The collision of two bodies is elastic if the kinetic energy before and after the collision is the same. Interaction between molecules is an example of elastic collision. Collisions are not perfectly elastic in most other cases (for example, snooker balls), and some kinetic energy is lost. Elastic collisions occur only if there is no net conversion of kinetic energy into other forms (heat, sound).
The equation of kinetic energy is given as:
Ek = 0.5 x m x v2 ( m is mass and v is velocity)
Table of Contents
Elastic Collision Formulas for Momentum and Kinetic Energy
Consider two particles, indicated by subscripts 1 and 2. Let m1 and m2 be the masses, u1 and u2 be the velocities before the collision and v1 and v2 be the velocities after the collision. The total kinetic energy after the collision is the same as the total kinetic after the collision.
Momentum before the collision = m1u1 + m2u2
Momentum after the collision = m1v1 + m2v2
momentum before the collision = momentum after the collision
m1u1 + m2u2 = m1v1 + m2v2
Using the same variables as before: The kinetic energy relations are given as:
Kinetic energy before the collision = 0.5 m1u12 + 0.5 m2u22
Kinetic energy after the collision = 0.5 m1v12 + 0.5 m2v22
Kinetic energy before the collision = Kinetic energy after the collision
0.5 m1u12 + 0.5 m2u22 = 0.5 m1v12 + 0.5 m2v22
Examples of elastic collision
- An elastic collision is one where kinetic energy is conserved
- Two rubber balls bouncing together would be elastic.
- Newton’s cradle uses four or more suspended balls to demonstrate energy and momentum conservation in a fairly elastic collision.
- Molecular collision in the air
Examples of Inelastic collision
- Two cars hitting each other would be inelastic, as the cars crumple, and do not bounce back.
- The ball is dropped from a certain height
- When an egg is dropped and splatters on impact, the collision is approximately inelastic.
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