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Lesson 2: The Law of Momentum Conservation
The Law of Action-Reaction (Revisited)
A collision is an interaction between two objects which have made contact (usually) with each other. As in any interaction, a collision results in a force being applied to the two colliding objects. Such collisions are governed by Newton's laws of motion. In the second unit of The Physics Classroom, Newton's third law of motion was introduced and discussed. It was said that...

... in every interaction, there is a pair of forces acting on the two interacting objects. The size of the force on the first object equals the size of the force on the second object. The direction of the force on the first object is opposite to the direction of the force on the second object. Forces always come in pairs - equal and opposite action-reaction force pairs.

Newton's third law of motion is naturally applied to collisions between two objects. In a collision between two objects, both objects experience forces which are equal in magnitude and opposite in direction. Such forces often cause one object to speed up (gain momentum) and the other object to slow down (lose momentum). According to Newton's third law, the forces on the two objects are equal in magnitude. While the forces are equal in magnitude and opposite in direction, the acceleration of the objects are not necessarily equal in magnitude. In accord with Newton's second law of motion, the acceleration of an object is dependent upon both force and mass. Thus, if the colliding objects have unequal mass, they will have unequal accelerations as a result of the contact force which results during the collision.

Consider the collision between the club head and the golf ball in the sport of golf. When the club head of a moving golf club collides with a golf ball at rest upon a tee, the force experienced by the club head is equal to the force experienced by the golf ball. Most observers of this collision have difficulty with this concept because they perceive the high speed given to the ball as the result of the collision. They are not observing unequal forces upon the ball and club head, but rather unequal accelerations. Both club head and ball experience equal forces, yet the ball experiences a greater acceleration due to its smaller mass. In a collision, there is a force on both objects which causes an acceleration of both objects. The forces are equal in magnitude and opposite in direction, yet the least massive object receives the greatest acceleration.

Consider the collision between a moving seven-ball and an eight-ball that is at rest in the sport of table pool. When the seven-ball collides with the eight-ball, each ball experiences an equal force directed in opposite directions. The rightward moving seven-ball experiences a leftward force which causes it to slow down; the eight-ball experiences a rightward force which causes it to speed up. Since the two balls have equal masses, they will also experience equal accelerations. In a collision, there is a force on both objects which causes an acceleration of both objects; the forces are equal in magnitude and opposite in direction. For collisions between equal-mass objects, each object experiences the same acceleration.

Consider the interaction between a male and female figure skater in pair figure skating. A woman (m = 45 kg) is kneeling on the shoulders of a man (m = 70 kg); the pair is moving along the ice at 1.5 m/s. The man gracefully tosses the woman forward through the air and onto the ice. The woman receives the forward force and the man receives a backward force. The force on the man is equal in magnitude and opposite in direction to the force on the woman. Yet the acceleration of the woman is greater than the acceleration of the man due to the smaller mass of the woman.

Many observers of this interaction have difficulty believing that the man experienced a backward force. "After all," they might argue, "the man did not move backward." Such observers are presuming that forces cause motion. In their minds, a backward force on the male skater would cause a backward motion. This is a common misconception that has been addressed elsewhere in The Physics Classroom. Forces cause acceleration, not motion. The male figure skater experiences a backwards force which causes his backwards acceleration. The male skater slows down while the woman skater speeds up. In every interaction (with no exception), there are forces acting upon the two interacting objects which are equal in magnitude and opposite in direction.

Collisions are governed by Newton's laws. The law of action-reaction (Newton's third law) explains the nature of the forces between the two interacting objects. According to the law, the force exerted by object 1 upon object 2 is equal in magnitude and opposite in direction to the force exerted by object 2 upon object 1.


http://www.glenbrook.k12.il.us/gbssci/Phys/Class/momentum/u4l2a.html


Notice that in a collision it is "Forces" and "Momentum" that govern no where is "emergy relationships mentioned

Notice that Energy IS NOT CONSERVED in enelastic Collisions, which is what a bullet hitting a Deer is

Well you got the half about hitting a deer right, in that it is an inelastic collision.

BUT YOU ARE WRONG in stating that energy is not conserved in an inelastic collision. In fact, both momentum and energy are conserved - what is not conserved is KINETIC energy. Instead, some kinetic energy is turned into other forms of energy, such as heat.

What leads you to believe that? For a good portion of my university education I was a physics major, and I can't see any reason why a transfer of energy would violate any of the 3 laws of motion.

When the balls collide, there is a transfer of momentum AND energy, the two are very finely intertwined.

I agree 100%. Keep in mind that at no time did I say that more energy equals greater killing power. I was simply evaluating and describing what happens when a bullet hits an animal in terms of physics. I'm not saying that energy kills, although a bullet certainly needs energy to kill an animal. Also remember that momentum is the mass multiplied by the velocity of an object, and kinetic energy is one half of the mass times the square of the velocity of the object. It is easy to see that both figures are VERY proportional to each other.

If you have momentum, you also have kinetic energy.

