# 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.

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
Initial velocity of body 1 = u1
Initial velocity of body 2 = u2
Final velocity of both the bodies = v

The final velocity for Inelastic collision is articulated as

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

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

Inelastic Collision – Solved Examples

Underneath are some questions based on inelastic collision which may be helpful for you.

Problem 1: The bullet of mass 0.02 Kg is fired from a gun of mass 5 Kg recoils with the speed of 8 ms-1. Compute the Velocity after the collision?

Known:

m (Mass of bullet)= 0.020 Kg,
M (Mass of gun) = 5 Kg
Let v be the final velocity, to calculate it we use the formula
M(0.08) = m(v)

$v\,&space;=\,&space;\frac{50\times&space;0.08}{20\times&space;10^{-3}}$

$=\,&space;200\,&space;ms^{-1}$

Problem 2: Compute the final velocity if an object of mass 2 Kg with initial velocity 3 ms-1 hits an other 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

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

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

$=\,&space;\frac{6}{5}$

$=\,&space;1.2\,&space;m/s.$