out.

 

[NoPoke]

what an interesting question..

The presence of a spring tells you that the collision will be elastic.

What can you say about the center of mass of the system in an elastic collision?

 

[port31]

I didnt think this one through very much, but will the center of mass stay the same.

 

[TSny]

A hint for answering the question about the motion of the center of mass: The total momentum of a system of particles is equal to the total mass of the system times the velocity of the center of mass.