I disagree. I would say that a bullet hitting a deer is an imperfect elastic collision, since the motion is transferred to the particles of the deer. The lung tissue, bone fragments, etc are put into motion by the bullet. It is true that kinetic energy isn't perfectly conserved, and therefore it isn't a perfectly elastic collision, but that doesn't mean that there is not a transfer of energy.

To illustrate a perfectly elastic collision, we can take two billiard balls with no friction colliding. The total kinetic energy in the system is the same after the collision as before.

To illustrate a perfectly inelastic collision, we can take a man running straight into a brick wall. All kinetic energy was lost in the collision.

Now that's splitting hairs

You're right though, energy cannot be created or destroyed, only converted into different forms.


I think the real discrepancy here in this debate lies in the fact that CONSERVATION isn't the same as a TRANSFER. I think we'll all basically agree about what causes the deer to die, but we need to understand that momentum is conserved and transferred, while kinetic energy is NOT conserved, but is TRANSFERRED, therefore energy figures are a poor measuring stick for killing power.

I can agree with that, Jordan except for the part about energy being transferred, it is transformed into other forms of energy, mostly thermal. That is why in an enelastic collison energy is figured as heat (Joules or BTU's)

I've always contended energy is not a perfect yardstick, not even close. Other factors being equal, what is more important is the amount of energy transferred and the time in which it is transferred. 3000fpe over a couple of milliseconds is going to hurt. Spread that energy out over a year and it doesn't do much at all.

One thing is very true, however - a bullet cannot transfer more energy than it starts with.

Go here and it clearly shows that Kinetic Energy is lost in enelastic collisions.

http://hyperphysics.phy-astr.gsu.edu/hbase/inecol.html#c1


I may be wrong and if so Physics is also wrong

A 250 pound NFL running back that runs a 10 second 100 yard dash has 3497 FPE< if energy was the primary wounding factor then the Morgue would be full of NFL players after each game

Apparently you have a reading comprehension problem. What I said was that in an inelastic collision "what is not conserved is KINETIC energy". In other words, kinetic energy is lost in inelastic collisions. That agrees with the link you provided.

To state that kinetic energy is lost, however, is not the same thing as saying energy is lost. In fact, energy and momentum are both conserved in both elastic and inelastic collisions. What is lost in inelastic collisions is KINETIC energy, as some of it is transformed to other types of energy, such as heat.

You stated "Energy IS NOT CONSERVED in enelastic Collisions" which is not correct. In other words, your statement was wrong.

Had you stated "Kinetic energy IS NOT CONSERVED in enelastic Collisions", you would have been correct (except for the misspelling of 'inelastic').

Oh the spelling police are out tonight I see.

Any how that still makes Energy an inaccurate way of rating Wound Trauma Incapacitation

.........Assuming you put a good hit into the vitals? Absolutely!!

A 180 gr from an `06 (in round #`s) has a MV of 2700 fps. Don`t have the BC #`s of the factory bullets. But as an example, if you were using a 180 gr. Nosler A/B, with a BC of .507 at a MV of 2700 fps, your down range energy at 400 yards is 1660 ft lbs at a velocity of 2038 fps.

As I`ve seen on TV`s "Best of the West" hunting show, if a Berger VLD hunting bullet from a 7mm mag can down elk at very long ranges out to 925 yards, with less down range energy at impact than what an `06 has at 400 yards, you`ll be fine.

The bullet difference however, is that the VLD`s (hunting bullet) give the animal an instant or much faster (DRT) shrapnel effect, causing enormous vitals damage with less down range energy. They are not a pass through bullet whether at higher impact speeds or at lower impact speeds.

Even though the VLD`s will do the same damage at hi impact speeds at the shorter ranges, as a suggestion and if you`re a reloader, on any future elk hunt even where you feel your shooting ranges maybe at 400 yards or better, for added longer range stopping assurance, consider the VLD hunting bullet.

On my next elk hunt, I`m loading up some 190 gr. VLD`s for my 300 WSM.

The reviews I`ve read from elk hunters as to its devastating stopping effects are excellent. Highly likely, you won`t need to track the animal.

The Berger Bullet site has a new audio/video showing that 925 yard shot on a bull elk and also shows computer graphics that illustrate what the VLD`s do from the instant of impact on big game.

Very informative.

I will take that as your concession that energy is conserved in an inelastic collision - so we agree on that point.


My original contention was this:


It seems to me we agree energy alone is an imperfect tool, but my contention is that it is better than nothing and can be used to good advantage if used wisely rather than stupidly.

I also took issue with the use of the term "any" in the statement in the book:


The falsity of this statement is easily seen by simply taking two identical bullets and launching them at a target at grossly different speeds. The example I like to use is the velocities which impart 0 fpe (0fps) and the velocity which imparts infinite fpe (infinite fps). On impact, the 0fpe bullet will do nothing, the other will destroy the universe as we know it. In both cases the effect of bullet impact is determined using "energy relationships" and both are quite accurate.

