# Elastic and Inelastic Collision

This topic is part of the HSC Physics course under the section Momentum, Energy and Simple Systems.

### HSC Physics Syllabus

• analyse and compare the momentum and kinetic energy of elastic and inelastic collisions (ACSPH066)
• conduct an investigation to describe and analyse one-dimensional (collinear) and two-dimensional interactions of objects in simple closed systems (ACSPH064)
• analyse quantitatively and predict, using the law of conservation of momentum Σmv_{before}= Σmv_{after} and, where appropriate, conservation of kinetic energy Σ1/2mv_{before}= Σ 1/2 mv_{after}, the results of interactions in elastic collisions (ACSPH066)

### Elastic Collisions

An elastic collision is a type of collision in which both momentum and kinetic energy are conserved. This means that the total momentum and total kinetic energy before the collision are equal to the total momentum and total kinetic energy after the collision.

In an elastic collision, the objects 'bounce' off each other with no loss of overall speed or kinetic energy. It's important to remember that individual velocities and energies may change, but the total energy and total momentum remain constant.

### Inelastic Collisions

An inelastic collision, on the other hand, is one where kinetic energy is not conserved, but momentum is conserved. The objects may stick together after the collision (completely inelastic) or may move separately (partially inelastic), but in both cases, some kinetic energy is lost. This loss of energy is typically converted into other forms, such as heat, sound, or deformation.

### Laws Governing Collisions

Two primary laws govern these collisions:

1. Conservation of Momentum: This law states that the total linear momentum of a closed system remains constant, regardless of any interactions happening between the objects within the system. In simple terms, the total amount of momentum before a collision equals the total amount of momentum after the collision.

2. Conservation of Energy: This principle maintains that energy cannot be created or destroyed; it can only change from one form to another. However, in elastic collisions, the kinetic energy remains constant, while in inelastic collisions, some kinetic energy is transformed into other forms of energy.

### Real-World Examples of Elastic and Inelastic Collisions

Real-world examples of these types of collisions are plentiful.

Elastic collisions are commonly seen in games of pool, where the balls bounce off each other, and the total energy and momentum are conserved. Atoms and molecules also undergo elastic collisions, where they exchange energy and momentum but retain their overall energy.

Inelastic collisions can be observed in a car crash, where the cars slow down and deform (kinetic energy is converted to heat, sound, and deformation). Another example is a sticky collision between a dart and a dartboard - after the collision, they move together, and kinetic energy has been transformed into potential energy.

Solutions to the following examples can be found in the video above.

### Example 1

A 2 kg mass is moving east at 5 m s–1 collides elastically with a 4 kg mass initially at rest. Calculate the final velocities of the masses.

### Example 2

A 2 kg mass is moving east at 8 m s–1 collides with a 4 kg mass initially moving west at 5 m s–1. The masses remain stuck together. Calculate the final velocity of the combined mass.