Coefficient of Restitution
Calculates the coefficient of restitution e=(v2-v1)/(u1-u2) for two bodies before and after collision.
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Coefficient of restitution: e = v_after / v_before
The coefficient of restitution e compares how fast two bodies separate to how fast they approached, taken in absolute value: e = |v₁' − v₂'| / |v₁ − v₂|. It has no units and lives between 0 and 1. At e = 1 the collision is perfectly elastic and kinetic energy is fully conserved. At e = 0 it's perfectly inelastic and the bodies stick together and move off as one. A tennis ball lands near 0.75, a basketball about the same, billiard balls around 0.85, and steel on steel above 0.9. Take an NBA-regulation ball: dropped from 1.8 m it has to bounce back between 1.2 m and 1.4 m, which works out to e ≈ √(h'/h) ≈ 0.82–0.88. The fraction of kinetic energy lost is 1 − e².
Applications
Sports bodies like FIFA, the NBA and the ITF set a legal bounce range for official balls, so manufacturers have to land on a precise e. Automotive engineers go the other way and tune e down in crash structures, because a low e in the crumple zones soaks up the most energy and shields the occupants. Crash tests read e off barriers to calibrate safety scores. And in billiards, players lean on e ≈ 0.85 to read how the balls will scatter after a strike.
FAQ
How do I measure e for a ball? Drop it from a height h and measure how high it bounces, h'. Since v² ∝ h, you get e = √(h'/h).
Why is e < 1 in real collisions? Some energy always leaks away as heat, sound, deformation and internal vibration. Only idealized atomic collisions actually reach e = 1.
Does e depend on temperature? It does. A cold tennis ball has a lower e because the rubber stiffens and gives up more energy, which is exactly why some tournaments have rules about warming the balls.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.