It’s no secret that black holes are objects to be avoided, were you to plot yourself a trip across the galaxy. Get too close to one and you’d find your ship hopelessly caught sliding down a gravitational slippery slope toward an inky black event horizon, beyond which there’s no escape. The closer you got the more gravity would yank at your vessel, increasingly more on the end closest to the black hole than on the farther side until eventually the extreme tidal forces would shear both you and your ship apart. Whatever remained would continue to fall, accelerating and stretching into “spaghettified” strands of ship and crew toward—and across—the event horizon. It’d be the end of the cosmic road, with nothing left of you except perhaps some slowly-dissipating “information” leaking back out into the Universe over the course of millennia in the form of Hawking radiation. Nice knowin’ ya.
That is, of course, if you were foolish enough to approach a non-spinning black hole.* Were it to have a healthy rotation to it there’s a possibility, based on new research, that you and your ship could survive the trip intact.
A team of researchers from Georgia Gwinnett College, UMass Dartmouth, and the University of Maryland have designed new supercomputer models to study the exotic physics of quickly-rotating black holes, a.k.a. Kerr black holes, and what might be found in the mysterious realm beyond the event horizon. What they found was the dynamics of their rapid rotation create a scenario in which a hypothetical spacecraft and crew might avoid gravitational disintegration during approach.
“We developed a first-of-its-kind computer simulation of how physical fields evolve on the approach to the center of a rotating black hole,” said Dr. Lior Burko, associate professor of physics at Georgia Gwinnett College and lead researcher on the study. “It has often been assumed that objects approaching a black hole are crushed by the increasing gravity. However, we found that while gravitational forces increase and become infinite, they do so fast enough that their interaction allows physical objects to stay intact as they move toward the center of the black hole.”
Because the environment around black holes is so intense (and physics inside them doesn’t play by the rules) creating accurate models requires the latest high-tech computing power.
“This has never been done before, although there has been lots of speculation for decades on what actually happens inside a black hole,” said Gaurav Khanna, Associate Physics Professor at UMass Dartmouth, whose Center for Scientific Computing & Visualization Research developed the precision computer modeling necessary for the project.
Like science fiction movies have imagined for decades—from Disney’s The Black Hole to Nolan’s Interstellar—it just might be possible to survive a trip into a black hole, if conditions are right (i.e., you probably still don’t want to find yourself anywhere near one of these.)
Electromagnetism is one of the fundamental forces of the universe, responsible for everything from electric and magnetic fields to light. Originally, scientists believed that magnetism and electricity were separate forces. But by the late 19th century, this view changed, as research demonstrated conclusively that positive and negative electrical charges were governed by one force (i.e. magnetism).
Since that time, scientists have sought to test and measure electromagnetic fields, and to recreate them. Towards this end, they created electromagnets, a device that uses electrical current to induce a magnetic field. And since their initial invention as a scientific instrument, electromagnets have gone on to become a regular feature of electronic devices and industrial processes.
How was our Universe created? How did it come to be the seemingly infinite place we know of today? And what will become of it, ages from now? These are the questions that have been puzzling philosophers and scholars since the beginning the time, and led to some pretty wild and interesting theories. Today, the consensus among scientists, astronomers and cosmologists is that the Universe as we know it was created in a massive explosion that not only created the majority of matter, but the physical laws that govern our ever-expanding cosmos. This is known as The Big Bang Theory.
For almost a century, the term has been bandied about by scholars and non-scholars alike. This should come as no surprise, seeing as how it is the most accepted theory of our origins. But what exactly does it mean? How was our Universe conceived in a massive explosion, what proof is there of this, and what does the theory say about the long-term projections for our Universe?
The basics of the Big Bang theory are fairly simple. In short, the Big Bang hypothesis states that all of the current and past matter in the Universe came into existence at the same time, roughly 13.8 billion years ago. At this time, all matter was compacted into a very small ball with infinite density and intense heat called a Singularity. Suddenly, the Singularity began expanding, and the universe as we know it began.
