If I'm hit by thrown object, is it momentum or energy that I want to minimize?

Factual Questions
1

In this thread I learned that a gun’s recoil is proportional to the bullet’s momentum and not the energy of the projectile. Indeed, I am informed that

[quote]
One thing to bear in mind is that recoil is proportional to momentum, which is bullet mass x bullet velocity (I’m going to ignore propellant gas mass and velocity, although that isn’t strictly valid.)

Muzzle energy on the other hand is half bullet mass x bullet velocity squared.

So if you double the bullet velocity and half the bullet mass, the recoil stays the same but the muzzle energy doubles.

[quote]

Okay. So now I am wondering this: The amount of Umph!, a highly technical term, that I feel coming toward me is proportional to the momentum rather than the energy, and it seems intuitive that the Umph! is what’s going to ruin my day–getting hit by an object with more Umph! is going to hurt more than getting hit by an object with less Umph!.

According to the above quote, if I was going to choose between being hit by someone throwing a bowling ball vs. someone throwing a cue ball, the cue ball may be preferable because even though it can be thrown with much greater speed, and therefore having much greater energy (since the squared term is the rate of travel and not the mass), the massive mass of the bowling ball will give that slow-moving orb a much higher momentum and therefore much more Umph!

Then again, my body is going to be the unwitting recipient of the kinetic energy of the thrown object, and it makes sense that more of that would be worse than less. For example, my dad, and engineer for GM, always told us that having a car crumple & fall apart during a crash was good because in doing so it absorbed more energy in the crash and transferred less to the driver. Then again, I may have misunderstood the argument!

So now I’m confused. As a knowledgeable person, which would you prefer: to be hit by a slowly thrown bowling ball with massive momentum, or by a quickly thrown cue ball with massive energy? Please explain to me why this choice is wise in terms that I, a lay-person, can understand.

Thanks much!

js_dodging-bowling-balls_africanus

2

I didn’t read your post, it’s just too long but I did read the last paragraph.

You want to minimize energy. Instead of explaining with math and discussing impulses and stresses or whatever, look at it this way.

A semi truck moving at about 0.05 miles per hours will have about the same momentum as a bullet fired from a gun. The bullet has more energy. As long as you’re not trapped bewteen the truck and a wall, you’d rather get hit by the very slow moving truck. Right?? In this case, you’ve minimized the energy. Same thing for a bowling ball.

NOTE TO YOU MATH TYPES: Do not check the math. I didn’t do any. I am just trying to get the point across. Maybe the truck would be moving slower or faster but not enough in either direction to invalidate my story.

3

It’s been a long time since I’ve taken Physics, but I don’t think your analogy is valid. The truck and the bowling ball will exert very different pressures on your body. The truck is spread out over your whole body, and the bullet makes contact with a small point.

If a corner of the truck were to make contact with your head, I don’t think it would be very pleasant.

4

Saranga refers to the physics term called ‘impulse.’ I’m not up on the math, but this is the idea relating the amount of energy/force to the time during which contact was made. A collision will have higher impulse if the force is increased or the time during collision is decreased. This is why parachuters bend their knees and do a controlled roll on landing, to lengthen the time of impact and spread out the force over time. This is directly analogous to automobile crumple zones.

5

Agree. Also note that in many circumstances, it would be possible to run out of the way of a slow moving truck, even after the initial contact. This has nothing to do with momentum v. energy though.

As far the OP goes, my understanding is that there has been much debate over what is more important to stopping power (as well as to lethality), momentum or energy. I believe that the question isn’t settled. Note that the answer arguably depends as much on human physiology as on physics.

6

Energy should be the key parameter when looking at bullet damage. Consider: the damage a bullet will do, if we simplify things, ought to be a function of how far it penetrates. The deeper the hole, the more it hurts, right? How do we calculate penetration distance? First, let’s look at acceleration. After impact, the bullet will be decelerating due to the force it takes to tear through flesh (F = ma, right?). If we assume that the force is constant (not a bad assumption, I think, if we assume constant tissue density), then the graph of the velocity will be the integral of acceleration: a straight line starting at initial velocity V[sub]0[/sub] at time = 0 and ending at zero velocity at some later time. That later time, in fact, is equal to [V[sub]0[/sub]/a] (graph it if you don’t believe me), which, since a = [F/m], is equal to [V[sub]0[/sub]m/F].

Now, the distance the bullet penetrates is the integral of the velocity, which in this case is the area under the triangle of the velocity graph. That area is [(1/2)(V[sub]0[/sub])(V[sub]0[/sub]m/F)] = [(1/2)mV[sub]0[/sub][sup]2[/sup]/F)]. And that equation has a factor of energy [(1/2)mV[sub]0[/sub][sup]2[/sup]] in it. And thus, the damage a bullet does is proportional to energy, assuming other factors are equal.

So if you were to take two projectiles with the same momentum, one with twice the mass and one with twice the velocity, the one with twice the velocity (and thus twice the energy) would do more damage, all other things being equal. The projectile with the greater mass would travel into your body for the same amount of time, but, due to its smaller velocity, it would travel a shorter distance.

