# Momentum and collision calculator (elastic and inelastic)

> Momentum and collision calculator: final velocities, total momentum and kinetic energy lost in an elastic, inelastic or partly elastic head-on collision.

സംവേദനാത്മക പതിപ്പ്: https://www.calcopenly.com/ml/science/momentum-collision-calculator
വിഷയം: ശാസ്ത്ര കാൽക്കുലേറ്ററുകൾ

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.

## ഇൻപുട്ടുകൾ

- **Collision** (തിരഞ്ഞെടുപ്പുകൾ: Elastic, Perfectly inelastic, Coefficient e)
- **Coefficient of restitution e**: Relative speed after ÷ relative speed before
- **Mass of body 1**
- **Velocity of body 1 before**: Signed: positive is to the right
- **Mass of body 2**
- **Velocity of body 2 before**: Body 2 starts to the right of body 1
- **Show velocities in** (തിരഞ്ഞെടുപ്പുകൾ: m/s, km/h, mph)

## ഫലങ്ങൾ

- Velocity of body 1 after (m/s) — പ്രധാന ഫലം
- Velocity of body 2 after (m/s)
- Total momentum (conserved) (kg·m/s)
- Kinetic energy before (J)
- Kinetic energy after (J)
- Kinetic energy lost (J)
- Share of kinetic energy lost
- Impulse on body 2 (N·s)

## സൂത്രവാക്യം

$$
v_1 = \frac{m_1u_1 + m_2u_2 + m_2e(u_2 - u_1)}{m_1 + m_2},\quad v_2 = \frac{m_1u_1 + m_2u_2 + m_1e(u_1 - u_2)}{m_1 + m_2}
$$

## പരിഹരിച്ച ഉദാഹരണങ്ങൾ

### Equal masses, elastic: velocities swap

- Collision: Elastic
- Mass of body 1: 1 kg
- Velocity of body 1 before: 2 m/s
- Mass of body 2: 1 kg
- Velocity of body 2 before: 0 m/s
- Show velocities in: m/s
- **Velocity of body 1 after: 0 m/s**
- **Velocity of body 2 after: 2 m/s**
- **Kinetic energy lost: 0 J**
- പരിശോധനയുടെ ഉറവിടം: OpenStax UP1 §9.4: equal-mass elastic collision exchanges velocities

### Car hits a parked car and they lock

- Collision: Perfectly inelastic
- Mass of body 1: 1000 kg
- Velocity of body 1 before: 20 m/s
- Mass of body 2: 1500 kg
- Velocity of body 2 before: 0 m/s
- Show velocities in: m/s
- **Velocity of body 1 after: 8 m/s**
- **Velocity of body 2 after: 8 m/s**
- **Kinetic energy before: 200,000 J**
- **Kinetic energy after: 80,000 J**
- **Share of kinetic energy lost: 60.00%**
- പരിശോധനയുടെ ഉറവിടം: Python 3.8 decimal: v = 20000/2500 = 8; KE 200000 → 80000 J

### e = 0.5 head-on

- Collision: Coefficient e
- Coefficient of restitution e: 0.5
- Mass of body 1: 2 kg
- Velocity of body 1 before: 3 m/s
- Mass of body 2: 1 kg
- Velocity of body 2 before: -1 m/s
- Show velocities in: m/s
- **Velocity of body 1 after: 1 m/s**
- **Velocity of body 2 after: 3 m/s**
- **Total momentum (conserved): 5 kg·m/s**
- **Kinetic energy lost: 4 J**
- പരിശോധനയുടെ ഉറവിടം: 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

### Heavy ball hits a light one, elastic

- Collision: Elastic
- Mass of body 1: 10 kg
- Velocity of body 1 before: 1 m/s
- Mass of body 2: 1 kg
- Velocity of body 2 before: 0 m/s
- Show velocities in: m/s
- **Velocity of body 1 after: 0.818182 m/s**
- **Velocity of body 2 after: 1.81818 m/s**
- പരിശോധനയുടെ ഉറവിടം: Python 3.8 fractions: v1 = 9/11, v2 = 20/11

### Equal and opposite, sticking: everything stops

- Collision: Perfectly inelastic
- Mass of body 1: 2 kg
- Velocity of body 1 before: 5 m/s
- Mass of body 2: 2 kg
- Velocity of body 2 before: -5 m/s
- Show velocities in: m/s
- **Velocity of body 1 after: 0 m/s**
- **Total momentum (conserved): 0 kg·m/s**
- **Share of kinetic energy lost: 100.00%**
- പരിശോധനയുടെ ഉറവിടം: Zero total momentum ⇒ common velocity 0, all 50 J lost (hand calculation)

## ചോദ്യങ്ങൾ

### What is the difference between elastic and inelastic collisions?

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.

### What is the coefficient of restitution?

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.

### How do you calculate momentum?

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.

### What happens when two equal masses collide elastically?

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.

### “Momentum and collision calculator (elastic and inelastic)” എത്രത്തോളം കൃത്യമാണ്?

കൃത്യത നിങ്ങളുടെ ഇൻപുട്ടുകളെയും രീതിയുടെ അനുമാനങ്ങളെയും ആശ്രയിച്ചിരിക്കുന്നു. ദശാംശ ഗണിതം 50 സാർഥക അക്കങ്ങൾ ഉപയോഗിക്കുന്നു. എന്നാൽ അനുമാനക്കണക്കുകൾ, സംഖ്യാത്മക രീതികൾ, ഉറവിട ഡാറ്റ എന്നിവയ്ക്ക് കൃത്യത കുറവാകാം; പ്രദർശിപ്പിക്കുന്ന മൂല്യം റൗണ്ട് ചെയ്യുന്നത് ഈ പരിമിതികൾ നീക്കില്ല. സ്വതന്ത്ര ഉറവിടങ്ങളിലെ പരിഹാരങ്ങളുമായി പരിശോധിച്ച ഉദാഹരണങ്ങൾ: 5. ഉദാഹരണത്തിന്, “Equal masses, elastic: velocities swap” എന്നത് OpenStax UP1 §9.4: equal-mass elastic collision exchanges velocities ഉപയോഗിച്ച് പരിശോധിക്കുന്നു.

### ഈ രീതിയുടെ ഉറവിടം എന്താണ്?

OpenStax University Physics Volume 1, §9.4 Types of collisions; HyperPhysics — Elastic and inelastic collisions; coefficient of restitution.

## സ്രോതസ്സുകൾ

- [OpenStax University Physics Volume 1, §9.4 Types of collisions](https://openstax.org/books/university-physics-volume-1/pages/9-4-types-of-collisions)
- [HyperPhysics — Elastic and inelastic collisions; coefficient of restitution](http://hyperphysics.phy-astr.gsu.edu/hbase/elacol.html)