Falling Feathers and Pennies: Did You Know This?

If you simultaneously release a feather and a penny, side-by-side, which will hit the ground first?  If you say, “The penny, of course,” the science of physics has news for you. That is not always true! Inherently, they reach the ground at the same time. Read on to understand why!

By the year 1604, Galileo Galilei had deciphered a long-standing mystery of physics: “The law of fall.” Until that time, “natural philosophers,” as scientists were called, had puzzled for centuries over the question: “Precisely how do physical bodies of mass like a feather and a penny fall to earth under the influence of gravity.” It was clear that objects seemed to fall faster the longer they fell – but according to what mathematical principles?

Do heavier objects fall faster than light ones? It would intuitively seem so! Is the instantaneous velocity of a falling object proportional to the distance traversed during fall – or perhaps to the time duration of fall?

By way of clever experimentation and logical deductions, Galileo deduced the law of falling bodies under the influence of gravity:

Every body subject to fall inherently accelerates at a
fixed rate as it falls, irrespective of its weight (mass).

With a fixed, equal rate of acceleration as decreed by the law of fall, motion physics tells us that two bodies released from rest will fall side-by-side all the way down. The law also dictates that objects in free-fall reach instantaneous velocities which are proportional to the time duration of fall from a rest condition. For objects here on earth, a falling object adds slightly less than 32.2 feet per second to its velocity for each additional second of fall.

The wording of “the law of fall” contains two important implications. First, the key word, “inherently,” implies that the falling body is subject only to a constant force of gravitational attraction. Second, the term “fixed” rate tells us that the acceleration is a fixed numerical value for all bodies of mass… in a given gravitational field. The earth’s gravity is essentially constant over all regions of the globe…at its surface. The moon’s gravitational field is also essentially constant at its surface, but its numerical value is just under one-third that of the earth. A specific body of mass will fall faster here, on earth, than it would on the moon.

Note that “mass” denotes the amount of material present in a body, while “weight” denotes the force of gravitational attraction acting on that mass. When you weigh yourself, you are measuring the force of the earth’s gravitational attraction on your mass!  Double the mass of a body, and you double its weight in a given gravitational field!

Everyday observation tells us that a penny always falls faster than a feather. How, then, do we reconcile our observations with the law of fall and the statement in the opening paragraph of this post? The key to the seeming impasse regarding the falling feather and the penny resides in the word, inherently, as used in the statement of the law of fall which assumes only gravity acting on the object. When objects fall, here on earth, there is an additional force acting on them besides the force of gravity as they fall, and that is the retarding force of air resistance!

If our feather and penny experiment is conducted in a tall glass cylinder with all of its air removed, the feather and the penny will fall precisely side-by-side. I witnessed this at the Boston tech museum many years ago.

The weight of the feather is much less than that of the penny, and the increasing force of air resistance generated during the fall becomes a much larger percentage of a feather’s weight (gravitational attraction) than in the case of a penny. This fact negates the equal acceleration during fall imposed by the law of fall. Physics has a name for the condition which is the basis for the law of fall: It is called the equivalence of  the “gravitational mass” and the “inertial mass” of a body (do not worry if this last comment is confusing to you; a further look into motion physics would quickly make its meaning clear).

Galileo was the first “modern” physicist. His ability to recognize and isolate the “secondary effect” of air resistance in the matter of falling bodies enabled him to bypass the confusion that our everyday experiences often injected into the early study of pure physics. Isaac Newton carried Galileo’s insights much further in his own, subsequent work on motion physics. Newton’s three laws of motion, which every beginning physics student studies, along with his theory of universal gravitation explain precisely the behavior of falling bodies that we have just examined.

One parting comment: Albert Einstein made careful note of the law of fall and the fact that the gravitational mass of an object is precisely equivalent to its inertial mass. Again, it is that latter relationship which dictates that all masses inherently fall with a fixed and equal value of accelerated motion in a given gravitational field. Unlike many fine scientists of the time, Einstein reasoned that the equivalence of gravitational and inertial mass was no coincidence of nature – that something very profound for physics was implied. His persistent curiosity in the matter led him to his theories of relativity which, in 1905 and again in1916, revolutionized all of physics as well as our concept of physical reality.

