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Newton's Laws of Motion and Beyond

Sir Isaac Newton, one of the greatest scientists of all time, established three fundamental laws of motion that revolutionized the world. Being simple in language, these laws dictate the governing dynamics of any objects on earth or any inertial reference frame. We may consider earth as an inertial reference frame, in which we analyze the dynamics or mechanics of a moving or stationary object with respect to the origin of that frame/coordinate system. Newton's laws of motion are very intriguing, especially the third law, which states "Every action has an equal and opposite reaction". How simple and easy this law is? Even, a layman would have no difficulty understanding this straightforward sentence! In this article, I will share my thoughts behind this law - its simplicity, elegance in nature and beyond. 

When I was 14 years old, I first came to know the Newton's laws of motion from our physics class. At that time, I didn't pay much attention to realize the beauty of the laws, I was just cautious to learn so that my grades were good. But, the third law of motion caught my attention a bit, made me ruminative about the nature. I think many of us including myself at some point envied and thought that if Newton did not state the law, we would have the opportunity to claim it. Anyway, let's get to the point. According to the third law, if someone punches a solid wall with a force, let's say, F; the wall must return the same magnitude of force to the angry person's fist where the direction is opposite, -F. So, we can write without any doubt that

F = -F

Now, the angry person obviously would get hurt if the wall was built by rock-solid concrete. Also, at the same time, the person would have realized that Newton's third law was the reason to get hurt as the equal amount of force was bounced back by the wall. What if the wall was made of a softer material, such as, lumber? The poor person would certainly not have experienced the same reaction as it was for the concrete, although the person had applied the same force. Now, the question arises: why did the forces applied by the that person to the wall were felt in a different way although the magnitude was the same? Does it mean that in second case, since the person experienced lesser reaction force, Newton's third law is inevitably wrong?

No, there is absolutely nothing mistaken with Newton's laws. In fact, over the years, many people self-proclaimed that they proved it wrong and attempted to seek attention from the scientific community. Unfortunately, nobody succeeded and will never be as these statements are proven facts, tested rigorously, and implemented in our day-to-day lives. When I was a teenager, I used to hear some rumors that someday somebody was about to publish a mathematical formulation that would eventually contradict the Newton's well-known, widely-used second law, F = ma, where F is the force, m is the mass, and a is the acceleration of the mass. These were just hearsays, and as a matter of fact, it's the trait of some of the human beings to spread some propaganda, to whisper some unfounded claims in your ear.

Newton and Einstein provided two benchmark laws, which are exquisite in its expression and easy to remember. Newton's F = ma and Einstein's E = mc², where E is the energy, m is the mass, and c is the speed of light - are phenomenal creations having majestic power in solving many problems in nature. Einstein's mass-energy conversion theory is ground-breaking, which helped us to enter into an atomic era. Now, let's get back to our original discussion on Newton's third law, remember again the poor person who was having difficulty understanding the physical significance of the statement. It is evident that applying the same force to different objects with different material properties does not produce the same reaction, but the third law still remains valid. So, is there any energy lost? No, according to the principle of conservation of energy, no energy is lost, but energy may be transferred or converted into another form - the total energy is always conserved. 

It brings a clear picture to us that there must be a contact or touching point or simply a medium of energy transfer for every action between two bodies. And that contact or medium may be represented by a spring that stores some of the energy. For example, if the wall is made of a relatively flexible material, then it may absorb some energy prior to bounce back the rest to the person. As a result, that angry person would experience a relatively mild reaction than the concrete wall. So, in this case, we may rewrite,

F = -F - C 

⇒ F = - F₁

Where, C is the energy stored by the wall. But look! Action and reaction forces are still the same. Actually, rigid coupling is not natural, it is a forced or ideal condition, just like F = -F. If we consider the contact (soft or hard) as a medium to transfer energy between two bodies, it makes more sense. In bond graph terminology, it is called 'integral causality', and the forced condition is termed as 'derivative causality'. In the end, the take-home message from this article is, whenever we consider Newton's third law, we also need to take into account the principle of energy conservation or energy transfer through contacts.

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