Why aren't guns impossible? (physics, not a debate)

Where is my error?

Newton taught us that for every action, there is an equal but opposite reaction. Imagine: Person A fires a gun at Person B, and Person B tries to catch the bullet with his bare hands. Since B’s hand is not strong enough to exert a force upon the bullet equal to the one placed upon it by the gun, the bullet pierces B’s hand.

Right?

OK - Now let’s rewind and look at Person A. How come his hand can withstand the force the bullet exerts back onto the gun? It seems to me that anyone trying to fire a gun should have their hand smooshed by the gun itself!

My brother tried to explain it to me by saying that the energy in the gun is expelled as light, heat, etc through the gun’s vents. But, it seems to me that f=ma and energy doesn’t enter into the equation at all!

I know I am wrong… but where?

There are several factors: First, the force of the bullet is applied to the gun, which has mass and therefore inertia. So the force will build slowly. Second, the acceleration of the bullet happens all the way down the barrel, but when it hits someone it is dissipated much quicker. Imagine if you could wear a bullet-absorbing pad that was as thick as a rifle barrel is long. If the bullet hit that and decelerated constantly until it just touched your skin, you’d be much more able to handle the force.

Finally, the force from the gun is distributed across a wider area on your body. The ultimate example of this is a bullet-proof vest, which distributes the impact forces of the bullet across your chest.

There are some heavy-caliber derringers on the market, but they are downright scary to shoot. I’ve heard of broken wrists from firing them. The main reason is that the gun has so little mass that the recoil shock impulse is much ‘sharper’, and the smaller profile of the gun distributes the force across a smaller part of your hand.

I just thought of a good example - rubber bullets. The design of a rubber bullet makes is spread out when it hits a person, so the force is distributed across a wider area. And, because the rubber takes time to compress, the highest ‘g’ force peak is flatter. As a result, rubber bullets are rarely fatal. I imagine if you taped one to the butt of a rifle and pressed it against your body so that the entire force of recoil went through it, it might feel very similar to a rubber bullet.

Wow this is weird, I was just thinking about this while driving down the road like 2 days ago. It basically just boils down to the size and shape of the gun vs. the size and shape of the bullet. I would imagine the momentum of the bullet would have a bit to do with it as well but if the back of a gun were shaped like a bullet I think it would do roughly the same amount of damage.

The energy is (Roughly) identical for both the bullet impacting the target, and for the gun recoiling into the user.

However, it’s a matter of surface area. Consider a punch with a fist, and a stab with a knife. Both are the same energy/force, but the knife is a much smaller contact area, therefor it penetrates, cutting deep into the target, instead of smacking against it over a wider area. Bullets are the same. An M16A2 would drive a bullet right through a person, but because of the relative size of the bullet and buttstock, the area of impact on the shooter is probably 100 times or more the size of the area of the bullet (Plus the buffer spring makes it more drawn-out instead of all at once). The mass of a gun can also slow the acceleration, so that it’s absorbed over a longer period, but the total force will remain the same.

However, it’s an excelent way to point out the flaws in hollywood portrayals of firearm that send the target flying. The actual physical force imparted on the target is no greater than the physical force imparted on the shooter.

The energy is (Roughly) identical for both the bullet impacting the target, and for the gun recoiling into the user.

However, it’s a matter of surface area. Consider a punch with a fist, and a stab with a knife. Both are the same energy/force, but the knife is a much smaller contact area, therefor it penetrates, cutting deep into the target, instead of smacking against it over a wider area. Bullets are the same. An M16A2 would drive a bullet right through a person, but because of the relative size of the bullet and buttstock, the area of impact on the shooter is probably 100 times or more the size of the area of the bullet (Plus the buffer spring makes it more drawn-out instead of all at once). The mass of a gun can also slow the acceleration, so that it’s absorbed over a longer period, but the total force will remain the same.

However, it’s an excelent way to point out the flaws in hollywood portrayals of firearm that send the target flying. The actual physical force imparted on the target is no greater than the physical force imparted on the shooter.

      • (Nitpicking) Mil .223’s tend to spin around in flesh; the only sure bet is that it won’t go right through. Try a 444 Marlin or a 45-70. <:D - MC

People who are shot IRL who are not already in motion tend to drop like a marionette with its strings cut, and/or have an immediate “guarding” response w.r.t. the wound.

Getting back to the point of Newton’s 3rd law “for every action there is an equal…”, the action is the IGNITION of the explosive and the reaction is the rapid acceleration of the bullet and the recoil.

Actually the action/reaction pair would be the bullet and propulsion gases being forced in one direction and the rifle in the other. The ignition pushes equally in all directions, and would exert a net force equal to zero (if the metal were strong enough to contain it. It’s not), except that there is only one direction for it to escape the chamber: Towards the bullet.

Or, if another reiterations was required, consider hitting something (say, a plank) firmly with a mallet, then doing the same again, with the same force, but with a nail in between the mallet and the plank*.

8[sup][Yes, I know that a mallet isn’t the right tool for driving nails)[/sup]

Quoth Phoenix Dragon:

No, no, no… The momentum of the gun and bullet is the same (but in the opposite direction). The energy of the bullet is much greater than the energy of the gun. If, for instance, the gun weighs 500 times as much as the bullet, then the bullet will have 500 times as much energy.

The difference in the amount of damage is the duration of the impact (longer for the butt hitting your shoulder, since the barrel is so long), and the fact that the recoil force is more spread out.

sdimbert said:

No. The problem is not the force, but the pressure. Specifically, the force and the area over which it is applied. Think of the old carny/fakir trick of the bed of nails. The mystic is able to “magically” lie on a bed of sharp nails and not get penetrated. How does it work? He uses enough nails spread across his whole body (or at least whole torso) that it distributes the force on any one nail down low enough not to pierce the skin.

