A slower cart has not destroyed its energy — Physics & Environmental Science

A cart slides to rest and a surface warms slightly. Mechanical energy decreased, but the complete system can still conserve energy through thermal changes, sound, deformation and transfers outside the boundary. Define the system first. Including Earth lets gravity enter as potential energy; selecting only the cart may count gravity’s external work instead. Counting both representations would duplicate the same transfer.

Momentum answers a different question. In a short collision, two carts can have negligible net external impulse while their internal forces transfer momentum between them. Total momentum can then remain constant even when the carts stick and kinetic energy decreases. Keep velocity signs and compare the same reference frame before and after. A shared final velocity follows total momentum divided by total mass.

A force–time trace connects collision evidence with impulse. Area gives momentum change; peak height alone does not. A longer stopping time reduces average force only for a comparable momentum change, and rebound can change that denominator. Separate this bounded model from claims about actual injury or protective performance, which require much more evidence.