Physics presentation: collisions

Consider the collision of these two cars. Or rather, the "interaction" of these two cars, as they exchange momentum with each other, and convert kinetic energy to deformation. We'll be seeing a lot of interactions in this presentation. But don't worry, nobody gets hurt. (Video link: "2009 Chevrolet Malibu and 1959 Chevrolet Bel Air.")

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

What will differentiate completely inelastic, inelastic, and elastic collisions is whether or not they stick to each other, and whether or not there is permanent damage.

In a 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.")

For an 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.")

And for an 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.")

Let's organize the types of collisions in a flowchart that differentiates between them by asking whether or not the two objects stick to each other, and whether or not the two objects are permanently damaged. Note that the elastic collision can be considered the most restrictive case, being a collision that is selected against both criteria (not stuck together, no permanent deformation).

Consider which conservation laws apply for these types of collisions.

Let's revisit our collision type flowchart with kinetic energy conservation in mind.

• 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.

As pointed out earlier, an elastic collision can be considered the most restrictive case, being a collision that is selected against in both criteria (not stuck together; no permanent deformation), and the only type of collision where kinetic energy is conserved, as none is lost to deformation.

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

Note there is no (cosmetic) damage to the bumper of this car in this slow-speed bumper test after it rebounds, which would make it a(n) ___________ collision, where kinetic energy __________ conserved. (Video link: "Bumper Crash Test: 2007 Toyota Camry.")

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).

Note the damage to the bumper of this car in this slow-speed bumper test after it rebounds, which would make it a(n) ___________ collision, where kinetic energy __________ conserved. (Video link: "Bumper Crash Test: '07 Volkswagen Passat.")

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).

Note the extensive damage to the truck in this high-speed frontal offset collision test, which would make it a(n) ___________ collision, where kinetic energy __________ conserved. (Video link: "2001 Ford F-150 frontal offset test.")

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...

So what conservation law(s) apply for collisions? Momentum can be considered to be conserved for 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.

What type of collision is this? Is kinetic energy conserved?

What type of collision is this? Is kinetic energy conserved?

What type of collision is this? Is kinetic energy conserved? (Video link: "Top Gear - Car hit by train - Car safety message - BBC.")

Observe this bullet being fired into a baseball (and passing through it, exiting out the other side). What type of collision is this? Is kinetic energy conserved? (Video link: "Will a .22LR Bullet go THRU a baseball? In Real SLOMO.")

Now consider this elephant gun being fired (a slug exits the gun to the right, and is included in the gun and person system). What type of collision could this be considered the time-reverse of? Is kinetic energy conserved? (Video link: "...Shooting 700 nitro GunTest.MP4.")