# How many Newtons of force would kill a person?

Gold Member
So yes, the atmosphere exerts a force of 100,000 newtons per square meter. A person's head, is obviously much less than a square meter (probably 0.15 meters on the side, which roughly translates to Pi*(0.15/2)^2 square meters). Anyways, for this matter this is irrelevant, as we are already in equilibrium with this force and so we're more concerned about extraneous forces. Now, I know this would depend *a lot* on where the force is exerted and how it's exerted. For this, I'm mostly curious about arbitrary falling objects (rather than, say, bullets). How many Newtons of force would it take to have, say, a 50% chance of killing a person? How many would it take to hurt a person?

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QuantumPion
Gold Member
I don't think there is any general answer for this. A bullet doesn't produce a particularly large force, its speed and density allow it to penetrate the body. On the other hand, a large but flexible ball could land on your head and produce a huge force without doing any damage.

It's far too complicated a subject to even begin to estimate a single force, because as you said it depends hugely on where the force is exerted and over what area. But let's look at two situations, a penetrative situation and a blunt impact.

Penetration (or indentation) is hugely dependent on contact area. So the force required to cause penetration or indentation to the same depth will be lower for a sharp knife than a blunt knife. Hence why it requires a lot less effort to cut a tomato with a knife once you've sharpened it. Essentially, the knife needs to create a stress at the interaction with the incident sample that is greater than the cutting strength of the material, which is related to at least compressive strength and fracture toughness.

Blunt trauma injuries can range from the fracture of bones to internal bleeding to brain damage and even stopping the heart. For many of these injuries there are different theories as to causal criteria. Essentially, for brusing and contusion it's a function of applied stress to soft tissues, and for head injuries acceleration (both linear and rotational) are important.

When it comes to impacts, the force that is experienced by your body is determined by a variety of things. The speed of the falling object at impact (relating to rate dependency of the surface being hit), the mass of the falling object (determining the kinetic energy of the object at impact e.g. a 10kg mass falling from 1m has 10 times the kinetic energy of a 1kg mass falling from 1m), and most importantly of all the deformation characteristics of the surface being hit, because in the case of an impact, the peak force experienced by your body is related to how the object is slowed down to rest. After that, you have to consider the area over which it's acting again in a similar way to the penetration example.

Staff Emeritus
2019 Award
QuantumPion touches on what is the key fact - damage is not done by force, but rather by the differences in force. If every atom in your body and the surrounding environment were suddenly and magically accelerated at a billion gravities, you would be perfectly fine.

D H
Staff Emeritus
Force isn't a particular useful concept when comes to addressing impacts. Impact forces can be extremely high. Even then, the concept of force is a bit fuzzy. You can get very different values just be changing how finely you want to divide time. Force does come into play in the sense that a high impact force is needed for a small object to penetrate skin and bone. To dispel the notion that force is the critical factor, consider the needle yielded by a nurse in a doctors office. The impact force of this needle is incredibly high. Unless the nurse pokes your jugular the needle won't kill. The impact forces in an auto collision are much smaller than the needle, but that car collision may well kill.

Momentum and energy are much important concepts than force. Which of momentum or energy is more important depends on the circumstances. Consider two collisions of some object with a person's head: A purely inelastic collision with a 10 gram bullet traveling at 350 meters per second versus a nearly elastic collision with a 0.43 kg soccer ball traveling at 25 meters per second. The bullet transfers 1225 joules of energy but only 3.5 newton-second of momentum to the head while the soccer ball transfers about 21.5 newton-second of momentum but only a small amount of energy to the head. The bullet can kill while the soccer ball might leave an red mark on the defender's head and give him a bit of a headache. Now bump the soccer ball's speed up some, say to 59 meters per second (the fastest recorded kick). Trying to head that ball away might well kill, but in this case it is the momentum transfer that does the damage rather than energy.

robphy
Homework Helper
Gold Member
Momentum and energy are much important concepts than force.
Certainly the elapsed time during which momentum or energy is transferred plays a role in this issue.

