The 'bullet video' and apparent momentum violation

[danR]

In a rather popular (probably because of the progressively hypnotic music) viral video, often just called 'the bullet video'



we see debris of fragmentation bullets (starting at 1:00 minute) seeming (if you take an informal eyeball-integration of the collective velocities) to go much (much) faster than the incident projectile.

[The early bullets are hard-jacketed, and those are not important.]

What gives? I'm pretty sure most of the debris of some of those bullets is going much faster than the incoming slug itself. I would expect kinetic energy loss into deformation, noise, and heat would actually make the debris move rather much slower, even leisurely.

 

[A.T.]

Of course there is a net loss in kinetic energy. It is only a tiny fraction of the bullets mass that might potentially move faster after the impact.

When you drop a water balloon from just about enough height to make it burst, it might also produce some droplets that fly higher than the drop height.

When you start pouring water into a vessel from some height, the initial splash might also be higher than the fall height.

 

[danR]

Of course there is a net loss in kinetic energy. It is only a tiny fraction of the bullets mass that might potentially move faster after the impact.

When you drop a water balloon from just about enough height to make it burst, it might also produce some droplets that fly higher than the drop height.

When you start pouring water into a vessel from some height, the initial splash might also be higher than the fall height.

I posted this for the very reason the video seems to show quite the opposite phenomenon of those premises ('might', 'some', 'start', 'initial'), and I don't say 'seems' lightly: the great bulk of the debris appears, or rather is, going faster than the incoming slug, and much of that going much faster. There can be no superficial comparison with the well-known water droplet effect.

Almost nothing remains of the slug at the end of impact, and from start to finish, the great bulk of the debris patently appears to be flying outward substantially faster than the speed of the original slug. I'm confident a quantitative analysis of the up and downward (normal to the camera view) debris, representative of all the circular-moving debris, would show an average velocity over the start to end impact time much greater than the incident velocity of the bullet.

Anyone want to look at it and see what I mean?

 

[A.T.]

Almost nothing remains of the slug at the end of impact,

Where do you see how much remains of the slug? Most non-penetrating clips end before you can clearly see the impact point. And even then it would be hard to see how much of the bullet is melted into the plate.

the great bulk of the debris patently appears to be flying outward substantially faster than the speed of the original slug.

As far I can see, some of it is faster, some is slower. Keep in mind that smaller objects appear faster, because they cover more of their own length than a large object at the same speed.

 

[danR]

Where do you see how much remains of the slug? Most non-penetrating clips end before you can clearly see the impact point. And even then it would be hard to see how much of the bullet is melted into the plate.

As far I can see, some of it is faster, some is slower. Keep in mind that smaller objects appear faster, because they cover more of their own length than a large object at the same speed.

All the clips in 1:00-1:50, approx. show tip to end impact, and a couple give as good a shot of the end-material and how much of it remains stuck at the impact point: preciously little; maybe the end millimeter or two of the slug is stuck on the steel plate.

Also around 6:50—. No question of how much remains. Indeed, the very last debris appears to be going somewhat slower than the slug, but the remainder, the bulk of it seems to be going faster.

If the phenomenon is not appearance, I would speculate the slugs have some composite plastic/lead construction whereby the momentum of the lead is being transferred to the light-weight plastic material. Such construction would be consistent with a round designed to disable rather than penetrate.

 

[zoobyshoe]

Interesting video. I see the bullet you're talking about. The debris spreads at a velocity well in excess of the bullet's forward velocity. It's really clear for that bullet, not so clear for others.

The only thing I can suggest is that you're seeing more than just momentum. There could be a pressure effect, such as when you force a column of water through a small orifice (as in a squirt gun). It reacts to the constriction by speeding up. At the interface of bullet and metal there is no room for the fragments to simply rebound straight back. They are forced under pressure to the circumference of the circle represented by the front of the bullet. That path is a great deal more constricted than if they were allowed to simply rebound, so they would be accelerated accordingly.

 

[A.T.]

...maybe the end millimeter or two of the slug is stuck on the steel plate.

You are assuming there nothing in the steel plate, which might be true, but it is not visible in the videos.

the very last debris appears to be going somewhat slower than the slug, but the remainder, the bulk of it seems to be going faster.

Make some screen shots at different times, measure the distances traveled, and calculate the velocity ratios of the debris created at different phases to the bullet velocity.

 

[chrisbaird]

In general, momentum is conserved, velocity is not. Momentum is mass times velocity. Very small objects (like the bullet debris) have much less mass and therefore must go much faster if they are to carry the same momentum.

 

[zoobyshoe]

If we take a 9mm bullet we have a circumference of 28.27mm.

If we consider it hitting a metal plate that is much harder and which it can't penetrate all the fragments must go sideways or back. As it hits the plate a thin column of fragmentation will develop at the plate/bullet interface. Let's guess this column will be an average of 1mm thick. Since the bullet's circumference is 28.27mm the area of the "orifice" through which all the fragments must escape is equal to a slit of 28.27 x 1mm = 28.27 square mm's.

The area of the circle represented by a cross section of a 9mm bullet is 63.62 square mm's.

If we envision the bullet as a column of water flowing in a pipe the "orifice" represented by the bullet/wall interface represents a reduction in pipe cross section area of 2.25 to 1 (63.62/28.27) The "water" would be forced to speed up there.

 

[Ken G]

It looks to me like the effect you get when you drop that toy with a pin in the center and four rubber discs stacked around the pin. The top disk, generally the smallest, comes shooting up with way more speed than the toy you drop. As said above, this toy works by conveying the velocity to a small amount of mass, conserving energy overall. The debris from the bullet does not come out all at the same speed, but your eye is drawn to the outer envelope of the debris, which is the fastest part. Most of the debris does not move with the speed of that outer boundary.

 

[zoobyshoe]

It looks to me like the effect you get when you drop that toy with a pin in the center and four rubber discs stacked around the pin. The top disk, generally the smallest, comes shooting up with way more speed than the toy you drop. As said above, this toy works by conveying the velocity to a small amount of mass, conserving energy overall. The debris from the bullet does not come out all at the same speed, but your eye is drawn to the outer envelope of the debris, which is the fastest part. Most of the debris does not move with the speed of that outer boundary.

This? :

http://www.google.com/products/cata...TuHbKMjnsQLJpsm6Aw&ved=0CGwQ8wIwAA#ps-sellers

 

[Ken G]

Sort of-- that one doesn't look like it's meant to be dropped. But it might behave the right way if you did drop it! Still, those look like wood, and you want rubber-- sort of like super balls, elastic bouncers.

 

[zoobyshoe]

Sort of-- that one doesn't look like it's meant to be dropped. But it might behave the right way if you did drop it! Still, those look like wood, and you want rubber-- sort of like super balls, elastic bouncers.

I've seen those but didn't know they behaved like that. I'm thinking it's like a Newton's Cradle with progressively smaller balls. With pendula, though, you can cut out the middle men and just have a large ball hitting a small one to show how it reflects with a greater velocity than the ball that hit it.

There's an upper limit, though. Halliday and Resnik state that when a large projectile hits a much smaller one (A>>B) the smaller one reflects with a speed twice that of the larger. It can't ever go more than twice as fast. I did a few calculations and got up to the larger object being 70 times more massive than the smaller before I got sick of trying to find the cut off point. At 70 to 1 the small object had a velocity something like 1.9 times the larger.

 

[Ken G]

Yes, that would demonstrate it nicely also.