1. The problem statement, all variables and given/known data Consider a simple 3-body problem in one dimension. One body (the projectile) has mass m. The second body (the target) is made up of two "atoms" each of mass M/2 (total mass = M). Assume an internal spring holds the two atoms together. If the projectile is sent toward the target and a second force makes the target reflect the projectile, what is the subsequent motion of the three bodies? 2. Relevant equations F (spring) = -kx F (electrical) = kQq/r^2 3. The attempt at a solution The "second force" is an electrical force, i.e. the three particles are similarly charged. To simplify things, I will consider a lengthless and massless spring and ignore frictional forces. The question also implies that energy is not conserved between the projectile and the target (but the target system itself conserves energy). I was thinking that as the projectile approaches the target with an initial speed (by Newton's First Law, speed should be constant because there are no external forces acting on it), the electrical force between the target and the projectile strengthens (due to an inverse relationship between electrical force, F, and distance, r, [F = kQQ/r^2]). As this occurs, the target is repelled by the projectile (from rest to an initial speed) and causes the nearest atom to compress the spring (because the projectile's electrical force on the farthest atom is weaker), causing the spring to gain potential energy [F = -kx]. Within the target, the potential energy of the spring will be converted into kinetic energy by bouncing back and forth with the two attached atoms, acting with and against the electrical force between the two atoms. Depending on the speed of the projectile, the distance the target travels before the projectile is repelled will differ (because the target is free to move). Does the spring take the kinetic energy of the target or does the target continue to move indefinitely in space (by Newton's First Law)? Does the spring eventually reach equilibrium due to the balance of electrical forces between the two attached atoms (which are similarly charged)? Thanks, any help will be appreciated!