When the cartridge fires, the force generated pushes in all directions equally. The expanding gasses push “out”. However, there are a couple factors that control the effect. For one, the bullet has a smaller mass than the gun, so it is accelerated more for the same force. The force pushes the gun and bullet equally – F=ma, so
m[sub]gun[/sub] a[sub]gun[/sub] = m[sub]bullet[/sub] a[sub]bullet[/sub]
That’s the intertia of the gun vs. inertia of the bullet, or resistance to change of motion.

Note that the pressure pushing sideways versus the gun is equally reacted by the barrel, so it doesn’t push either direction. There is some twisting caused in automatics and semi-autos by the release of the gas to cycle the chamber and by ejecting the empty cartridge. There is also some jerk of the gun upward caused by off-center loading of the stock vs. the bullet.

If the stock has springs or is rubbery instead of rigid, it can also absorb some of the kinetic energy of the shot.

Bullet-proof vests use two factors. First is it distributes the force across your whole chest. Second, the collapsing of the fibers dissipates energy. The first probably plays a greater role, but with kevlar the second has some benefit.

Actually, sometimes they do. It depends on where you get hit.

Sorry you didn’t get to stay in Phoenix longer or I could have given you a real world demonstration of the physics involved. (from the shooting end, not the target end naturally)

Aside from the relative masses involved - the handgun can easily have 100 times the mass of the bullet - the design of a handgun doesn’t put all the recoil energy into your hand. The barrel of a handgun is well above the grip. On firing there is a rearward push but since the force vector isn’t aligned with your wrist the gun rotated upward at the barrel.

All bullets spin but military rifle bullets are particularly prone to tumbling once they hit a target. The 5.56mm NATO (.223) in particular uses a bullet that it aerodynamically unstable - it wants to fly backwards. Gyroscopic force is the only think that makes it fly sraight. The bullet is small, about 1/7 of an ounce for the 62 grain SS109 bullet (even more unstable and more prone to fragment than the bullet it replaced), but it’s moving at almost 3,000 feet per second out of the barrel and spins at one revolution every seven inches - about 25,000 rpm. It makes for something most unpleasant to be hit by.

Padeye,

I should have realized that you would post to this thread!

BTW, what happened to those pictures?

Thanks for the info, everyone.

Or a thousand times, if it’s a rifle. ( A 55 or 62 grain 5.56mm bullet is about 4 grams; an M16 is 4.2 Kilograms)

Another element to consider is that the weapon is not a body “moving towards you” at the recoil speed, you are holding it. So essentially you make up a system of the weapon + your not-too-rigid body as a sort of uber-buffer.

The way I had always figured it was:

  1. F = m*a
    The detonation exerts force equally in all directions but only has effect along the barrel axis (since that’s where motion is possible). If the round’s weigh is 5 grams and the gun’s weight is 1 Kilogram, the acceleration imparted to the weapon is barely 0.5% of the acceleration upon the bullet.

  2. Conservation of momentum:
    (bullet mass)(bullet speed)= -[(gun mass)(gun speed)]

If the round’s muzzle velocity is 800m/s, the backwards velocity of the gun would be 4m/s.

  1. Kinetic Energy = 0.5 * (mass) * (speed^2)

KE of bullet: 0.5 * (.005) * 640000 = 1600 joules
(hitting you all at one tiny spot)

KE of gun: 0.5 * (1) * 16 = 8 joules (spread over your arm and shoulder through the grips and stocks)

And that it was concentrated KE that did the damage.

How much of the energy is dispersed through the generation of sound waves? For instance, if you use a silencer, are more of the soundwaves absorbed into the silencer which, in turn, is converted into more recoil? In other words, if you use a silencer is there a greater recoil?

Phoenix Dragon wrote:

Many people think that the head shot that killed President Kennedy, with his head snapping back violently to the left and back, is evidence of a shooter to his front right. However, as you point out, the momentum of the bullet, even if had been stopped inside his head, wouldn’t be enough to cause this reaction. I guess people believe those idiotic conspiracy theories partially because of Hollywood’s protrayal of gun shots.

then wishbone wrote:

As Chronos pointed out, the factor here is momentum, not energy. The momentum of all the stuff leaving the barrel is the same as the momentum of the recoil against your shoulder/hand. The stuff leaving the barrel is partially air, and partially bullet. I’m not positive about how a silencer works, but it probably catches some of the air as it’s leaving the barrel, so this would tend to decrease the recoil, but it seems like it would be slight at most.

Well, depends :slight_smile: I wish I could find the source I got them from, but I found some drawings depecting the 5.56x45mm NATO going through a body. Assuming it doesn’t hit bones, it travels up to 34cm, enough to go through the body from a front shot.

But you’re right, it won’t -always- go through all the way. Too many factors to include :slight_smile:

Errr… I must be missing something here? Energy is a mater of velocity and mass, correct? If you apply some 2 kilojoules of energy to accelerate a bullet, the gun is affected by the same energy. The difference being, while the incredibly light bullet may be going some 300-900 meters a second, the much, much hevier gun, with the same energy applied, would probably be accelerated to less than 1 meter per second. Right? It seems that momentum and energy could be used interchangably… Though it -has- been a long time since my last physics class, so I could be wrong (In which case, please explain it to me, so I don’t make myself look like even more of a fool :wink: ).

For anyone who knows: How many cc’s of gas is created when a bullet is discharged? I heard that it was about the same volume as an elephant. Is this an exaggeration?