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!

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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.

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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

Grandpa, Baseball, and Physics

Last Wednesday, I was taking care of my two grandsons, Matthew and Luke, while daughter Ginny enjoyed a much-needed respite at our local Peets coffee house. Life has been very busy for her and husband Scott who has been back on the east coast for several days. Peets is her favorite place to sip tea, meditate and work on her blog and books-in-progress. She desperately needed a short break from the kids to just unwind and have some quiet time to write. When Ginny asked if I could watch the boys for a while, I said, “Sure.” I love spending time with my grandsons…and my two granddaughters whom we do not get to see as often because of distance. The two boys are really great kids, but they do keep Mom hopping when Dad is not available to share the load.

Matthew will be entering the second grade this fall and loves sports – especially soccer, football, and baseball – and he is very good at all of them! Luke is going into Kindergarten and, being two years younger, is not yet the accomplished athlete that Matthew is.

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While Matthew and I played baseball catch in the backyard, Luke got busy with a plastic “fat bat”, a “whiffle” ball, and a T-ball hitting post. He is now beginning to hit that stationary ball much better off the “T.” Matthew, as usual, was pleading for greater challenges in the form of high fly balls and, characteristically, was making a lot of circus “near-catches.” I say “near-catches” because the tennis ball we were using with our baseball gloves, would often pop out of the hollow of his glove after he made some pro-style moves to even get his glove on the ball! We were using a tennis ball because we could not find my baseball.

A Teachable Moment is at Hand!
Why Tennis Balls and Baseball Gloves Don’t Work

I, too, was having trouble holding on to the tennis ball; it all too often popped out of my glove, even in routine catches! I thought briefly about why we were having so much trouble catching the ball. Here was a teachable moment, an opportunity to explain to Matthew why a tennis ball is considerably more difficult to catch than a regulation hardball as used in baseball. One might initially think it would be the other way-around, but no. Newtonian physics, as gifted to us by Sir Isaac Newton in 1687, can supply the reasons why catching a tennis ball is more challenging.

A baseball is easier to corral in a baseball glove than a lighter tennis ball for two primary reasons. First, the hardball has a greater mass (mass is a measure of the amount of atomic material present in an object…and related to its weight) than does a tennis ball. Even so, a tennis ball dropped from a tall platform has almost the same velocity profile in fall as does a heavier baseball. If we neglect the small effects of air resistance, they both will fall exactly side-by-side despite the difference in their masses, and consequently, their weights. Give Galileo Galilei credit for that revelation – early in the seventeenth century!

The mathematical product (multiplication) of a body’s mass and velocity yields a quantity called “momentum” in physics. Two falling bodies with the same physical shape and size (like a tennis ball and a baseball) will make depressions in a sand-pit which reflect their individual momentum at impact. If the two velocities are equal at impact, a deeper impression in the sand will be made by the more massive of the two, due to its greater momentum (and kinetic energy, too).

Substituting a leather baseball glove for the sand-pit, the heavier baseball will burrow more deeply into the leather “pocket” of the glove than will the tennis ball. If the baseball’s trajectory is slightly misaligned with the center of the glove’s pocket as the ball enters the glove (the fielder’s fault!), it soon reshapes the pocket as it burrows deeply in – and it stays put. A tennis ball will not burrow deeply; in a similar circumstance, it tends to quickly “ricochet’ off the side of the pocket without significantly burrowing in. That gives the fielder little time to react and squeeze the glove around the ball, thus capturing it. A tennis ball is elastic, or “springy,” and that, in conjunction with its lighter mass, enables it to rebound quickly off the glove before the fielder can react and “squeeze” it. The elasticity of a tennis ball constitutes the second reason that catching a tennis ball presents a special challenge.

I explained this to Matthew, and, bright boy that he is, he seemed to understand at a certain level. I long ago deduced that he is a natural athlete, one of those youngsters who instinctively understand body mechanics in sport, almost without coaching. At quite an early age, he was “whacking” whiffle balls off the “T” post with great power and relatively little instruction from me or anyone else. This also held true for the much greater challenge presented by balls which were pitched to him. He is very quick on his feet and with his feet. When Linda and I play soccer with the boys, it is now almost impossible to contain Matthew once he begins to take the ball down the field toward the goal. As a former track man in high school, I can still run at seventy-three years of age, but I am rapidly becoming no match for my seven and a-half year-old grandson.

