# [Calculator] Elastic and Inelastic collision Tanvesh
Masters in Structural Engineering | Research Interest - Artificial Intelligence and Machine learning in Civil Engineering | Youtuber | Teacher | Currently working as Research Scholar at NIT Goa

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## 3 Types of collisions

When two or more objects collide with each other, there are three types of collisions that can be theorized.

1. Perfectly elastic collision
2. Perfectly inelastic collision
3. Inelastic collision

### What is coefficient of restitution

Coefficient of restitution is defined as ratio of impulse during restitution to impulse during deformation

Coefficient of restitution can also be defined as ratio of relative velocity of separation to relative velocity of approach.

e=\frac{\left(v_{2}-v_{1}\right)}{\left(u_{1}-u_{2}\right)}

Where u1 and u2 are initial velocities before impact of object 1 and 2 respectively whereas v1 and v2 are final velocities of objects 1 and 2 respectively after the impact has taken place.

***Relative velocities are only to be considered along line of impact

Therefore this equation is valid only along line of impact.

## Perfectly Elastic Collision

In a perfectly elastic the coefficient of restitution is taken to be 1.

This has a physical meaning that if two objects of similar mass and shape properties are colliding head on i.e. their line of collision and initial velocity directions are all aligned, then in an perfectly elastic collision both would rebound with same velocity as initial velocity and no loss of energy is taken place.

A perfectly elastic collision is rather an ideal scenario and rarely occurs in real life, where only closest scenario would be objects having coefficient of restitution of nearly 0.98 to just less than 1.

## Perfectly Inelastic collision

In a perfectly inelastic collision, the coefficient of restitution is 0.

As opposed to perfectly elastic collision, perfectly inelastic collision is possible and is considered in those cases where there is complete loss of energy in a collision and none of the energy is utilized in separating the collided objects.

Example of perfectly inelastic collision can be a sticky clay ball thrown on a wall, or a two highly deformable objects colliding with each other.

When two objects colliding with each other and having direction of velocities along the line of collision then in an perfectly inelastic collision their final velocity will be 0.

## Inelastic collision

Inelastic collision is a real life scenario in which partial energy is utilized in giving a final velocity to the objects.

In an inelastic collision the coefficient of restitution lies between and excluding 0 and 1, therefore 0<e<1.

In all collision cases the law of conservation of momentum is maintained.

m_{1} u_{1}+m_{2} u_{2}=m_{1} v_{1}+m_{2} v_{2}

This forms one equation encompassing the masses of both objects their initial and final velocities.

The second equation is formed using coefficient restitution equation relating the initial and final velocities.

e=\frac{\left(v_{2}-v_{1}\right)}{\left(u_{1}-u_{2}\right)}

Solving these two equations simultaneously we can find the final velocities of the objects after collision.

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