Elastic and inelastic collisions

In this lesson, we will learn:

• Meaning of elastic and inelastic collisions
• What happens to kinetic energy in a collision?
• Understanding perfectly inelastic collisions
• Problem solving with elastic and inelastic collisions

• Total momentum and total energy are conserved in collisions. However, kinetic energy is not always conserved, since it can be converted into other forms of energy.
• Elastic collision: collision where no kinetic energy is lost
• Inelastic collision: collision where part of the kinetic energy is converted to other forms of energy
• Perfectly inelastic collision: collision where the maximum possible amount of kinetic energy is converted to other forms of energy; objects stick together.

Conservation of Momentum

$\sum\vec{p}_i = \sum\vec{p}_f$

$\vec{p}_i:$ initial momentum, in kilogram meters per second (kg·m/s)

$\vec{p}_f:$ final momentum, in kilogram meters per second (kg·m/s)

Conservation of Energy

$\sum\vec{E}_i = \sum\vec{E}_f$

$\vec{E}_i:$ initial energy, in joules (J)

$\vec{E}_f:$ final energy, in joules (J)

Kinetic Energy

$KE = \frac{1}{2}mv^2$

$KE:$ kinetic energy, in joules (J)

$m:$ mass, in kilograms (kg)

$v:$ speed, in meters per second (m/s)

Potential Energy

$PE = mgh$

$PE:$ potential energy, in joules (J)

$g:$ acceleration due to gravity, in meters per second squared (m/s²)

$h:$ height, in meters (m)