## My mind on my money and my money on my mind

This is an excerpt from quite possibly the geekiest forensic pathology article I have ever read. Three pathologists discuss the physics of how a Mexican coin ended up in the brain of a dead shooting victim.

They speculate he may have been holding it in his hand while shielding his head and the bullet impacted on the coin and both ended up deep in the brain. Oh, but with maths.

The images on the left are an artist’s reconstruction of the position of the man when shot and the path of the bullet, and a photo of the coin in the dead man’s brain.

Items that become accessory or secondary projectiles usually possess a minimal amount of energy, producing superficial or insignificant wounds. The secondary projectile in this case, a coin, gained sufficient kinetic energy to penetrate the scalp, skull, and brain. We believe the coin was being held by the decedent in his left hand next to his head at the time of the shooting. The bullet passed through the hand, producing the described injury and picking up the coin as a secondary projectile before entering the head.

The coin, a 1970 Mexican 50-centavo piece, was 25 mm in diameter with a weight of 6.4 g. In comparison, the diameter of a 1970 U.S. quarter dollar coin is 24.3 mm with a weight of 5.6 g. Both coins contain a mixture of copper and nickel, and the U.S. coin is coated with silver. The mixture of nickel and copper is relatively soft and permits deformation, as seen in this case. The primary projectile, a .380-caliber automatic Colt pistol 9- √ó 17-mm Winchester Silvertip bullet, weighs 5.1 g, with a rated muzzle velocity of 304 m/second (1000 feet/second). The mass of the conjoined projectile more than doubled with addition of the coin, yet retained sufficient velocity to produce the described lethal injury.

We attempted to see if this would be theoretically possible using some simple physical principles. Under ideal conditions, this event represents a form of an inelastic collision. We assumed that there was conservation of momentum between the oncoming bullet and the departing conjoined bullet-coin mass that subsequently penetrated the skull and brain. If momentum is conserved during this collision, then the mass of the bullet multiplied by its velocity would equal the mass of the conjoined bullet and 50-centavo coin multiplied by their departing velocity. The velocity of the bullet just prior to striking the coin is unknown and could not be determined.

For our calculations, we used the known muzzle velocity of this ammunition, understanding the limitations of such an assumption. We also calculated the kinetic energy and momentum of the oncoming bullet and exiting conjoined bullet-coin before and after collision. The results indicate two things: as expected in an inelastic collision, the kinetic energy of the conjoined bullet and coin is much less than that of the oncoming bullet, and the velocity of the conjoined projectile drops by greater than a factor of two. No doubt some of this loss in kinetic energy resulted from the energy expended in deforming the Mexican coin. The calculated loss in velocity of the bullet postcollision slows this projectile (i.e., the conjoined bullet/coin) to <150 meters per second (<450 feet/second). However, this velocity would still be well in excess of the minimal velocity needed to penetrate skin and bone, which has been reported to be about 66 meters per second (200 feet/second).

Forensic pathology has this morbid deadpan geekiness about it which just makes it so interesting to read.

You can just see them in the pathology room, arguing about what happened and sketching calculations on the back of envelopes.

Link to PubMed entry for article.