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Collisions Explained: Conservation of Momentum and Impulse

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In mechanics, momentum (mass × velocity) is a vector quantity that helps predict the outcomes of interactions. For a closed system—one with negligible external forces—the total momentum remains constant during a collision or explosion. This conservation principle holds even when kinetic energy is not conserved.

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The idea of impulse links forces to momentum change. When a net force acts over a time interval, the product of average force and time equals the change in momentum. Increasing contact time—by using padding, crumple zones, or airbags—reduces the average force for the same change in momentum, which is why such designs improve safety.

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Collisions are categorized by how much kinetic energy they preserve. In an elastic collision, both momentum and kinetic energy are conserved. In a perfectly inelastic collision, objects stick together, momentum is conserved, but some kinetic energy is transformed into other forms such as heat or sound.

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The coefficient of restitution summarizes “bounciness” on a scale between 0 and 1. Values near 1 indicate nearly elastic rebounds (as with a superball on a hard surface), while values near 0 indicate large kinetic-energy losses (as when clay hits the ground and deforms).

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Real systems are rarely perfectly closed. Friction, air resistance, or external pushes can alter total momentum if their effects are significant over the interaction time. Still, for brief impacts where such influences are small, conservation models are remarkably predictive.