# Why are conservative forces responsible for elastic collisions?

In elastic collisions, such as the collisions of two snooker balls, it is stated that conservative forces are responsible for the collision being elastic.

Why is it that these elastic collisions have to be due to conservative forces?

Since the energy is conserved, by definition, the total work done is $0$ (since $W=\Delta E_k=0$). Now, the work $W$ along a path $S$ is given by $$W=\int_S\mathbf{F}\cdot d\mathbf{r}=0$$ so the forces are conservative.