Natural athletes come with a seemingly built-in physics “primer” which operates at a sub-conscious level, allowing them to more easily do the things they do. Physics principles are at the heart of all high-performance endeavors – especially sports, and even music! There are many sport clinics today which utilize complex technology to visually display and analyze body mechanics for athletes – even weekend duffers who are attempting to improve their golf swing. In addition to other gifts like foot-speed, natural athletes have the ability to visualize their body mechanics without cameras and to sub-consciously employ sound physics principles in their technique and in their performances.

 Fun for Grandpa Who Loves Sports and Physics!

I love the chance to inject physics into sport, for the edification of my grandchildren. The combination of sport, body mechanics/coaching, and physics is a fascinating trio of disciplines which, when mastered, combine to make champions and prodigies of the lucky few.

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As for me, I have had to methodically learn much of what I have done in sports and music the usual way – through hard work! Much effort, experimentation, and analysis was required on my part to discover “the correct/best way.” Such learning experiences and the resulting insights have proven to be quite satisfying in their own right over the years – as compensation for the struggles.

With my grandsons and my older granddaughters, I relish the opportunity to witness, first-hand, life’s learning processes whereby some people must work hard for their accomplishments while others can go farther and more quickly in the challenging disciplines of sport, music, and academics. The grandkids are truly a blessing in so many ways. If they do not turn out to be champions, prodigies, or geniuses, I will love them none the less. It is the journey well-traveled, not the ultimate destination that really matters in life.

Charles Darwin, known for his scientific curiosity and intellect, was, in addition to a great scientist, a devoted father and grandfather – a great family man. I recall reading the stories of how he loved observing his offspring and their development, much as he loved observing nature in general. They were to him, not some scientific experiment to be recorded in his notebooks; rather, they were a precious window on life’s processes and human nature which afforded him a most wonderful, satisfying, and entertaining view. I get that.

A Postscript: Speaking of baseball and natural athletes, there was none better than the great Willie Mays who played his major league baseball in the early years for the New York Giants. I think Willie knew all he needed to know about the physics of baseball without ever taking a physics course – he was born with an instinctive knowledge of the subject along with other major gifts.

I will never forget my personal memory of, undoubtedly, the greatest outfield catch in the history of baseball. A claim like that in sports almost always invites rebuttals and accounts of something even better. This is one of those rare instances where there really is no dispute. The play was especially notable because it occurred in a World Series game and very well may have determined that series outcome. The fact that the series was nationally televised and the game was played in New York only added to the drama.

Mays' Catch_1

“The Catch” occurred on September 29, 1954, during game one of the 1954 World Series between the Cleveland Indians and the New York Giants. The scene: the old Polo Grounds in New York, the Giants’ home park, with its cavernous outfield. With the score tied 2-2 in the top of the 8th inning and men on first and second base with no outs, Cleveland had a marvelous opportunity. Cleveland slugger Vic Wertz was at the plate. Wertz crushed his fourth pitch to deep center field where Willie Mays was playing rather close-up to the infield. Mays wheeled around, and calling on his great foot-speed sprinted straight out to the 420 foot mark in the cavernous Polo Grounds stadium. As the ball neared the grass at the tail end of its towering trajectory, Mays, still on a dead run directly toward the center field bleachers, stretched out his glove and caught the ball as it came directly over the back of his head. How he could even have seen where the ball was as it passed over his head is a mystery exceeded only by the miracle of such natural ability. Most would agree, there was probably no one else playing ball at the time (and likely, since) who could have made that catch on that big stage. The instant Mays had captured the ball in his glove by literally outrunning it, he stopped, wheeled around and made a great throw to the infield to keep the runner at second from scoring after tagging the base. The side was subsequently retired with no runs scored, and the Giants went on to win the game and sweep the series.

On that sunny September day in 1954 I was a freshman at San Mateo High School, leaving my algebra class and heading to my next class. Someone had a radio nearby, and I had the privilege of hearing that catch “live,” and I do consider it a privilege! I was quite a Cleveland fan at that time, and I was bitterly disappointed at that moment. When Wertz connected and the announcer shouted, “There’s a long drive waaay back in center field….waaay baack…,” I thought Cleveland had this game in the bag. That was just before Willie Mays made a statement that is still heard today. What a ballplayer – probably the greatest ever! What a memory!