Every collision here conserves momentum exactly between the two bodies involved — that's Newton's third law expressed as an equal and opposite impulse, and it holds regardless of what you set elasticity to. The total momentum you see in the readout still drifts, though — walls (in Free Collision) and the pivot bar's string tension (in Newton's Cradle) are external forces acting on the system, exactly like a real wall or a real support would. Kinetic energy is different again: it's only conserved when e = 1 (perfectly elastic). Anywhere below that, some kinetic energy converts to heat, sound and deformation on every impact, and the chart below shows exactly how much survives each collision.
Pull back 2 balls on a 6-ball cradle and release with e = 1: the two end balls stop dead on contact and exactly 2 balls fly out the far side at the same speed — not because the cradle is special, but because equal-mass elastic collisions simply swap velocities, and touching balls do it in an instant, unbroken chain.
Solving the conservation equations for momentum and kinetic energy simultaneously with m₁ = m₂ has exactly one non-trivial solution: the two velocities exchange. It looks like the balls passed through each other, but they didn't — they just handed off exactly what they carried.
Because the swap happens ball-by-ball down the line, near-instantaneously since they're touching. Two balls arriving together deliver two separate velocity handoffs in the same instant, which only has room to land on the last two balls in the chain — that's the whole trick, not a separate rule.
Momentum still balances exactly, but each impact bleeds off some kinetic energy — set the slider below 1 and watch the sharp cradle "click" turn into a duller, more clustered motion where balls tend to move together rather than cleanly handing off velocity.
Yes — unequal masses never fully swap velocities even at e = 1. A light ball hitting a heavy one mostly bounces back; a heavy ball hitting a light one barely slows. Toggle "vary ball mass" to see the clean cradle click become a mix of different responses.