As for Galileo, his formal statement of the law of fall did not occur until the year 1638, four years before his death. Even though he had reached his major conclusions by 1604, it took him that long to firmly claim priority of his findings by publishing his classic book of science, Discourses on Two New Sciences.

The Master and his most important scientific book

For much more information on this and other aspects of motion physics, see my book, The Elusive Notion of Motion: The Genius of Kepler, Galileo, Newton, and Einstein. See also, several other posts on Galileo, Newton, and Einstein by clicking on the “Home” page in the blog header and searching the archives using a keyword such as “science” or by going to the “science” categories in the archives.

My book and how to order it can be found by clicking on the link below:

My Motion Physics Book

Jet Engines and Michelangelo’s “Moses”

What do these two “finished products” have in common?

The “reason” side of us acting alone would likely prompt the quick response, “Not much!” After some careful thought, our “reflective” side could provide some convincing arguments to support the contention that these two seemingly diverse objects, one from the world of technology, one from the art world, actually have much in common. Here is the way I see it.

The famous “Moses” at Rome, sculpted in hard marble by Michelangelo, represents the epitome of man’s ability to represent life and human nature using artistic mediums. In Moses, the inherent artistic genius of Michelangelo is brought to full bloom by the countless hours of diligent study and practice he devoted to mastering the techniques of working with marble. One man’s extreme dedication to his artistic cause has given us such priceless art as Moses, the Pieta, and the Sistine Chapel just to name a few.

As with Michelangelo’s Moses, the modern turbojet engine used in today’s airliners is the epitome of a product which demanded extreme dedication to a cause – only, here, the dedication extends over decades, indeed centuries, as armies of thinkers, scientists, and engineers fought to understand nature and natural forces.

Michelangelo’s Moses began as nothing more than a rudimentary “chunk” of marble; correspondingly, man’s knowledge of the various technologies inherent in modern turbojet engine designs ranged from rudimentary to non-existent as recently as four hundred years ago – well after Moses emerged from his marble prison. Michelangelo at least had his toolbox of fairly refined chisels and sculpting tools with which to work. The early “natural philosophers,” as early scientists and technologists were called, had little with which to work. They initially faced a confusing scramble of nature’s puzzle-pieces requiring painstaking assembly into a larger picture before true technology was possible.

Even allowing for whatever handed-down knowledge the artist might have received from mentors and colleagues, I see Moses more as the ultimate tribute to a single man’s talent and determination. I see the modern turbojet engine (and virtually all other technological wonders) as the ultimate tribute to mankind as a whole – the cumulative outcome of generations who worked to build our technology hierarchies. The iPhone, the modern automobile, the internet – these and all such technology triumphs are a tribute to the human spirit and its desire to “know.”

Highly-Polished Works of Art!

Michelangelo sculpted Moses cut-by-cut, chip-by-chip. And when Moses’ rough form finally emerged from the block of marble, he polished the innumerable rough spots – over and over again until the rippling muscles in Moses’ forearms fairly glistened of sweat. Like Moses, the modern turbojet engine is a highly-polished work…of the technological art, but with a much-extended gestation period and many fathers!

We recently returned from a two-week trip to New England, made possible by the marvels of modern aviation…and, specifically, the turbojet engine. Whenever I travel, I am cognizant of this monument to man’s ingenuity and dedication. Today, these engines are called upon to power countless tons of aircraft, passengers, baggage and cargo into the sky, hour after hour, trip after trip, week after week, without hesitation and without the need for frequent maintenance. Today, jet engine performance and reliability are so highly refined that travelers rarely think twice about flying over the rugged, isolated regions of polar routes in a large aircraft with only two engines.

A Bit of Historical Perspective

Jet engines were not so reliable in early aircraft. As a young boy, I recall numerous accounts of early jet fighter planes going down due to “flameouts” where the continuous fiery combustion and expelling of combustion materials out the back ceases and all thrust is lost. That problem and other major issues have long been solved. Today’s engineering efforts are focused on fuel efficiency and performance/cost factors along with quieter operation.

I also recall the public interest and excitement when the first U.S. commercial jet airliner service began – in 1959. My family lived not too far from San Francisco International Airport at the time. We could see the earliest American Airlines Boeing 707 jetliners off in the distance on final approach to the airport. It is interesting, today, to recall the fascination and excitement attendant to the advent of the commercial jet age, especially in light of today’s tendency to take it all for granted – which is a shame. I am a firm believer that when society loses its sense of wonder and perspective, it has lost something vital and precious.