Dale
Mentor
damage is not done by force, but rather by the differences in force.
To further emphasize this, these differences in force are called http://en.wikipedia.org/wiki/Stress_(physics)" [Broken] is much stronger in compression (205 MPa) than in shear (65 MPa).

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QuantumPion touches on what is the key fact - damage is not done by force, but rather by the differences in force. If every atom in your body and the surrounding environment were suddenly and magically accelerated at a billion gravities, you would be perfectly fine.
Is this true that you can accelerate from 0m/s to 30x10^8m/s without killing yourself?

Is this true that you can accelerate from 0m/s to 30x10^8m/s without killing yourself?
He said if every atom in your body were accelerated that fast at the same time. So he is right. But practically no. Top fuel Drag racers for example, experience 5G's of deacceleration. Their retinas detach from their eyes after repeated races.

Also TIME DOES play a huge role. I learned that when I read this:
http://www.motorcyclistonline.com/gearbox/motorcycle_helmet_review/index.html
You can take 200G's of force to your head for a very very small amount of time.

As noted earlier soft things like balls extend the time of impact. Hard things don't. I think I could use derivatives to explain this. I think I'll ponder this over.

Rap
Is this true that you can accelerate from 0m/s to 30x10^8m/s without killing yourself?
Yes, as long as every bit of your body accelerates at the same rate. If you are in free fall towards a planet, you are accelerating, yet you feel nothing. The more massive the planet, the greater the acceleration. No matter how huge and massive the planet was, you would be fine... until you hit. Then different parts of your body would decelerate at different rates, and you would not be fine.

DrGreg
Gold Member
Is this true that you can accelerate from 0m/s to 30x10^8m/s without killing yourself?
30 × 108 m/s is ten times the speed of light, so nothing can ever reach that speed.

Rap
30 × 108 m/s is ten times the speed of light, so nothing can ever reach that speed.
LOL - right. The original poster said a billion gravities, which got changed to that. You could survive a billion gravities, as long as every bit of your body was subjected to that same acceleration.

LOL - right. The original poster said a billion gravities, which got changed to that. You could survive a billion gravities, as long as every bit of your body was subjected to that same acceleration.

I thought due to relativity we are pretty much, being the size of the universe, being subjected to many gravities.

As well as us moving at 1000 +/- mph.......every atom on this planet is accelerating that much.

And yet when you drive a car. You are accelerating only in the car?

Is there a possibility that a large enough object could strike this planet at 1000+/- mph and stop us?

I assume we would be subjected to a fatal force, that is. everything on this planet

Yeah kind of let my brain flow on this post.....

Pythagorean
Gold Member
it takes very few Newtons to kill someone with a knife or a needle in the right spot, since pressure is force/area; objects with a very small area of contact can create a tremendous pressure.

As a martial artists I'm intrested in the damage cause by blunt force trauma as this is effectively what is suffered in unarmed combat.
I don't think there is any general answer for this. A bullet doesn't produce a particularly large force, its speed and density allow it to penetrate the body. On the other hand, a large but flexible ball could land on your head and produce a huge force without doing any damage.
This is a misleading statement. Although I'm not a doctor I believe the reason a bullet or knife, or any penetrating object kills is because they severe major blood vessels and organs and fluids seep into body parts that are not suppose to have said fluid. This leads to infections, loss of volume and shock which are the ultimate cause of death. It's not the "force" of the impact nor pressure at the point of impact that cause one to die. As evidence of this I point to people who walk around with bullets or shapnel in them that can't be removed surgically.

In the past I've usually wondered if its the force or energy of the impact. I have discounted momentum as a modality of damage. Since energy and momentum are made up of the same components (ie mass and velocity). If you think about what happens if you are hit with a baseball bat that is swung in an arc. You can move inside the swing and take the impact away from the head of the bat, even a little bit, you can really reduce the damage done to you by the bat. Since the tangential velocity is proportional to the radius of the arc, the momentum of a point halfway down the bat is half of that at the tip (I'm assuming the bat is rotating around the grip end and not being swung by a human arm which will add lenght to the radius). Yet the kinetic energy is 1/4. Thus small changes in velocity yield big changes in damage.

