Elastic Collisions in 1 Dimension

Working from the Conservation Laws



The Problem:

A particle of mass m1 and velocity v collides elastically (in one dimension) with a stationary particle of mass m2. What are the velocities of m1 and m2 after the collision?

Before diagram
after diagram

A particle of mass m1 and velocity v collides elastically with a particle of mass m2, initially at rest.

After the collision, m1 has velocity v1, and m2 has velocity v2. What are v1 and v2?


Since no external forces do work on the two-particle system, it is an isolated system and momentum is conserved. Therefore,

momentum is conserved

Also, since the collision is elastic, the total kinetic energy of the system is conserved.

ke is conserved (Equation 2)

Equations 1 and 2 form a system of 2 equations with 2 unknowns (v1 and v2). All you have to do is solve it. Alternatively, you can remember the solution for the general case.