Assuming a frictionless / "perfect" environment, and given a ball held in an elastic sling (like a hand-held catapult) where the pocket is lighter than the projectile itself, what is the point at which the ball separates from the sling pocket? At the start of the shot, or as the sling-pocket passes through its at-rest position?
My thoughts -- please confirm or refute:
Hooke's Law tells us that the force applied to the sling-pocket is directly proportional to the distance from the rest position.
Given the pocket's lower weight, I suppose then that it's velocity (resulting from the applied elastic force) would be greater than that of the projectile itself; thus it should be pushing the projectile (and thus be in contact with it) until such point as we pass the rest position for the first time (assuming sinusoid motion of the band as it vibrates)
In passing the rest position, the force now begins to be applied in the opposite direction and thus reduces the forward velocity of the pocket to be less than that of the projectile, which is travelling at a constant, maximal velocity.
I am a programmer, not a physicist, so your patience is appreciated. Also note that I am trying to keep certain factors, eg. momentum, out of the picture here, as it is not necessary for what I am building (due to certain shortcuts taken). It is really just force, acceleration, mass and velocity I am concerned with.