The fundamental principle of physics which explains rocket and jet propulsion was first formally identified by Isaac Newton in his scientific masterpiece of 1687 – his book known as the “Principia” (See my post of Oct. 27, 2013, “The Most Important Scientific Book Ever Written: “Conceived” in a London Coffee House).

The third of Newton’s foundational “three laws of motion” states:

For every action, there exists an equal and opposite reaction

Despite this revelation and other fundamental physical principles so expertly articulated by Mr. Newton in 1687, much more physics and many new technologies were required for the first baby-steps on the long journey necessary to produce “engines” capable of powering our human desire to travel. The critical mass of required knowledge had not materialized until the nineteen-thirties when Frank Whittle, an English engineer, built the first laboratory version of a jet engine; it was operating by 1937.

An early Whittle engine

As with so many technologies, potential military applications provided great momentum to the product development cycle of the jet engine. The first airplane to fly powered solely by a turbojet was the German Heinkel 178, in 1939. In the 1944/45 time frame of World War 2, German engineering produced the Messerschmitt 262, the first jet-powered operational aircraft.

Messerschmitt 262

While much faster than the propeller-driven aircraft of the Allies, the planes were too few, too late, and plagued with reliability issues (including its pioneering jet engines) for it to be a decisive weapon in the war.

The die was cast by the end of the war, however; the jet engine’s rapid maturation and future domination was inevitable. One of the technologies which quickly matured out of necessity was the science of materials which dealt with the  “strength of materials” and their physical properties. The multiple internal turbine-fans spinning at very high speeds are populated with hundreds of turbine “blades.” The metallurgy to insure that these relatively small blades withstand the extreme forces and temperatures they experience requires a sophisticated metallurgical knowledge.

An interesting aside: One of the very first “textbooks” on the strength of materials was written by Galileo Galilei in 1638. The first half of Discourses on Two New Sciences is Galileo’s pioneering analysis of material strength and reliability – one of the “two new sciences.” The second half consists of his milestone revelations on the developing science of motion physics. The latter work qualifies this book as one of the most important science books ever published, one tier below Newton’s Principia of 1687 – like all other books except Darwin’s On the Origin of Species.

The next time you are at an airport, you might make it a point to observe jet aircraft which pull into a gate, power down, and sit there awaiting the next flight. The engine turbine fans can be seen still spinning 45 minutes after power-down, thanks to the superb, ultra low-friction ball-bearing designs which support the rotor shafts. You might notice also a “curly-cue” spiral painted on the front of the fan assembly just inside the engine cowl. They are there to provide easy visual indication that an engine is powered-up and turning at very high RPM. The tremendous appetite of these engines for air creates enough suction at the front-end to actually ingest ground crew members who get too close. This has, in fact, happened many times over the decades. Like the whirling propellers on older aircraft, jet engine intakes pose a deadly hazard to the folks who work around them.

Engine manufacturers such as General Electric and the U.K.’s  Rolls-Royce have learned enough of nature’s secrets to manufacture this product with an almost inconceivable reliability and performance capability. There is one aspect of nature which has proven stubborn to control and deal with, however.

Modern Jet Engines are NOT for the Birds!

The greatest enemy of the jet engine appears to be …birds! Our science and engineering capabilities have not figured out how to prevent the ingestion of our fine feathered friends into the compressor blades of these engines; it happens all too often. Do you recall Captain “Sully” Sullenberger and his short trip into the Hudson River minutes after takeoff from LaGuardia in New York? No engine is tough enough to digest a large bird and spin merrily along as if nothing happened. Oh well, even Moses has always been susceptible to “chipping” if not handled carefully.

One final comment about the similarities drawn between Michelangelo’s Moses and the highly developed modern jet engine: I am certain that jet engine technology will continue to evolve and that the end-product will improve even beyond today’s high standard. I am not sure there will be anyone coming along anytime soon who will improve upon Michelangelo’s “design!”

