1. The problem statement, all variables and given/known data An assembled system consists of cart A of inertia mA, cart B of inertia mB, and a spring of negligible inertia, clamped together so that the fully compressed spring is aligned between the front end of cart B and the back end of cart A. The internal energy of the system, stored in the compressed spring, is Es. The system is put on a low-friction track and given a small shove so that it moves to the right at speed vi, with cart A in front. Once the system is moving, the clamp is released (by remote control, so that the motion of the system as a whole is not affected in any way). As the spring expands, the carts move apart. Find the final Velocity of a A and B respectively in terms of Espring, mA, Mb, and vi. 2. Relevant equations dK + dEspring = Sum of Kinetic Energy + dEspring = 0 3. The attempt at a solution Here is the solution for A: vA = vi + sqrt[ (2mB * Es) /( mA * (mA +mB))] Which was given to me after I gave up on the problem, (this is from online homework) from it I just changed a sign and a couple terms under the radical to get vB. So I've already turned in this home work, and did well on this section covering conservation of momentum and energy. The fact that this problem has been so hard for me to solve makes me feel like I'm missing something fundamental to my understanding of how this stuff works. vA = vi + sqrt[ (2mB * Es) /( mA * (mA +mB))] Any insight into how to solve, or think about this problem would be much appreciated! I've tried a bunch of different approaches that result in an ugly quadratic with way too many vA's, and Vb's to cancel out. I think it's going to come down to just making the right substitutions but I just keep coming up short. The other very simple explosive separation problems I've solved always start with an object that has no initial velocity. So how can I apply conservation of momentum mathematically when the final velocities are being increased by the internal energy of the spring? We already took the test on this section and I did well (there weren't any like this), but I still want to understand this problem! Unfortunately, I can't devote too much more time to it right now, since we're moving along quickly into new material! I'm sure I'm going to feel silly once it clicks, but I'll accept that humiliation if helps me grow my understanding! Thank you all for your help!