# How Can a Collision Conserve Momentum, But Not Kinetic Energy?

When two objects interact in a collision, momentum is conserved where momentum (p) is defined as the product of mass (m) and velocity (v). However, if the kinetic energy also depends on mass and velocity (1/2 mv²) then shouldn’t it also be conserved? Nope. Let’s work through the whole thing.

# Simple Collision Between Two Point Particles

Let’s start with the simplest example possible (maybe). Imagine that there is a particle with mass m moving in the x-direction with a velocity v (called particle A). It collides with another particle with mass m, but that’s stationary (particle B). Oh, it’s a head on collision so that every stays in 1 dimension (the x-direction).

The key thing idea is that during the collision object A pushes on B and B pushes back on A. But these are the SAME interaction such that the magnitude of A on B is equal to B on A. Now let’s consider the momentum principle. It says the following: