In physics, an inelastic collision occurs, when the maximum amount of kinetic energy of a colliding objects/system is lost. The colliding particles stick together in a perfectly inelastic collision. In such cases, kinetic energy lost is used in bonding the two bodies together. Problems involving collisions are usually solved using the conservation of momentum and energy.

*The above schematic diagram illustrate a perfectly inelastic collision.*

- Inelastic collision
- Elastic collision

## Inelastic Collision Definition

An inelastic collision is such a type of collision that takes place between two objects in which some energy is lost. In the case of inelastic collision, **momentum is conserved but the kinetic energy is not conserved**. Most of the collisions in daily life are inelastic in nature.

### Perfectly Inelastic Collision

The special case of inelastic collision is known as a perfectly inelastic collision. Here, after collision two objects stick together. Refer to the figure above. Example: when wet mudball is thrown against a wall, the mudball sticks to the wall.

## Inelastic Collision Formula

When two objects collide under inelastic condition, the final velocity with which the object moves is given by-

\(V=\frac{(M_{1}V_{1}+M_{2}V_{2})}{(M_{1}+M_{2})}\)Where,

- V= Final velocity
- M1= mass of the first object in kgs
- M2= mas of the second object in kgs
- V1= initial velocity of the first object in m/s
- V2= initial velocity of the second object in m/s

### Inelastic Collision in Two Dimension

Inelastic collision in two dimensions, conservation of momentum is applied separately along each axis. Since Momentum is a vector equation and there is one conservation of momentum equation per dimension. Similarly, there is only one conservation of energy equation.

## Inelastic Collision Examples

Most of the collision we see in our day to day life falls under inelastic collision. Some of them are listed below.

**Real World Examples Of Inelastic Collision**

- The ball is dropped from a certain height and it is unable to rise to its original height.
- When soft mudball is thrown against the wall, it will stick to the wall.
- The accident of two vehicles
- A car hitting a tree

## Inelastic Collision Kinetic Energy

In the case of inelastic collision, the kinetic energy is not conserved. The loss of kinetic energy is due to internal friction. It may turn into vibrational energy of the atoms, causing a heating effect and the bodies are deformed.

**Elastic Collision**

Any collisions in which the collided objects get separated after the collision is known as an elastic collision. In case of elastic collision kinetic energy gets conserved. One must use both conservations of momentum and conservation of energy to find the motions of the objects later.

Some examples of elastic collisions are ping-pong balls, billiards, etc.

## Inelastic Collision Problems

#### Problem 1:

Shankha is going by a slippery snowy hill. He has a mass of 20kg, and he is sliding the hill at a velocity of 5m/s. Shankha’s elder brother has a mass of 30kg. His brother is moving slower with a velocity of 2m/s. Shankha collides to his brother. Then both of them keep going down the hill as one unit. Calculate the resulting velocity of Shankha.

#### Solution:

Given,

M1= 20kg

M2= 30kg

V1= 5m/s

V2= 2m/s

\(V=\frac{(20kg)\times (5m/s)+(30kg)\times (2m/s)}{(20kg+30kg)}\\ \\ =\frac{100\: kg.m/s+60\: kg.m/s}{50\: kg}\\ \\ =\frac{160\: kg.m/s}{50\: kg}\\ \\ =3.20\: m/s\)Thus, after Shankha collides, the combined velocity of Shankha and his brother is 3.20m/s.

#### Problem 2:

Shankha driving a 200kg truck and travelling eastwards at a speed of 10m/s. He hit the rear end of a 1400kg car at the stop signal. The collision caused both vehicles to stick together. What is the final momentum of the vehicle?

#### Solution:

Given,

Mt =200kg

Mc -1400kg

Vt =10m/s

Vc = 0m/s

Formula : Momentum P = MV

According to the conservation of momentum Pi = Pf

(MV)t+(MV)c = (Mt+Mc)v

(2000×10)(1400×0)=(2000+1400)×V

20000/3400 = V

V=5.8m/s

Thus, after collision Shankha’s truck and car striking together will move with a speed of 5.8m/s.

## Frequently Asked Questions – FAQs

**Q1: Is momentum conserved in the case of an inelastic collision?**

**Ans:** Yes, momentum is conserved in an inelastic collision.

**Q2: Is Kinetic energy conserved in an inelastic collision? **

**Ans: **No, Kinetic energy is not conserved in an inelastic collision.

Hope you have got a brief knowledge of inelastic collision, formulas, terms, examples and applications. For a better understanding of collision, do read the related articles and answer the practice questions.

### Related Physics Concepts

Elastic And Inelastic Collisions In One And Two Dimensions |

Law Of Conservation Of Linear Momentum |

Kinetic energy |

Newton’s Second Law Of Motion And Momentum |

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If two objects collide head-on and then stick together, do we need to consider one of the object’s velocities as negative value?

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