What do Albert Einstein, Neils Bohr, Paul Dirac, and Marie Curie have in common? They each won the Nobel prize in physics. And today, Takaaki Kajita and Arthur McDonald have joined their ranks, thanks to a pioneering turn-of-the-century discovery: in defiance of long-held predictions, neutrinos shape-shift between multiple identities, and therefore must have mass.
The neutrino, a slight whiff of a particle that is cast off in certain types of radioactive decay, nuclear reactions, and high-energy cosmic events, could be called… shy. Electrically neutral but enormously abundant, half the time a neutrino could pass through a lightyear of lead without interacting with a single other particle. According to the Standard Model of particle physics, it has a whopping mass of zero.
As you can imagine, neutrinos are notoriously difficult to detect.
But in 1956, scientists did exactly that. And just a few years later, a trio of physicists determined that neutrinos came in not just one, not two, but three different types, or flavors: the electron neutrino, the muon neutrino, and the tau neutrino.
But there was a problem. Sure, scientists had figured out how to detect neutrinos—but they weren’t detecting enough of them. In fact, the number of electron neutrinos arriving on Earth due to nuclear reactions in the Sun’s core was only one-third to one-half the number their calculations had predicted. What, scientists wondered, was happening to the rest?
Kajita, working at the Super-Kamiokande detector in Japan in 1998, and McDonald, working at the Sudbury Neutrino Observatory in Canada in 1999, determined that the electron neutrinos were not disappearing at all; rather, these particles were changing identity, spontaneously oscillating between the three flavor-types as they traveled through space.
Moreover, the researchers proclaimed, in order for neutrinos to make such transformations, they must have mass.
This is due to some quantum funny business having to do with the oscillations themselves. Grossly simplified, a massless particle, which always travels at the speed of light, does not experience time—Einstein’s theory of special relativity says so. But change takes time. Any particle that oscillates between identities needs to experience time in order for its state to evolve from one flavor to the the next.
Kajita and McDonald’s work showed that neutrinos must have a mass, albeit a very small one. But neutrinos are abundant in the Universe, and even a small mass has a large effect on all sorts of cosmic phenomena, from solar nuclear physics, where neutrinos are produced en masse, to the large-scale evolution of the cosmos, where neutrinos are ubiquitous.
The neutrino, no longer massless, is now considered to play a much larger role in these processes than scientists had originally believed.
What is more, the very existence of a massive neutrino undermines the theoretical basis of the Standard Model. In fact, Kajita’s and McDonald’s discovery provided some of the first evidence that the Standard Model might not be as airtight as had been previously believed, nudging scientists ever more in the direction of so-called “new physics.”
This is not the first time physicists have been awarded a Nobel prize for research into the nature of neutrinos. In 1988, Leon Lederman, Melvin Schwartz, and Jack Steinberger were awarded the prize for their discovery that neutrinos come in three flavors; in 1995, Frederick Reines won a Nobel for his detection of the neutrino along with Clyde Cowan; and in 2002, a Nobel was awarded to Raymond David Jr., the oldest person ever to receive a the prize in physics, and Masatoshi Koshiba for their detection of cosmic neutrinos.
Kajita, of the University of Tokyo, and McDonald, of Queen’s University in Canada, were awarded the prestigious prize this morning at a news conference in Stockholm.
When it comes to understanding our place in the universe, few scientists have had more of an impact than Nicolaus Copernicus. The creator of the Copernican Model of the universe (aka. heliocentrism), his discovery that the Earth and other planets revolved the Sun triggered an intellectual revolution that would have far-reaching consequences.
In addition to playing a major part in the Scientific Revolution of the 17th and 18th centuries, his ideas changed the way people looked at the heavens, the planets, and would have a profound influence over men like Johannes Kepler, Galileo Galilei, Sir Isaac Newton and many others. In short, the “Copernican Revolution” helped to usher in the era of modern science.
