Momentum and collision calculator: final velocities, total momentum and kinetic energy lost in an elastic, inelastic or partly elastic head-on collision.
புதுப்பிக்கப்பட்டது சரிபார்க்கப்பட்ட எடுத்துக்காட்டுகள்: 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.
சரிபார்ப்பின் மூலம்: OpenStax UP1 §9.4: equal-mass elastic collision exchanges velocities
சரிபார்ப்பின் மூலம்: Python 3.8 decimal: v = 20000/2500 = 8; KE 200000 → 80000 J
சரிபார்ப்பின் மூலம்: 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
சரிபார்ப்பின் மூலம்: 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.
துல்லியம் உங்கள் உள்ளீடுகளையும் முறையின் அனுமானங்களையும் சார்ந்தது. தசமக் கணக்கீடு 50 முக்கிய இலக்கங்களைப் பயன்படுத்துகிறது. ஆனால் மதிப்பீடுகள், எண் முறைகள், மூலத் தரவுகள் குறைந்த துல்லியத்தைக் கொண்டிருக்கலாம்; காட்டப்படும் மதிப்பை வட்டமிடுவது இந்த வரம்புகளை நீக்காது. சுயாதீன மூலங்களின் தீர்வுகளுடன் சரிபார்க்கப்பட்ட எடுத்துக்காட்டுகள்: 5. எடுத்துக்காட்டாக, “Equal masses, elastic: velocities swap” என்பது OpenStax UP1 §9.4: equal-mass elastic collision exchanges velocities உடன் சரிபார்க்கப்படுகிறது.
OpenStax University Physics Volume 1, §9.4 Types of collisions; HyperPhysics — Elastic and inelastic collisions; coefficient of restitution.
இந்தக் கணிப்பானில் சுயாதீன ஆதாரங்களிலிருந்து பதில்கள் பெறப்பட்ட 5 தீர்க்கப்பட்ட எடுத்துக்காட்டுகள் உள்ளன. இவை சோதனைத் தொகுப்பில் இயங்குகின்றன; இங்கேயும் அவற்றை இயக்கலாம்.
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