# Why don't guns kill the shooter?

Since momentum is conserved, why doesn't shooting a gun cause massive injury to the shooter's hand? If this has to do with the surface area of the bullet vs the handle of the gun, would gluing a bullet to the opposite end of the gun, pressing the tip of the bullet on your chest, and firing the gun kill you? If not, why?

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hilbert2
Gold Member
It has to do with the surface area difference as you noted, and probably also the relative velocities that the gun and the bullet get with same momentum, as a bullet penetrating biological tissue is affected by velocity-dependent friction forces.

Staff Emeritus
2019 Award
Why don't hypodermic needs not pierce the flesh of the nurse using it?

rumborak and anorlunda
Nugatory
Mentor
Since momentum is conserved, why doesn't shooting a gun cause massive injury to the shooter's hand?
It's not the momentum that does the damage, it's the kinetic energy. Although the recoiling gun and the bullet have the same (strictly speaking, equal and opposite) momenta, their kinetic energy is different; most of the energy released by firing the gun goes into the bullet.

[Edit: There's more to it than just the kinetic energy; the bullet also concentrates the kinetic energy in a small region which increases the damage done. In your hypothetical about gluing a bullet to the butt of the gun, the recoil might give the shooter a smaller and nastier bruise. The damage is still limited because most of the kinetic energy went with the fired bullet]

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sophiecentaur
hilbert2
Gold Member
Why don't hypodermic needs not pierce the flesh of the nurse using it?
Yeah, a sharp needle can pierce soft material even in a "quasistatic" way, where you can keep the velocity as close to zero as you want throughout the whole process.

sophiecentaur
Gold Member
It's not the momentum that does the damage, it's the kinetic energy.
It may be worth pointing out, yet again, that, whilst Momentum is P = mv, Kinetic energy is E = mv2/2 so, as soon as v gets big, E starts to get massive.

I think it's also worth considering the relative mass of the bullet to the gun when we treat the explosion initiating the gunshot as F. Using Newton's third law, we know that the force applied to the bullet by this explosion will be equal and opposite to that applied to the gun. This means that the resulting acceleration will depend on each object's mass.
Let's call F 100N, m of gun 1.18Kg, and m of bullet .0075Kg. Now using the formula: F=ma, we can determine that under these circumstances, the bullet will accelerate at 13333.3m/s^2, and the gun will accelerate at 84.75m/s^2. Although these values may not be exactly true to real life, the relationship they demonstrate is accurate and significant. The masses used reflect that of a generally realistic relationship using data found online (didn't bother with force which was constant in comparison), and taking that into consideration, the answer can be seen. If we choose to measure an object's relative ability to cause damage in the amount of kinetic energy each element carries, we can work out the following:
Ratio of mass of gun to mass of bullet: 157.333:1
Ratio of acceleration (therefore final velocity given constant distance) of gun to bullet: 157.325:1
K=.5mv^2
In the formula, since v in terms of K has a higher influence than m given its degree, the amount of kinetic energy the object in question possesses will depend most significantly on its velocity. For this reason, a bullet traveling at a higher velocity than a gun even with as little mass it has in comparison to the gun, will have more kinetic energy, and will generally cause more damage. The values found indicate this relationship.

NTL2009
So many elaborate explanations here, but the real reason is that people aren't killed by the recoil of the bullet. They are killed by the effects of the path of the bullet, that is the tearing of blood vessels. Usually nobody dies of being shot in the leg, whereas a shot through the chest usually does you in. Physically, they are the same.

Drakkith
Staff Emeritus
So many elaborate explanations here, but the real reason is that people aren't killed by the recoil of the bullet. They are killed by the effects of the path of the bullet, that is the tearing of blood vessels. Usually nobody dies of being shot in the leg, whereas a shot through the chest usually does you in. Physically, they are the same.
The implied meaning of the original question is why does a bullet tear through your skin and internal organs but the gun does not. The question of why this results in death is not the topic of discussion.

davenn and sophiecentaur
sophiecentaur
Gold Member
The situation with bullet and gun is directly equivalent to the situation with a rocket and its ejecta. The share of energy of the high speed (less massive) member of the pair is far greater than for the low speed (more massive) member. Rockets have 'pathetic' efficiency at the start, when they are near stationary. It gets better as they get faster because the incremental increase in Momentum produces even greater increase in Kinetic Energy, once the rocket has gained some speed.

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PeroK