Consider the time interval from when the two carts are released until just after they collide. For the system consisting of only the two carts, indicate whether the total mechanical energy increases, decreases, or remains the same. (The carts start out at rest and then stick in the collision btw)
Don’t you need the distance between the two carts to even first calculate the Ug? I would say that Conservation of energy ( Ki+Ui=Kf+Ur) does not apply here because there is an unbalanced external force acting on the system of only the two carts; that force is the force of gravity due to the earth, which is very significant. But how would you know/prove that it increased or decreased? Because technically, as the carts get closer, their U between each other decreases and their K increases, which makes it very fuzzy and intuitively ambiguous.
****A lot of people misunderstand and say U=mgh. I know for sure this is NOT what this question asks though, because there is another of the exact same question with the two cart - AND earth system, where that U=mgh is true. But here it is regular Ug=Gm1m2/r equation I think.