For some, alcohol is the indispensable commodity. For others, it is drugs. For a number of us, books prove to be irresistible and foremost among those things in life that we cannot do without. It is fascinating to reflect on why that should be the case for millions of booklovers all over the world. The answers to such musings are many and varied, I suspect. The feelings of attachment can be very strong.

“The Bookworm” by Carl Spitzweg

When she was ill and dying, Jacqueline Kennedy reportedly asked to have some of her favorite books moved into her room. Presumably, she was not embarking on a final reading binge; she apparently wanted them near so she could spend just a bit more time with old and dear friends before the end came. I can completely understand that impulse, for a true bookworm becomes very attached to books.

The Allure of Books

What is it about books? Where to start? For fiction fans, there is the pure entertainment factor and the escape from life’s hum-drum. The ability of a well-written story to whisk the reader away from today’s here-and-now troubles, even for a little while, is a powerful draw. The literary voyage can transport one anywhere, from the exotic capitals of civilized Europe, to the darkest jungles of Africa – even to the contradiction of Antarctica’s desolate yet serenely beautiful landscape of white. Time is equally capricious; the story can take place hundreds of years in the past, or, just as plausibly,at some time in the far distant future – as in science fiction. And what adventures await the reader/voyager along the way and at the final destination? Anything a creative writer can imagine is possible! Espionage and intrigue, great battles fought long ago, a journey to newly discovered planets – the list is endless.

The most effective fiction books, as with screenplays, are those that weave their spell using superb character development and portrayal. Human nature and societal behavior, as vividly displayed in text, is seemingly among the most inexhaustible of captivating themes. The great novelists all had superb skills in that regard; Charles Dickens always comes to mind for me.

Fiction allows the reader to live vicariously through the main characters – like Walter Mitty. Readers enjoy tagging along with characters who, perhaps unlike themselves, dare to live life to the fullest while dismissing danger, forsaking the conventional, and ignoring social taboos.

There is a large divide between fans of fiction and readers of strictly non-fiction books. Sure, there is often much overlap in interests, but I find that people tend to reside in one camp or the other. Followers of this blog have surely deciphered how I spend most of my reading hours. Although I am aware of missing out on something very good, I do not read much fiction. Why is that? I am in the vexing position of the kid in the candy store when it comes to reading – too many wonderful choices, both fiction and non-fiction. “Too many books, too little time” constitutes the short version of my plight. I have on my shelves, a small selection of excellent fiction; these are books I have obtained mainly because of their universal appeal as great literature and because of the fact that I know I would enjoy them. I really want to read The Great Gatsby, The Adventures of Huckleberry Finn, The Last of the Mohicans, etc. It is the fault of those not-yet read non-fiction books on my shelves that I have not gotten very far into my carefully selected fiction shelf. I will read them in due time, God willing.

Fact Is Stranger than Fiction

At first that may seem a trite expression, but I find its declaration to be quite true. I gravitate toward true stories for two reasons: First, because they are true – they really happened to real people; second, because, often, “you just can’t make this stuff up” as the saying goes. Why read fictionalized history when the real thing is every bit as intriguing and the real-life protagonists are just as remarkable as any character imaginable? Well, that’s just my take!

The name of this blog is Reason and Reflection: Reason as in science, mathematics, and logical thought – knowledge; Reflection as in a fascination with the human side of life – wisdom. The name reflects my eclectic interests in pretty much everything – from science and mathematics to the nature of the human condition.

Books as Repositories of Knowledge and Wisdom:
This, for Me, Is the Ultimate Attraction

This concept, this view of books as precious repositories of mankind’s accumulated knowledge and wisdom, is the glue which forms such strong bonds to many booklovers. The ideas and discoveries which have changed the nature of human existence have virtually all surfaced, or at least survived, on pages nestled between the covers of books – books which silently preside over the years, the decades, the centuries, on library shelves….somewhere. After 1454 and the emergence of Gutenberg’s printing press, the holy-grail of such printed repositories has been the first editions which initially made the breakthroughs of great thinkers readily available to their fellow man. In rare cases, the “earliest available versions” of books are ancient, one-of-a-kind, hand-written texts which have managed to survive. The printed book is clearly the workhorse of this early “information age,” however. And many of the thoughts and discoveries disseminated in books have fundamentally changed man’s view of himself and his place in the cosmos. See my earlier post on Isaac Newton’s Principia (in the archives) from October 27, 2013, The Most Important Scientific Book Ever Published: Conceived in a London Coffee House.

