# Inelastic Collision

Collisions occur when one object strikes another. Problems involving collisions are usually solved using conservation of momentum and energy.

It is categorized into two types,

• Inelastic collision
• Elastic collision

### What is Inelastic Collision?

Inelastic collision is such a type of collision that takes place between two objects in which some energy is lost. The special case of inelastic collision is known as perfectly inelastic collision where after collision two objects stick together. Incase of inelastic collision momentum is conserved but the kinetic energy is not conserved. Most of the collisions in daily life are inelastic in nature.

### Elastic Collision:

Any collisions in which the collided objects get separated after collision is known as elastic collision. In case of elastic collision kinetic energy gets conserved. One must use both conservation 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.

#### Formula for Inelastic Collision:

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

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

#### Example of inelastic collision:

Reuben 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. Reuben’s older brother has a mass of 30kg. His brother is moving slower with a velocity of 2m/s. Reuben reaches to his brother. Then both of them keep going down the hill as one unit. Calculate the resulting velocity of Reuben?

#### Solution:

Given,

M1= 20kg

M2= 30kg

V1= 5m/s

V2= 2m/s

$$V=\frac{(20kg)\times (5m/s)+(30kg)\times (2m/s)}{(20kg+30kg)}\\ \\ =\frac{100\: kg.m/s+60\: kg.m/s}{50\: kg}\\ \\ =\frac{160\: kg.m/s}{50\: kg}\\ \\ =3.20\: m/s$$

After Reuben collides, the combined velocity of Reuben and his brother is 3.20m/s.