Marksmanship & Universal Physics - the real reasons behind a bullet's final mushroom shape -
After firing a rifle bullet into a distant target, the marksman asks his friend, who is well-trained in the science of Modern Physics, to explain the event.
"The chemical energy of the firing is converted into Kinetic Energy of motion along with an increase in momentum for the now-speeding bullet which, due to the reluctance of the inertia of its mass, upon striking the target causes considerable damage as its Kinetic Energy performs work on the target and its momentum is reduced back to zero."
There is a long silence....
"But what about force and acceleration?", asks the marksman. "I thought the force of the explosion accelerated the bullet along my smooth-bore barrel producing a high closing speed between the bullet and the target. Then, during the collision with the target, equal and opposite forces exist between the bullet and the target causing
acceleration for each in opposite directions inversely proportional to their mass. If the target is another bullet turned around and freely resting on a smooth support, at the moment of nose-to-nose impact as much as the fired bullet slows down, the target bullet speeds up since acceleration will be equal for each."
There is another long silence....
"That is the old Newtonian way of looking at a collision. I assure you the Modern Physics energy method is superior since it takes into account all forms of energy present during this event."
"That's interesting, but is any of it real for the bullet or the target?", questions the marksman. "After all, you have the speeding bullet's high Kinetic Energy of motion performing work on and thereby causing damage to the target, yet when I locate both bullets, I know I will find equal damage to each. Equal damage indicates to me that at the moment of collision, the speeding bullet is not in any way different from the target bullet. Equal forces causing equal accelerations resulting in equal damage to each bullet."
At this point, the marksman notices that his friend is looking a bit flustered.
"You don't understand. The speeding bullet is way different from the target bullet due to its high velocity of motion. The target bullet is just sitting there at static rest on its support. Then during the collision, the dynamic speeding bullet transfers its momentum and Kinetic Energy of motion to the target bullet causing the target bullet to speed up and away from the impact site."
"Are not all motions relative?", queries the marksman. "I mean, we see the target bullet at rest because we as observers, the target bullet, and Earth all share the same high-speed motion in orbit of the Sun. From our non-impartial perspective, it is easy to think of the fired bullet as "speeding" and the target bullet at "rest". But if we were to travel alongside the fired bullet on its way to the target, if you can imagine the air missing, as it is in space, I think you could easily reach out, take hold of the fired bullet, and handle it as being the same as any other bullet at rest. In fact from this "alongside" perspective where the fired bullet is seen at rest, the target bullet will now be seen in high-speed approach. Upon impact, this time it is the fired "resting" bullet alongside that will speed up in the opposite direction from the impact site."
"No, I tell you, the energy of the explosion definitely causes an increase in the bullet's motion and therefore an increase in its momentum and Kinetic Energy ratings."
"Definitely? Suppose I am firing the rifle in the direction opposite to Earth's high-speed motion along its orbital path, like firing a rifle out the back of an airplane. I think Earth's orbital speed is 18 miles/second forward and my bullet's speed is 0.5 miles/second backward. Then is not the force from combustion actually causing a decrease in the fired bullet's motion along this same orbital path from 18 mi/sec to 17.5 mi/sec?"
"I suppose so, but your example doesn't seem fair. If the bullet slows relative to Earth-speed then the Kinetic Energy of motion of the Earth-speed target performs work on the slow bullet bringing its motion back up to Earth-speed. Energy Physics works fine either way."
"Not really," the marksman responds while taking mental aim at his friend's arguments. "In the first event where we see the fired bullet's motion increasing relative to a "resting" Earth, you credit a conversion of the chemical energy of the explosion into Kinetic Energy of motion which then performs work on the target. In the second event where we see the fired bullet's motion decreasing relative to Earth at orbit-speed, you credit the Kinetic Energy of the target's motion as performing work on the bullet. What happens to the chemical energy of the explosion? How can it be the cause of work in one event and not in the other? In truth, is this not just one event viewed from two different perspectives? Your Kinetic Energy rating appears to be as relative as motion itself. If the bullet's Kinetic Energy rating can be viewed by different observers as both increasing and decreasing at the same time for the same fired bullet, then I think we have just proved that Kinetic Energy is imaginary and therefore not real for the bullet."