In the more practical world, consider 180g Partition bullets at .30-30 and .300 win Mag speeds as an example. If we assume velocities of 2200fps and 3100fps respectively, one could reasonably come to the conclusion the faster bullet would perform the same at 495 yards (2200fps, 1934fpe) as the slower bullet would at the muzzle (also 2200fps, 1934fpe). In fact, if we know how either bullet performs at any range, we can reasonably expect the other to perform the same at the range at which it has equal energy (and by derivation, the same velocity and same momentum).

Or we can abuse the energy tool and try to predict results using grossly different bullets at grossly different velocities. If the statement in the book had read "Attempts to derive the effect of bullet impact in tissue using energy relationships are often ill advised and wrong...". I would have been in full agreement. But the meaning of that statement is much different than what was written.

No doubt that VLD does a great job on camera when the wapiti stands in the open for a broadside hit to the chest....and since it's an "intelligent bullet" that seems to know when it has gotten into the chest to blow up on broadside shots,I'm not sure it understands what it is "supposed" to do on a long angling shot...

This will not matter to those amateur bullet "testers", mesmerized by computer graphics,and awash in ballistic minutia.

I find all the furor over using target bullets that fly apart on big game to be rather interesting,as this type of bullet performance was what drove people like John Nosler and Jack Carter,Bill Steigers,and Lee Reid to give us stuff like Partitions, Bear Claws,Aframes, etc.Interesting to discover that Berger bullets had the BIG SECRET all these years....

Any one with any experience killing elk instead of just watching it done knows that exploding bullets in the chest cavity are no sure bet for DRT's; and the elk will be killed no quicker with the Berger than with the Partition.No doubt hitting the wapiti at 900 yards will be easier with the Berger,if you are into that sort of "thing"...which is great Saturday afternoon TV entertainment,like Looney Tunes,but hardly typical of most elk hunting.

No doubt the fabulous accuracy,and high BC, of the Bergers are a big assist to hitting at long range;and the tin-foil jackets help them "'splode" in the chest (assuming you hit them there).But I would not want them in my rifle for general purpose elk hunting,or for a long-angling shot in the timber.

I doubt Berger ever deliberately "developed" a "hunting" bullet; the comtemporary fascination with 1000 yard kills drove a bunch of people to try them;and the slick nonsense they show in their computer generated depictions is Madison Ave marketing at its' best.

Jeepers guys...

Energy is a valuable metric as long as there's some common sense involved; for example within the context of hunting bullets of a given weight. Knowing the energy of, say, a 180-gn .30 cal Partition means you know a lot about it's potential to wound.... As long as you "know sumptin'"... Grin... Guys like JWP will spin it every which way, comparing a .17 caliber bullet at ungodly speeds to a normal bullet at normal speeds in an attempt to discredit energy as a useful metric... But with even a little common sense, energy figures are one more tool, and just a tool, for getting one's brain around what a cartridge/bullet/load might do...

JWP told me that my Accubond exploded in an elk chest, and that the wound extending to the far side hide, that I could comfortably stick my thumb into, was not from a bullet per se, but rather a tiny fragment that then vaporized, amazingly enough, leaving no trace- other than a thumb-thick channel through the neck muscle. Wow. That's some physics, there. Uh... Particle physics, I guess.

Anyway, my position is that energy figures are an interesting number to gack about, within the common-sense context of the zietgiest of known bullet performance. Do they tell the whole story? Of course not. Can zealots like JWP beat a dead horse into the ground using "energy" as his club? Guess so.

That's not complicated, really, but some like to make it so. BSEG.

BOBIN......I take it then, that you haven`t tried the VLD hunting bullets on elk? It would appear so! I`ve never used them either on the 9 elk I`ve killed. But, I`m always willing to try different things now and again and keep an open mind with far less skepticism as yourself.

The last time I checked animal (elk) anatomy, the vitals are located in the center of the animal, not on the other side of the animal. A bullet need not pass through to kill an elk. With elk, I have never needed to take a quartering or angled shot at a less than desirable angle. Lucky I guess.

True! I wasn`t there to see the shots and verify those distances for myself in person, but I will not necessarily discount what I saw several times on TV either. I certainly cannot disprove it.

And I will not discount the reviews and reports from others who have used the VLD hunting bullets on elk.

Of course, no bullet is a 100% guarantee of having an immediate DRT affect. If I remember correctly, the Berger hunting bullets are constructed a little differently than their non hunting match bullet counterparts?

Do you happen to know of a report or a reference where someone used the hunting VLD on elk and was not satisfied? If so, I would appreciate that reference. Rather than relying upon the opinions or speculations of those who haven`t used them, if there is enough valid and proveable evidence for me not to use them on my elk hunt late this year, then I won`t use them.

Would appreciate any reference you can find!

How in the hell did you dream that up? Hearing voices at night?

Are you saying that energy is not energy? That energy is different at different speeds?

You certainly deserve the "Paper Hat" No wonder you won that award on "As Real As It Gets"