We'll be emphasizing how to categorize collisions into one of three types, and determining which conservation laws apply to these collision types.

*completely inelastic*collision between two objects, they will stick to each other. Also note the permanent deformation of the car afterwards. (Video link: "Insane Volvo brake test epic fail.")

*inelastic*collision (sometimes known as a

*partially inelastic*collision, to distinguish it from a completely inelastic collision), the two objects rebound off of each other, but there is permanent deformation afterwards. (Video link: "Most Small Cars Aren't Economical for Crash Repairs Ford Foc.")

*elastic*collision, the two objects rebound off of each other, and (ideally) there is no permanent deformation afterwards. (Note that even though there is no cosmetic damage in this collision, there was minor structural damage, but this is close to an ideal elastic collision.) (Video link: "Crash Test of Ford Explorer and Ford Taurus 2004.")

Consider which conservation laws apply for these types of collisions.

- If two cars stick to each other in a
*completely inelastic*collision, then they convert as much kinetic energy as they can into permanent deformation, so kinetic energy is definitely*not*conserved. - If two cars deform and then rebound in a
*(partially) inelastic*collision, then some kinetic energy goes into permanent deformation, while some of it is converted back to into kinetic energy (such that the cars will rebound off each other), so kinetic energy is also*not*conserved. - If two cars deform, and rebound completely without any permanent damage in an
*elastic*collision, then no kinetic energy is lost, so kinetic energy*is*conserved for this type of collision.

Let's practice categorizing collisions, and determining whether kinetic energy is conserved or not.

Answers (highlight to unhide): elastic; kinetic energy is conserved.

Answers (highlight to unhide): (partially) inelastic; kinetic energy is

*not*conserved.

Answers (highlight to unhide): completely inelastic; kinetic energy is

*not*conserved.

For this high-speed collision, ideally the vehicle crumple zones would absorb as much kinetic energy as possible, as opposed to the low-speed fender benders shown above, where the vehicle bumper would deform and rebound back, to minimize cosmetic damage.

What about momentum conservation? If collisions occurred on frictionless roads, and/or the drivers did not apply their brakes, then momentum would be conserved with no external forces/impulses. However, let's limit our discussion to looking at the initial state just before a collision, and the final state just after the collision--since vehicle collisions happen in fractions of a second, even if the external friction forces are large, their impulse would be negligible due to the relatively brief time that collisions take place in, typically fractions of a second. Thus we can set the left-hand side of this equation equal to zero, and the two objects during a collision merely exchange momentum: whatever one object loses in momentum must correspond to an increase in the other object's momentum. Consider this next time you are about to get into an accident...

*any*collision (whether completely inelastic, inelastic, or elastic) provided that it is sufficiently brief, where the initial and final states are just before and just after the collision. However, kinetic energy is only conserved for elastic collisions, as that is the only type of collision where none of it is permanently lost in deformation.

Let's take a look at more examples of brief collisions (such that momentum would be conserved), classify their collision type and consider whether kinetic energy is conserved or not.

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