Momentum and collision calculator: final velocities, total momentum and kinetic energy lost in an elastic, inelastic or partly elastic head-on collision.
Aktualisiert Geprüfte Beispiele: 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.
Prüfquelle: OpenStax UP1 §9.4: equal-mass elastic collision exchanges velocities
Prüfquelle: Python 3.8 decimal: v = 20000/2500 = 8; KE 200000 → 80000 J
Prüfquelle: 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
Prüfquelle: 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.
Die Genauigkeit hängt von Ihren Eingaben und den Annahmen der Methode ab. Die Dezimalrechnung nutzt 50 signifikante Stellen, doch Schätzungen, numerische Verfahren und Quelldaten können ungenauer sein. Die angezeigte Rundung beseitigt diese Grenzen nicht. Anhand unabhängiger Quellen geprüfte Rechenbeispiele: 5. Beispielsweise wird „Equal masses, elastic: velocities swap“ anhand von OpenStax UP1 §9.4: equal-mass elastic collision exchanges velocities geprüft.
OpenStax University Physics Volume 1, §9.4 Types of collisions; HyperPhysics — Elastic and inelastic collisions; coefficient of restitution.
Dieser Rechner enthält 5 Rechenbeispiele mit Ergebnissen aus unabhängigen Quellen. Sie laufen in der Testsuite und können auch hier ausgeführt werden.
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