3.2.2 Elastic & Inelastic Collisions

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Elastic Collisions

When two objects collide, they may spring apart retaining all of their kinetic energy. This is a perfect elastic collision
An elastic collision is one where kinetic energy is conserved

Kinetic energy equation, downloadable AS & A Level Physics revision notes

Equation for kinetic energy

Since kinetic energy depends on the speed of an object, in a perfectly elastic collision (head-on approach) the relative speed of approach = the relative speed of separation

Worked example

Two similar spheres, each of mass m and velocity v are travelling towards each other. The spheres have a head-on collision. What is the total kinetic energy after the impact? WE - Elastic collision question image, downloadable AS & A Level Physics revision notes

Exam Tip

Despite velocity being a vector, kinetic energy is a scalar quantity and therefore will never include a minus sign. This is because in the kinetic energy formula, mass is scalar and the v² will always give a positive value whether its a negative or positive velocity

Inelastic Collisions

Whilst the momentum of a system is always conserved in interactions between objects, kinetic energy may not always be
An inelastic collision is one where kinetic energy is not conserved

Equation for kinetic energy

The kinetic energy is transferred into other forms of energy such as a heat or sound
Inelastic collisions can be when two objects collide and they crumple and deform. Their kinetic energy may also disappear completely as they come to a halt
A perfectly inelastic collision is when two objects stick together after collision, as shown in the example below

Worked example

Two trolleys X and Y are of equal mass. Trolley X moves towards trolley Y which is initially stationary. After the collision, the trolleys join and move off together. Prove that this collision is inelastic.