## Pages

### 2.2 Dynamics (Elastic and Inelastic Collision)

What is collision?
• A collision is an event where momentum or kinetic energy is transferred from one object to another.
There are mainly two types of  collision we'll discuss, the Elastic collision and Inelastic collision.

Firstly, the definition.
Elastic collision: Collisions in which both momentum and kinetic energy are conserved. The total system momentum and kinetic energy before the collision equals the total system kinetic energy after the collision.

Exercise: Suppose ball's mass of $2kg$ is moving with initial velocity $u_{1}$=$10ms^{-1}$ and collides head on with the stationary ball whose mass of $6kg$. If the collision is elastic, what are the final velocities of the balls. Friction is not taken into account in this problem.

Soln: Since it's given that the collision is elastic, we know that Momentum conservation and Kinetic energy conservation must hold true, we then have
$$m_{1}u_{1}+m_{2}u_{2}=m_{1}v_{1}+m_{2}v_{2}$$
And from the Kinetic energy conservation,

$$\frac{1}{2}m_{1}u_{1}^{2}+\frac{1}{2}m_{2}u_{2}^{2}=\frac{1}{2}m_{1}v_{1}^{2}+\frac{1}{2}m_{2}v_{2}^{2}$$
given that, $u_{1}=12ms^{-1}$, $u_{2}=0$ , $m_{1}=2kg$ and $m_{2}=6kg$, so  solving  for $v_{1}$ and $v_{2}$ we get,
$v_{1}=-5ms^{-1}$, $v_{2}=5ms^{-1}$

Inelastic Collision: If in collision the total kinetic energy is not conserved but the total momentum is conserved, then the collision is referred to as an inelastic collision. The diagram below represents 'perfect' inelastic collision.

Exercise: Suppose ball's mass of $2kg$ is moving with initial velocity $u_{1}$=$10ms^{-1}$ and collides head on with the stationary ball whose mass of $3kg$. If the collision is inelastic, what is the final velocities of the balls. Friction is not taken into account in this problem too.

Soln: Since it's given that the collision is elastic, we know that Momentum conservation must hold true but not kinetic energy conservation, we then have
$$m_{1}u_{1}+m_{2}u_{2}=m_{1}v+m_{2}v$$
given that, $u_{1}=10ms^{-1}$, $u_{2}=0$ , $m_{1}=2kg$ and $m_{2}=6kg$, so  solving  for $v$ we get, $v=\frac{10}{4}ms^{-1}$.

Here's a useful video,