The reason I ask this question (force vs energy) has to do with acceleration. If the force of a strike is the vehicle for damage then the ability to accelerate a weapon and not the velocity at impact is the critical factor. In that case, Bruce Lee's famous 6 inch punch can cause as much damage as the same punch thrown from 24 inches(assume arm's lenght). If, however, energy is important then the punch thrown from 24 inches, although striking with the same force (assuming uniform acceleration throughout the execution of the punch), will strike with a higher velocity (thus have more kinetic energy) and cause more damage.

Lastly I wonder how much "Jerk" plays into this (da/dt).

I'd be interested to hear from an MD on this.

QuantumPion
Gold Member
This is a misleading statement. Although I'm not a doctor I believe the reason a bullet or knife, or any penetrating object kills is because they severe major blood vessels and organs and fluids seep into body parts that are not suppose to have said fluid. This leads to infections, loss of volume and shock which are the ultimate cause of death. It's not the "force" of the impact nor pressure at the point of impact that cause one to die. As evidence of this I point to people who walk around with bullets or shapnel in them that can't be removed surgically.

In the past I've usually wondered if its the force or energy of the impact. I have discounted momentum as a modality of damage. Since energy and momentum are made up of the same components (ie mass and velocity). If you think about what happens if you are hit with a baseball bat that is swung in an arc. You can move inside the swing and take the impact away from the head of the bat, even a little bit, you can really reduce the damage done to you by the bat. Since the tangential velocity is proportional to the radius of the arc, the momentum of a point halfway down the bat is half of that at the tip (I'm assuming the bat is rotating around the grip end and not being swung by a human arm which will add lenght to the radius). Yet the kinetic energy is 1/4. Thus small changes in velocity yield big changes in damage.

The reason I ask this question (force vs energy) has to do with acceleration. If the force of a strike is the vehicle for damage then the ability to accelerate a weapon and not the velocity at impact is the critical factor. In that case, Bruce Lee's famous 6 inch punch can cause as much damage as the same punch thrown from 24 inches(assume arm's lenght). If, however, energy is important then the punch thrown from 24 inches, although striking with the same force (assuming uniform acceleration throughout the execution of the punch), will strike with a higher velocity (thus have more kinetic energy) and cause more damage.

Lastly I wonder how much "Jerk" plays into this (da/dt).

I'd be interested to hear from an MD on this.
How is my statement misleading? What do you think is the cause of death due to any other large force? Hitting concrete at terminal velocity? A brick landing on your head?

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How is my statement misleading? What do you think is the cause of death due to any other large force? Hitting concrete at terminal velocity? A brick landing on your head?

I beg to lengthen your answer. A person can die so many ways from all different forces. The one thing I can think of off the top of my head is if you are wearing a very good helmet and get into a crash, the force per unit area is dispersed, and the impact is very small thanks to the collapsing foam liner (think air bags) Yet the person may still die. The brain continues moving inside the skull, and hits it. so the threshold all over the body is different. I can also see other factors playing a role, like the time the force is applied, and impact.

How is my statement misleading? What do you think is the cause of death due to any other large force? Hitting concrete at terminal velocity? A brick landing on your head?

Is this fact or merely speculation??? Have there been studies?? I'd like to see them. You may be correct and the more I think about it the more reasonable the stress, as an answer, becomes to me but I'd like to know if this has been studied? I know in the case of bombs there have been studies and the overpressure or blast wave is the largest contributor to mortality and this would tend to support your theory.

Is this true that you can accelerate from 0m/s to 30x10^8m/s without killing yourself?
Well.. forgetting that the fact that the speed you just expressed is faster than the speed of light; no, you could travel at the speed of light if you either slowly accelerated to it, or if you teleported on a vehicle already traveling at the speed of light.

Acceleration is what matters, not speed. That is why Newtons second law is F=ma (force equals mass times acceleration) instead of force equals mass times speed.