The Great Books: A Once-in-a-Lifetime Experience at Stanford University

Several years ago, Stanford University offered a course on “The History of the Book” through its continuing education program. I fortunately heard about it through my younger daughter, another great fan of books and reading. The several-week course convened on campus in the rare book library. Led by one of the university’s rare book librarians, the classes were structured as two hours of lecture and one hour of “show-and-tell.” The lectures were fascinating, and covered all aspects of “the book” from early forms of books and their construction to printing and collation (organization and page-numbering), bindings, and historical importance. Many of history’s greatest books were covered, from science to philosophy.

During the lecture phase, the instructor would produce, from his ever-present cart, a book to illustrate his point. The books he chose were often first editions of the most important books that exist. I cannot accurately recall them all, but a typical lot would reflect authors like Pliny, Copernicus, Vesalius, Galileo, Kepler, Hobbs, Newton, Adam Smith, Darwin, Freud, Einstein, Fitzgerald, Hemmingway, and so-on. After each lecture, the books on the cart were wheeled over to join others open for perusal on the long library tables. The class of approximately twenty adults was invited to roam about and personally examine, even “thumb-through,” some of the greatest books ever written – many of them present in their rare, first editions. The instructor was available to answer any and all questions, and there were many.

Often, when the class was over and we had filtered out of the rare book library and into the dark, pleasant coolness of the spring evening, my head was spinning as I contemplated what I had seen…and touched. We students had the privilege of holding, in our own two hands, the well-springs which revealed much of humanity’s accumulated knowledge and wisdom – centuries-worth, many in their original, first edition formats. The total value of such books on the rare book market, today, is very high; their true value: Priceless.

A Reference Library – Steps Away

I have, over many years, accumulated a reference library on science and the history of science. These are books that, while very affordable, are valuable resources on scientific milestones and biography. Since I enjoy writing on matters scientific, it is handy to have these books nearby.

Above, you can see what happens when there are too many books and not enough bookshelves!

My wife loves books, too, and she has her own collection. She is a fan of the author/illustrator, Tasha Tudor, and this is one of her favorite items. Long live books!

The Key to Physical Attraction…It’s Called “Gravity” (and “Love”)

As unlikely as it may seem, the language of science has expressions in common with the language of love. The notion of  “physical attraction”  has roots in both. We humans are selectively attracted to others during our lifetimes, yet we are constantly attracted, in reality, to everyone and every thing in the universe as revealed by Isaac Newton in his masterwork of science, the Principia. Two marbles, one inch apart on a smooth table, exert an attractive force on one another which would tend to draw them together, except that the force is too small to overcome the rolling friction on the table. Yet, on the larger scale of the sun and planets, the forces of attraction between such massive bodies are immense.

“Falling” in love may happen but rarely in our personal lives, yet we are, in fact, constantly falling – even though we are not conscious of the reality. All earth-bound denizens fall constantly… toward the sun as the earth orbits our nearest star. That motion, due to gravity, of continually “falling toward the sun” works in concert with a component of planetary motion tangential to the orbit to define the path of our earth around the sun. That tangential component of motion represents the inertial path the earth would take if the gravitational attraction to the sun suddenly ceased. The concept of  “gravity” has historically been one of mankind’s greatest comprehension challenges – one of nature’s great mysteries.

Early man’s curiosity as to why things apparently fall toward the center of the earth was at least temporarily assuaged (for hundreds of years) by Aristotle’s assertion some two thousand years ago that the earth’s center was the “natural center of the universe,” hence the logical place for objects to congregate (prior to Copernicus in 1543, the sun and planets were assumed to revolve around the earth). The great mathematician/scientist, Johannes Kepler, in the early seventeenth century was an early disciple of Copernicus’s sun-centered solar system and one of the first to seriously contemplate what kind of natural, physical mechanism was at play to keep the planets moving around the sun as they do. He conjectured that perhaps some form of solar, “magnetic” winds or vortices swept the planets along in their almost-circular paths. It was generally believed, prior to Newton, that whatever phenomena, or “force,” that caused apples to fall to earth was distinct and different from the celestial forces that held the heavens together. For a long time, celestial motions beyond the moon were even attributed to divine influence and motivation.