Note some assumptions were made in this post to simplify, but I don’t think the assumptions invalidate the conclusion, they just make the calcuations harder. And the truck analogy is somewhat misleading, too, despite coming to the correct conclusion.

7

Physics-type here:

a) First off, energy IS related to momentum. Even if not a direct relation, there IS still a relation! Both kinetic energy and momentum HAVE a “m” (mass) term and a “v” (velocity) term. So, they are linked, so to speak. In short, a reduction in “m”, “v”, or both “m” and “v” terms will reduce both energy and momentum.

b) As for what you’d rather be hit with, those who mention that the front of a truck has a greater surface area are correct. You must consider the area over which the force is spread. The less surface area, the more pressure. But, personally, you don’t want to be hit by either one.

c) But, how do you find the force? Impulse will yield the force felt if you know the length of time of impact. But, impulse relates to momentum, but we’d need to know the time it took for the bullet (or truck) to go from “v” to zero. Impulse requires us to know the change in velocity over what length of (change in) time.

d) Skipping the math, the ballistics problem is solved by considering total energy (potential + kinetic) AND momentum…to find muzzle velocity, the typical unknown. You CAN’T separate them! This is, perhaps, the trickiest thing to get used to for me and my fellow classmates always were pre-programmed just to look at energy alone. This may be the same trap you are falling into…and concept with which you are struggling.

You must use techniques of simultaneous equations to solve for “vmuzzle”. You have to remember the momentum of the system before has to equal the momentum of the system afterwards. A ballistics pendulum and a fast camera is often used to gather the necessary data.

e) The same problems affect how a satellite changes its orbit. Dang, it’s the ole conservation of energy + conservation of momentum simultaneous problem again!

  • Jinx
8

Just checking: Would it be four times the energy, since the velocity is squared?

Right. But that doesn’t mean that they have the same minima & maxima. Suppose I’m at the fair and I want to win one of those sledge hammer & bell things. Suppose also that my strength is fixed and my ability to accelerate the hammer is decreasing with the hammer’s mass. I can choose to go for maximal momentum by, let’s say, choosing a huge sledge hammer; or, I can choose to go for maximal energy by choosing a small sledge hammer. Which should I choose? (I’m told that the key to those is to swing as fast as possible and not as hard as possible.)

Now, if I’m gonna get hit by something, we should assume away stuff like surface area since I’m asking about momentum vs. energy, and those vs. the impulse.

Well, I was kind of thinking of just getting hit generally, rather than by bullets specifically. Though I think I follow your argument.

So this is much trickier than I had assumed? I’m getting the impression that I have to decide on all sorts of things to get a specific answer, and that answer will change with my assumptions. For example, if I am wearing a stiff breast-plate so that the impact is spread out over the same area for the bowling & cue balls, and I’m against a brick wall so that the length of impact is essentially the same for both, then I may get one answer.

If we assume instead that I’m taking it on an unprotected sternum, the answer may be something else because how much my ribcage distorts will affect the length of impact & therefore the impulse.

Then if it is a penetrating bullet we have not only the depth of penetration, but things like hydraulic shock to think about, which may give me a third answer.

Or, going back to the sledgehammer & bell game at the fair, if the former carnie I knew was correct, then swinging fast is the answer for that game, I imagine for the same bullet argument zut gave. But if the same carnie was trying to smash a brick wall, he may choose a heavier hammer for some reason that I don’t understand–maybe because impulse relates to momentum as Jinx has indicated.

Am I justifiably confused?

9

Yes, sorry. I was thinking of the fact that the projectile with “twice the velocity” had “twice the energy” of the one with “twice the mass”, and thus four times the energy of the baseline. I just didn’t get all my factors of two straightened out in the post.

Well, yeah, you have to make some assumptions about impact area and so forth and so on, but I would think that a good rule of thumb would be that damage to your body roughly scales with particle energy.

Consider a slightly different argument: Energy during an impact is neither created nor destroyed. For an impact where a relatively small object hits a relatively large one and sticks (a bullet hitting your body, e.g.), the final kinetic energy is very small compared to the initial KE. The rest of that energy goes somewhere.

Now, it takes a certain amount of energy to pull apart atomic bonds. Pulling apart atomic bonds = tearing or breaking tissue or material. More energy = more bonds broken = more damage.

As a rule of thumb.

10

another way to express momentum is force * time;

thus if you can spend more time slowing down an object you will experience less force. a slow moving object will give you plenty of time to slow it down with ease. a bullet of same momentum will only give you microseconds to slow it down so the force will be enormous and it will go right through you.

using same logic if we have two objects of same energy but different momentum, like object A and ojbect B that is 1/2 speed and 4X mass. then the object with bigger momentum ( B ) will still do more damage even at same energy. because you will have 2X time to stop 4X mass, so the net force will still be 2X more.

thus it seems to me you want to minimise both momentum and energy, err … :slight_smile:

11

Energy, assuredly. When you fire a rifle, momentum is conserved. That is, the momentum of the bullet is equal and opposite to the momentum of the recoiling rifle. Will you be hurt worse by the recoil or by the bullet? :smiley:

12

Disagree, vasyachkin, I think. You’re assuming that force is a function of initial velocity and mass. Why would that be? The force is externally applied. I can see the force as being a function of the whatever the projectile is hitting, and a function of projectile size and shape, but why would force change with projectile velocity? Or mass?

