Re: [Phys-l] Final velocity of bullets

["Jeffrey Schnick" <JSchnick@Anselm.Edu>]

The web site at
http://www.loadammo.com/Topics/March01.htm
indicates that the degree of injury to a person for a given impact point
and angle is proportional to the kinetic energy of the bullet at impact.
Assuming that the force of air resistance is Cv^2 and that the bullet is
at terminal velocity, we have
mg = Cv^2
mv^2 = m^2 g/C
Let D be a characteristic length of the bullet.  Assuming that C scales
as D^2 and that m scales as D^3 we find that the kinetic energy is
proportional to D^4.  These considerations suggest that the danger posed
by a bullet shot straight up depends strongly on the caliber of the
bullet.  Depending on how the shapes and tumbling motions compare, a .45
caliber bullet would have roughly 16 times as much kinetic energy at
impact as a .22 caliber bullet would have.

Jeff Schnick

> -----Original Message-----
> From: phys-l-bounces@carnot.physics.buffalo.edu 
> [mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf 
> Of Ken Caviness
> Sent: Thursday, January 25, 2007 11:24 AM
> To: Forum for Physics Educators
> Subject: Re: [Phys-l] Final velocity of bullets
>
> Very nice!  Thank you, David, for the lucid explanation.