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

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.

What is the final speed of the cart A?

Express answer in terms of the variables mA, mB, Es, and vi.

vA =