13

Anyone who has a smattering of physics and who has played both squash and tennis can answer this. The answer is energy.

Imagine a ball, say one of those superbouncy plastic ones. Say it gets thrown at you at a certain speed and bounces off your head. The ball will ricochet off at nearly the same speed it hit you at. The momentum imparted to you is high, but the energy mostly stays with the ricocheting ball. Your head will be fine.

Now imagine a ball like a squash ball that is not very bouncy. In fact, imagine a ball of something that splats against you when it hits. Say the ball is the same weight and is travelling at the same speed as the last one (ie same energy). When it hits it imparts all its energy (more or less) to you and it hurts like hell.

14

I think this answer is the best so far. It’s obviously correct, the bullet and the rifle do have the same momentum, but different kinetic energies. The bullet will kill you, but the rifle won’t.

The only other difference is in the impact area. The bullet has a smaller area than the stock, so the pressure from the bullet would be greater even if the force was the same.

With a pen-gun, the impact area in the heel of the palm is almost the same as the impact area of the bullet. Firing the pen-gun might hurt, but won’t break the skin. Unlike the bullet that comes out the other end.

15

because the projectile must be brought to a stop by your body, if it doesnt stop it makes a hole in you and you die.

to bring it to a stop you have to absorb its momentum, which is Mass * Velocity and another measure of momentum is like i said Force * Time. Because Force/Mass = Acceleration and Acceleration * Time = Velocity so the two formulas for momentum can be derived from each other.

The faster it travels the less time your body will have to stop it, because if it moves fast and takes a long time to stop - by the time it has stopped it will already have penetrated all the way through - again, you die.

and the less time you have to stop it the greater the stopping force will have to be etc …

16

in case of bullet and recoil it just so happens that energy of bullet is high and momentum is low. you can’t jump to conclusion from this that it is the energy that kills.

you can come up with a different example where energy is low and momentum is high and you still end up dead. like take an average truck like dodge ram, accelerate it to just 5 mph and have a person stand in front of a concrete wall when the truck hits him. at only 5 mph the energy will not be that high, but the the person will get squashed, and that despite the fact that the front of the truck does not have a pointy shape like a bullet. if you hade a bullet shaped rod at the front of the truck it would probably penetrate the person at even 1/2 mph.

17

Everyone, including the OP, has been discussing projectiles up to this point. Your Dodge Ram squishing someone is not really relevant, because it’s a different class of problem.

Crushing someone’s head in a vise is the ultimate extension of the Dodge Ram example. There’s still energy involved, but momentum can be made arbitrarily small by slowing the speed of the jaws.

The bit about the rod doesn’t really add anything either, because again the momentum can be made arbitrarily small.

18

Now I think I understand something I saw about tank projectiles. Some Discovery show or other on military tanks said that a solid projectile shot by a moder battle tank has as much energy as a locomotive hitting a brick wall at 70 mph.

But that doesn’t mean that if you put a tank on a railroad crossing and hit it with a train going 70 mph, then the tank would only rock as though it had just fired a shot, while the train would be stopped dead in its tracks. The train will have massive momentum relative to the projectile, and the impact with the tank would be unpleasant for the occupants of the tank, indeed.

Looking for momentum, I came across Wikipedia’s physics of firearms[/ur] and I followed the link to ballistics, and then took the second external link under ballistics, then took the link to [url=www.mindspring.com/~ulfhere/ballistics/myths.html]Myths, Misconceptions & Miscalcuations, and I see the author state:

According to this author, if I am reading him correctly, it is the energy absorbed in the form of penetrating into and pushing out, i.e. creating a cavity, that is harmful to the target–similar to zut’s discussion of the bullet. Momentum-wise, there really isn’t too much to worry about.

So in the billiard ball vs. bowling ball scenario, if my stomach mucsles are strong and I take the balls in the gut, the bowling ball might be more unpleasant since the momentum will compress my stomach and knock the wind out of me, whereas my abs could absorb the higher energy of the cue ball and I’d be okay. But if I’m getting hit in the head, the energy of the cue ball will be absorbed in the form of my cracking skull, which would be bad, whereas the bowling ball might rattle my head without enough energy to do any real damage. Am I on the right track with this?

19

…Looking for momentum, I came across Wikipedia’s physics of firearms and I followed the link to ballistics, and then took the second external link under ballistics, then took the link to Myths, Misconceptions & Miscalcuations…

20

So if I understand the discussion so far, your body has to deal with both the energy and momentum of a projectile. In the case of a bullet the energy is far more of a concern. Is this correct?