[Physics] How to calculate a collision which is partly elastic and partly inelastic

Question

(For the purpose of this question, "calculating a collision" means: given the velocities and masses of two objects in a collision, figuring out the new velocities of both objects after the collision).

I know how to calculate a totally elastic collision, and how to calculate a totally inelastic collision.

But I don't know how to calculate a collision which is part elastic and part inelastic. I don't know where to start.

Guidance will be appreciated.

_{(Go easy on the math please).}

Answer 1

There is not such thing as a "partially elastic" collision. Classical collisions between particles can be separated into two categories: elastic and inelastic. Elastic collisions are defined as collisions in which no energy leaves the system (i.e. $E_i = E_f$). All other collisions are inelastic, as some energy is lost ($E_i > E_f$). A perfectly inelastic collision is a type of inelastic collision where all the kinetic energy of the system is lost ($E_f = 0$).

Edit: I should mention that these definitions apply to a CM (center-of-mass) frame of reference. For a non-CM frame, a perfectly inelastic collision becomes one where the maximal amount of kinetic energy is lost. Thanks to David Z. for mentioning this.