# Inelastic Collision Formula

The crash in which kinetic energy of the system is not conserved but the momentum is conserved, then that collision is termed as Inelastic Collision.

## Formula of Inelastic Collision

The inelastic collision formula is articulated as

$m_{1}u_{1}\,&space;+\,&space;m_{2}u_{2}\,&space;=\,&space;\left&space;(&space;m_{1}+m_{2}&space;\right&space;)v$

Where
mass of body 1 = m1

mass of body 2 = m2
The initial velocity of body 1 = u1
The initial velocity of body 2 = u2
The final velocity of both the bodies = v

The final velocity for Inelastic collision is articulated as

$v\,&space;=\,&space;\frac{m_{1}u_{1}\,&space;+\,&space;m_{2}u_{2}}{m_{1}+m_{2}}$

The inelastic collision formula is made use of to find the velocity and mass related to the inelastic collision.

### Inelastic Collision Solved Example

Problem 1: Compute the final velocity if an object of mass 2 Kg with initial velocity 3 ms-1 hits another object of mass 3 Kg at rest? (Collision is inelastic)
Known:
m1 (Mass)= 2 Kg,
m2(Mass) = 3 Kg
u1 (Initial Velocity of first mass)= 3 ms-1
u2 (Initial velocity of second mass) = 0

$The\,&space;Final\,&space;Velocity\,&space;is\,&space;given\,&space;by\,&space;v\,&space;=\,&space;\frac{m_{1}u_{1}+m_{2}u_{2}}{m_{1}+m_{2}}$

$=\,&space;\frac{2\times&space;3+0}{2+3}$

v = 6/5

v = 1.2 m/s