It took the genius of Isaac Newton to declare, in his 1687 milestone book on science and mathematics, that earthly gravity and heavenly forces are one and the same – hence, universal. Indeed, Newton claimed that all objects of mass in the universe attract all other objects to greater or lesser degrees via the force of universal gravitation. He stated that the nature of gravity and the equation which describes how it works is applicable everywhere and at all times – a truly “universal” law of nature! Although Newton explained the scientific version of “physical attraction,” he wisely made no attempt to explain the underpinnings of the version expressed in the language of love. Nor will we! That remains as captivating and mysterious as ever and seemingly beyond the ability of science and mathematics to explain.

But Newton really did not explain what gravity is or why it acts the way it does; he admitted so in the 1713 second edition of the Principia stating: “Non fingo hypotheses,” which, translated from Latin declares, “I feign no hypotheses!” He was criticized by his peers for his advocacy of this mysterious force-at-a-distance; they asked, “How can a body like the sun transmit, through empty space, the tremendous forces necessary to steer the planets?” His contemporary critics should have called to mind that other mysterious force which travels through space – magnetism, in the form of the magnetic field – which also has the power to attract objects. Newton was sage enough and courageous enough to stick by his contentions even though he could not explain them all. Although his famous equation does not hint at why gravity works the way it does, it describes precisely how it works – well enough to be used by NASA for its precise orbital computer computations. Despite the tremendous success of his theory of gravity and his numerical analysis of it, Newton did not – could not at that time – grasp the true essence of gravity. This is a remarkable situation which aptly reflects the reality that science will continue to inexorably peel-back, layer by layer, the deepest mysteries of our existence. Sometimes, genius like Newton’s transcends the state-of-the-art and “the possible”…for a while.

Albert Einstein Peels Back Another “Layer” of Gravity

It took Albert Einstein’s 1916 general theory of relativity to go Newton “one better” and unmask the true face of gravity. Planets including the earth go around the sun in almost-perfect circles (ellipses) and not off into distant space not due to an explicit force of attraction between themselves and the sun as Newton proposed; Einstein showed that they are merely following a “natural path” determined by the curvature of four-dimensional space-time around the sun. That curvature is caused by the presence of the sun’s mass. All bodies of mass curve space-time in their vicinity. Einstein advanced physics immeasurably by contributing this radically unique physical interpretation of all gravitational effects. The complexity of Einstein’s mathematics in the general theory of relativity required to demonstrate this conclusively dwarfs Newton’s simple equation for an attractive force as presented in the first illustration of this post. Nonetheless, Newton’s achievement regarding gravity remains one of the greatest milestones in the history of science.

The Makers of  Universes!

George Bernard Shaw’s famous toast to Albert Einstein who was sitting near him at a tribute dinner held in 1930 at the Savoy Hotel in London, is well-known and oft-referred to. After extolling the virtues of mathematicians and scientists who, through the ages, have built “universes” instead of merely fractious empires like Napoleon and others, Shaw concluded by saying, “Ptolemy [the early astronomer/philosopher] made a universe which lasted 1400 years; Euclid [the great mathematician and founder of modern geometry] also made a universe which has lasted for 300 years; Einstein has made a universe, and I can’t tell you how long that will last!” Einstein is shown in the grainy black and white film footage clearly letting-go a big belly-laugh. Science does move relentlessly forward – always with a great assist from mathematics. Look at where we are today. Love and science do go together: To love studying the history of science and its impact on humanity is to experience what I call the “joy of science.”

Despite the phenomenal track record science has compiled while continually advancing the state of our knowledge and well-being, the greatest of all mysteries may prove to be beyond the comprehension of science: Who is the ultimate maker of universes and what can we truly know about that?

One of Einstein’s famous quotations says it beautifully: “The most beautiful emotion we can experience is the mysterious. It is the fundamental emotion that stands at the cradle of all true art and science. He to whom this emotion is a stranger, who can no longer stand rapt in awe, is as good as dead, a snuffed-out candle. To sense that behind anything that can be experienced there is something that our minds cannot grasp, whose beauty and sublimity reaches us only indirectly: this is religiousness. In this sense, and in this sense only, I am a devoutly religious man.”