We'll be emphasizing how to categorize collisions into one of three types, and determining which conservation laws apply to these collision types.
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 (ideally all of that energy went into temporarily "squishing" the bumper, which rebounded and returned that energy).
Answers (highlight to unhide): (partially) inelastic (the cars are separated after the collision); kinetic energy is not conserved (as some of that energy went into damaging the bumper).
Answers (highlight to unhide): completely inelastic (the truck is stuck to the collision barrier); kinetic energy is definitely not conserved (nearly all of that energy went into crumpling the front of the truck).
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...
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.