Seeing that his perplexed friend is slow to respond, the marksman continues. "I think this collision event is caused by the release of chemical energy of combustion, causing force, causing acceleration of the fired bullet's matter, resulting in a closing velocity being established between the fired bullet and the target bullet. If the friction of air is absent, no difference exists between the fired bullet seen in uniform motion compared to the target bullet seen in uniform rest. In fact if I change my perspective by travelling alongside the fired bullet I will view it as being at uniform rest and the rapidly approaching target bullet in uniform motion. I think these are really just two names for the same state where acceleration is absent. Rest-motion is a better name for this non-acceleration state, don't you think?"
By this time, the friend's eyes are starting to glaze over! All this talk of rest being the same state as motion and Kinetic Energy increasing and decreasing at the same time for the same fired bullet is taking its toll. He is beginning to wish he had asked more questions during his Physics lessons.
But then he recalled that asking too many questions was frowned upon by his professors. At this point he found himself questioning the reality of Kinetic Energy. He thought: 'Maybe it really is nothing more real than a way of rating an object's observed motion relative to some frame of reference thought to be at rest or in rest-motion.' He was also bothered by the identical damage to the two bullets. 'If the fired bullet actually did possess a Kinetic Energy capable of performing damage to the target bullet, what "energy" source did the target bullet use to perform equal damage to the fired bullet?'
I'll let you in on a secret. Prior to engaging with his Physics friend in this discussion, the marksman had improved his own understanding of the absolute forces and absolute accelerations present in every collision by studying the several articles published on the subject in the Internet journal located at Universal Physics.
What then is going on in this fired-bullet collision event? Is the bullet fired down a smooth barrel any different from an identical bullet at relative rest? Actually it is not. After firing, an absolute closing velocity is established between the fired bullet and the target bullet. It matters not whether this velocity is thought to be possessed by the fired bullet or the target bullet or a portion shared by each. The marksman is right,  Newton's LAW I tells us that an action force is required to cause acceleration for each bullet. At the moment of collision an acceleration/Action (a/A) contact force exists between the two bullet noses. As much as one head of this two-headed or bipole a/A force accelerates (changes the motion of) the fired bullet, the opposite head accelerates (changes the motion of) the target bullet. Each a/A head force causes the reactive generation of its own acceleration/Reaction (a/R) support force just as predicted by  Newton's LAW III. This a/R force is composed of a myriad of internal forces sourced from within each accelerating component of each bullet's matter as indicated in the impact drawing by the small gray arrows.
Normally, the fired bullet is spin stabilized. To keep conditions identical for both bullets I have chosen to use a smooth-bore rifle. Accepting that it is possible for the two all-lead bullets to be perfectly aligned at the moment of impact, the nose of each will stop relative to the other as they forcefully "butt heads". Here at the centre of each nose, the acceleration rates are extremely high. Not so for the remainder of each bullet's body where the rates are progressively lower the farther back one goes. Thus with different portions of each lead bullet experiencing different rates of acceleration, the bullet is forced to change shape. The lead behind the nose not only experiences high linear acceleration as it is slowed to a relative stop, it also experiences a brief centripetal acceleration as it is turned aside from a straight-line motion by the already stopped central nose lead resulting in the familiar mushroom shape. Even the lead behind the mushroomed head will show signs of acceleration forging as the bullet's caliber size is noticeably swollen or increased in diameter.
Modern jacketed and mono-metal bullets, while designed to behave differently from the all-lead bullets described above, are never-the-less subjected to the same acceleration/Action and acceleration/Reaction forces.
Isaac Newton's work on force and acceleration, as presented in  PRINCIPIA, does and always will represent the true explanation of cause in these bullet firing and impacting events. These forces and the attendant rates of acceleration are absolute, meaning that they will always test the same magnitude and direction for each and every non-accelerating observer. The rating systems of Kinetic Energy and momentum do not hold to this absolute standard as each will give a different result for each different observer.
Above all, know that these man-invented rating systems, however useful, are not the cause of any event.
"Article written at the request of and edited by Koos Geldenhuys - 2006."
About the Author:
Ethan Skyler is known for his independent analytical review of the collection of works that represents the science of Physics. Many of his articles are available complete and without charge at Universal Physics Journal.
An example of the bullet mushrooming action in motion as captured in 2009.