A collision in one dimension happens when two objects hit each other while moving along a single straight path, like two billiard balls on a narrow track.

The Law of Conservation of Momentum

In every collision, the total momentum stays the same. Momentum is simply how much 'oomph' an object has, calculated by multiplying its mass by its velocity. If Object A hits Object B, the total momentum before the crash is exactly equal to the total momentum after the crash. This holds true as long as no outside forces, like friction, interfere during the tiny moment of impact.

Elastic vs. Inelastic Collisions

Collisions are categorized based on what happens to energy. In an elastic collision, kinetic energy (the energy of motion) is perfectly conserved. Imagine two super-bouncy rubber balls hitting and bouncing off with the exact same speed they started with. No energy is lost to heat or sound. In an inelastic collision, some kinetic energy turns into other forms, such as heat or a dent in the metal. If two clay balls hit and stick together, that is a perfectly inelastic collision, where they move forward as one single mass.

Key Formulas for Calculations

To solve problems involving one-dimensional collisions, we use these fundamental steps:

• Conservation of Momentum: (Mass A × Velocity A) + (Mass B × Velocity B) = (Mass A × Final Velocity A) + (Mass B × Final Velocity B).
• Velocity Change: If the objects stick together, you treat them as one large object with a combined mass for the second half of the equation.

Real-World Examples

You see one-dimensional collisions everywhere. When a moving train car bumps into a stationary one on a track, it is a one-dimensional collision. Even a dropped ball hitting the floor is a one-dimensional collision, as the ball moves down and then straight up along the same axis. By measuring how high the ball bounces, physicists can tell if the collision was elastic or inelastic.