# Force of a bullet?

1. Jan 16, 2012

### Kevlarji

Hi,

I'm modelling a bullet impacting with a wall, I wish to know how much force the bullet hits the wall with.

Will it simply be a case of F=mv ?

2. Jan 16, 2012

### technician

Force is rate of change of momentum.
i.e the change in momentum/time taken
If you have some idea how long it takes the bullet to come to rest you should be able to get an answer or at least an estimate.

3. Jan 16, 2012

### Matterwave

The easiest quantity to estimate is the impulse, which is just the change in momentum of the bullet. For this, all you would need to know is the initial and final velocities of the bullet, and the mass of the bullet. Obviously this quantity will vary.

From the impulse, if you know the time it takes to make the bullet change velocities, you can get the average force of this bullet via F=I/t.

Probably more important than the force would be the pressure which is simply P=F/A, where A is the area of the bullet head. This will give you an idea of the penetrating power of bullets.

4. Jan 16, 2012

### trueacoustics

I believe you could look at this inversely. A bullet works by projecting a particle with certain speed through combustion. When this combustion occurs, a large pressure it built up within the chamber of the barrel behind the bullet. This pressure will then seek to equalize, projecting the bullet forward. This pressure's ability to project the bullet is proportional to the volume of the barrel. A certain amount of pressure will displace a certain amount of air. The barrel of a hand gun is usually smaller then this amount, and only a fractional portion of the pressure is used for projection. Once the bullet is outside the barrel, the pressure will dissipate in the atmosphere. We can then assume that maximum velocity is reached at the tip of the barrel. Once beyond the barrel, external factors begin to slow it. Therefore, the barrel length must be considered.
Luckily, this is understood by the ammo companies. Their products almost always list the bullet weight (in grains), velocity (in ft/s), and the test barrel's length for that particular round (in inches). Using the information above, kinematic equations, Newton's laws, and bullet specifications we can find the force of a particular bullet upon leaving the barrel of a gun.
Looking at Speer's 45 Auto Gold Dot specs, we have a test barrel length of 5in, bullet weight of 230gr, and muzzle velocity of 890ft/s.
First we use kinematics to find the bullets acceleration. We are given the initial velocity (0m/s), final velocity [890ft/s (271.27m/s)], and distance [5in (.127m)], and we need to find acceleration. Find and use the appropriate equation.
We now have both acceleration and mass [230gr (.015kg)]. This enables us to use Newton's second law to find the force.
The force at different distances can also be found using the same process and the other specs. I have attached the full specs in case you want find these other forces.