I have a problem in which two carts are attached by a compressed spring. I have found that cart $A$ moves at $1.1~\mathrm{m/s}$ to the right and has a mass of $0.39 ~\textrm{kg}.$ Cart $B$ has a mass of $0.18~\textrm{kg}$ and moves at $2.382~\mathrm{m/s}$ in the opposite direction. How do I use the equation $U = kx^2$ to find what the potential elastic energy is?
It isn't making sense to me because I don't know what the displacement of each cart is.
This looks like a explosion type conservation of momentum problem where the kinetic energy after the event (releasing the carts) is greater than the kinetic energy before the event (=0?).
If there were no external forces acting on the 2 carts & spring system then the source of all of the kinetic energy which the carts have must have been the elastic potential energy stored in the spring.
Note that the elastic potential energy stored in a spring is $\frac 1 2 k x^2$.
The best you can do is to get the change in potential energy of the spring, and you can do that that only if you assume that the two carts started from rest (and you want the change in potential energy from rest). Also, your equation for U is missing a factor of 2.
