Conservation of Momentum in an Isolated System

Picture two carts colliding on a track. During the crash, kinetic energy can vanish into heat and sound, and the carts crumple or stick together. But total momentum survives, because of Newton's third law. Whatever force cart A exerts on cart B during the collision, cart B exerts the exact opposite force back on A, at every instant. Those two forces are equal and opposite, so the impulses they deliver are equal and opposite too. One cart's momentum gain is the other's momentum loss, so the total never changes. Momentum is conserved not because nothing happens, but because whatever happens inside the system cancels out.

Calling a system isolated does not mean no forces act on it. It means no net external force acts on it, or that external forces act for such a short time during the collision that their impulse is negligible compared to the huge internal forces of impact. Gravity and the normal force from a table are both present throughout a cart collision, but they are vertical, equal, and opposite, so they cancel and never touch the horizontal momentum. That is why you can treat horizontal momentum as conserved even though vertical forces are active the whole time. Checking isolation means asking which direction you care about and whether outside forces have any component there, not whether any forces exist at all.

This idea is the collision-analysis partner to impulse and momentum bar charts introduced earlier in the unit: those tools describe one object's momentum changing over time, while conservation of momentum tracks the whole system, linking directly into the next topic of classifying collisions as elastic or inelastic.