# Momentum and penetration depth

1. Feb 5, 2006

### bernhard.rothenstein

Many textbooks derive the relativistic momentum from the penetration depth of a bullet in a resistive media, considering that momentum is proportional with the penetration depth. Do you know a transparent and correct way to the problem?

2. Feb 5, 2006

### Astronuc

Staff Emeritus
Bullets are of such relatively large mass and low velocity that relativistic mechanics does not apply, rather classical mechanics is appropriate.

The problem is one of energy transfer as well as momentum, and the actual problem is not so simple in general. It is relatively simple, and more a matter of the properties of the resistive material, e.g. density and viscosity, if the bullet does not deform, although bullet shape and diameter would be a factor.

See - http://www.angelfire.com/art/enchanter/terminal.html (bad link to physics forums archives)

There is a thread on Physics Forums that addresses this issue of terminal ballistics and stopping power.

Momentum is just the rate of change of force, and that is a function of the shear stresses, as well as the density of the resistive media and mass of the bullet.

3. Feb 5, 2006

### bernhard.rothenstein

thanks

thanks for your answer. The problem has a pedagogic value, because if the penetration is proportional to the momentum then an y penetration ensures the invariance of the y component of the momentum.