Well.. forgetting that the fact that the speed you just expressed is faster than the speed of light; no, you could travel at the speed of light if you either slowly accelerated to it, or if you teleported on a vehicle already traveling at the speed of light.

Acceleration is what matters, not speed. That is why Newtons second law is F=ma (force equals mass times acceleration) instead of force equals mass times speed.
Someone stated earlier that if the acceleration is uniform it can be as high as anything and you wouldn't be harmed. If every piece of matter in your body is accelerated at the same rate there's no damage done. How you would achieve this I don't have any ideas off the top of my head.

and I apply the force of 5000 newtons to your head, uniformly, for just 1 microsecond. The acceleration of your head will be 1000 m/s^2 , or 100 g, which by itself won't kill you (you can suffer more when you bump your head on something wearing a helmet). The speed gained, for 1 microsecond, will be 1 millimetre per second. However, if this force is applied for more than a small fraction of second, your head is going to gain enough momentum to break your neck.
Furthermore, if same force of 5000 newtons is applied to a small spot, it can break the skull.

edit: haha even better... suppose that you are in spacesuit... a force of 1 newton is applied to you (due to e.g. leak of the suit) accelerating you until you crash into the space station. Or this force is applied off axis, and makes you spin until you exceed maximum survivable centrifugal force. In short, the safe limit on force really depends to circumstances. Pretty much any amount of force is survivable if applied for short enough time.

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and I apply the force of 5000 newtons to your head, uniformly, for just 1 microsecond. The acceleration of your head will be 1000 m/s^2 , or 100 g, which by itself won't kill you (you can suffer more when you bump your head on something wearing a helmet). The speed gained, for 1 microsecond, will be 1 millimetre per second. However, if this force is applied for more than a small fraction of second, your head is going to gain enough momentum to break your neck.
Furthermore, if same force of 5000 newtons is applied to a small spot, it can break the skull.

edit: haha even better... suppose that you are in spacesuit... a force of 1 newton is applied to you (due to e.g. leak of the suit) accelerating you until you crash into the space station. Or this force is applied off axis, and makes you spin until you exceed maximum survivable centrifugal force. In short, the safe limit on force really depends to circumstances. Pretty much any amount of force is survivable if applied for short enough time.
Exactly. You can take 200g's to the head, with a Snell approved helmet for about 2 milliseconds. More force applied for more time to the head could certainly kill you, but the same force applied to your toe will only break it and at worst, with proper medical care ofcourse, you will be missing a toe, but won't die.

Someone stated earlier that if the acceleration is uniform it can be as high as anything and you wouldn't be harmed. If every piece of matter in your body is accelerated at the same rate there's no damage done. How you would achieve this I don't have any ideas off the top of my head.
I wouldn't be so much worried about individual atoms as I would be organs.. But yes, in theory that would work.. But in practice, there could really only be one way to achieve that, which would be a teleportation device or something similar, that would bring a life form down to it's atomic level via de-materialization, send it to it's destination at the speed of light and then re-materialize it at the other end..

I wouldn't be so much worried about individual atoms as I would be organs.. But yes, in theory that would work.. But in practice, there could really only be one way to achieve that, which would be a teleportation device or something similar, that would bring a life form down to it's atomic level via de-materialization, send it to it's destination at the speed of light and then re-materialize it at the other end..
Well gravity doesn't need a medium to travel through. So in theory if we produce artificial gravity by creating a black hole in front of a space ship, and have the black hole move so the space ship never enters the center......Oh..wait....well we'll never see any of the likes within our lifetimes right? ;) So I guess we'll never know for sure.

Well gravity doesn't need a medium to travel through. So in theory if we produce artificial gravity by creating a black hole in front of a space ship, and have the black hole move so the space ship never enters the center......Oh..wait....well we'll never see any of the likes within our lifetimes right? ;) So I guess we'll never know for sure.
Why would we use a Black Hole for artificial gravity? The ship would not be able to escape the gravitational pull from the Black Hole and eventually get pulled past the Event Horizon.