Momentum and collision calculator: final velocities, total momentum and kinetic energy lost in an elastic, inelastic or partly elastic head-on collision.
Mis à jour Exemples vérifiés : 5
In this elastic collision momentum stays at 5 kg·m/s; body 1 leaves at 0.333333 m/s and body 2 at 4.33333 m/s, and 0% of the kinetic energy is lost.
e = 1 keeps all kinetic energy; e = 0 means the bodies move off together.
In a collision between two bodies, the total momentum m₁u₁ + m₂u₂ is the same before and after. The coefficient of restitution e, the ratio of separation speed to approach speed, supplies the second equation: e = 1 is a perfectly elastic collision and e = 0 means the bodies stick together. The two equations give both final velocities, and comparing ½mv² before and after gives the kinetic energy lost.
The default, a 2 kg body at 3 m/s meeting a 1 kg body moving at −1 m/s elastically, sends them off at 0.333 m/s and 4.333 m/s. A 1,000 kg car at 20 m/s that locks onto a parked 1,500 kg car moves off at 8 m/s, and 60% of the kinetic energy goes into deformation, heat and sound.
Motion is along one line: choose a positive direction and give velocities the other way a minus sign. External forces such as road friction are taken as negligible during the impact.
Source de vérification : OpenStax UP1 §9.4: equal-mass elastic collision exchanges velocities
Source de vérification : Python 3.8 decimal: v = 20000/2500 = 8; KE 200000 → 80000 J
Source de vérification : Python 3.8 fractions: v1 = (5 + 1·0.5·(−4))/3 = 1, v2 = (5 + 2·0.5·4)/3 = 3; KE 9.5 → 5.5 J
Source de vérification : Python 3.8 fractions: v1 = 9/11, v2 = 20/11
Both conserve momentum; only an elastic collision also conserves kinetic energy. In a perfectly inelastic collision the bodies stick together and lose the most kinetic energy that momentum conservation allows. When a 1,000 kg car at 20 m/s locks onto a parked 1,500 kg car, momentum stays at 20,000 kg·m/s while kinetic energy falls from 200 kJ to 80 kJ. Most real collisions fall between the two extremes.
It is the relative speed after a collision divided by the relative speed before, e = (v₂ − v₁) ÷ (u₁ − u₂), a number from 0 to 1. For a ball dropped onto a rigid floor, e = √(bounce height ÷ drop height). The ITF requires a type 2 tennis ball dropped from 254 cm onto concrete to rebound 135–147 cm, which corresponds to e between 0.73 and 0.76.
Momentum is mass times velocity, p = mv, measured in kg·m/s. It has a direction, so velocities in opposite directions carry opposite signs. A 1,000 kg car at 20 m/s has 20,000 kg·m/s. With no outside forces the total is the same before and after a collision, which is why two 2 kg carts meeting head-on at 5 m/s and sticking together stop dead.
They swap velocities. A 1 kg ball at 2 m/s hitting an identical ball at rest stops, and the second ball leaves at 2 m/s with all the kinetic energy; a Newton's cradle shows the same effect. With unequal masses the lighter body leaves faster: a 10 kg ball at 1 m/s sends a 1 kg ball off at 1.82 m/s and slows to 0.82 m/s.
La précision dépend de vos données et des hypothèses de la méthode. Le calcul décimal utilise 50 chiffres significatifs, mais les estimations, méthodes numériques et données sources peuvent être moins précises ; l’arrondi affiché ne supprime pas ces limites. Exemples résolus vérifiés à partir de sources indépendantes : 5. Par exemple, « Equal masses, elastic: velocities swap » est vérifié à l’aide de OpenStax UP1 §9.4: equal-mass elastic collision exchanges velocities.
OpenStax University Physics Volume 1, §9.4 Types of collisions; HyperPhysics — Elastic and inelastic collisions; coefficient of restitution.
Ce calculateur comprend 5 exemples résolus dont les réponses proviennent de sources indépendantes. Ils font partie de la suite de tests et peuvent aussi être exécutés ici.
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