Copernicus’ Early Life:
Copernicus was born on February 19th, 1473 in the city of Torun (Thorn) in the Crown of the Kingdom of Poland. The youngest of four children to a well-to-do merchant family, Copernicus and his siblings were raised in the Catholic faith and had many strong ties to the Church.
His older brother Andreas would go on to become an Augustinian canon, while his sister, Barbara, became a Benedictine nun and (in her final years) the prioress of a convent. Only his sister Katharina ever married and had children, which Copernicus looked after until the day he died. Copernicus himself never married or had any children of his own.
Born in a predominately Germanic city and province, Copernicus acquired fluency in both German and Polish at a young age, and would go on to learn Greek and Italian during the course of his education. Given that it was the language of academia in his time, as well as the Catholic Church and the Polish royal court, Copernicus also became fluent in Latin, which the majority of his surviving works are written in.
In 1483, Copernicus’ father (whom he was named after) died, whereupon his maternal uncle, Lucas Watzenrode the Younger, began to oversee his education and career. Given the connections he maintained with Poland’s leading intellectual figures, Watzenrode would ensure that Copernicus had great deal of exposure to some of the intellectual figures of his time.
Although little information on his early childhood is available, Copernicus’ biographers believe that his uncle sent him to St. John’ School in Torun, where he himself had been a master. Later, it is believed that he attended the Cathedral School at Wloclawek (located 60 km south-east Torun on the Vistula River), which prepared pupils for entrance to the University of Krakow – Watzenrode’s own Alma mater.
In 1491, Copernicus began his studies in the Department of Arts at the University of Krakow. However, he quickly became fascinated by astronomy, thanks to his exposure to many contemporary philosophers who taught or were associated with the Krakow School of Mathematics and Astrology, which was in its heyday at the time.
Copernicus’ studies provided him with a thorough grounding in mathematical-astronomical knowledge, as well as the philosophy and natural-science writings of Aristotle, Euclid, and various humanist writers. It was while at Krakow that Copernicus began collecting a large library on astronomy, and where he began his analysis of the logical contradictions in the two most popular systems of astronomy.
These models – Aristotle’s theory of homocentric spheres, and Ptolemy’s mechanism of eccentrics and epicycles – were both geocentric in nature. Consistent with classical astronomy and physics, they espoused that the Earth was at the center of the universe, and that the Sun, the Moon, the other planets, and the stars all revolved around it.
Before earning a degree, Copernicus left Krakow (ca. 1495) to travel to the court of his uncle Watzenrode in Warmia, a province in northern Poland. Having been elevated to the position of Prince-Bishop of Warmia in 1489, his uncle sought to place Copernicus in the Warmia canonry. However, Copernicus’ installation was delayed, which prompted his uncle to send him and his brother to study in Italy to further their ecclesiastic careers.
In 1497, Copernicus arrived in Bologna and began studying at the Bologna University of Jurists’. While there, he studied canon law, but devoted himself primarily to the study of the humanities and astronomy. It was also while at Bologna that he met the famous astronomer Domenico Maria Novara da Ferrara and became his disciple and assistant.
Over time, Copernicus’ began to feel a growing sense of doubt towards the Aristotelian and Ptolemaic models of the universe. These included the problematic explanations arising from the inconsistent motion of the planets (i.e. retrograde motion, equants, deferents and epicycles), and the fact that Mars and Jupiter appeared to be larger in the night sky at certain times than at others.
Hoping to resolve this, Copernicus used his time at the university to study Greek and Latin authors (i.e. Pythagoras, Cicero, Pliny the Elder, Plutarch, Heraclides and Plato) as well as the fragments of historic information the university had on ancient astronomical, cosmological and calendar systems – which included other (predominantly Greek and Arab) heliocentric theories.
In 1501, Copernicus moved to Padua, ostensibly to study medicine as part of his ecclesiastical career. Just as he had done at Bologna, Copernicus carried out his appointed studies, but remained committed to his own astronomical research. Between 1501 and 1503, he continued to study ancient Greek texts; and it is believed that it was at this time that his ideas for a new system of astronomy – whereby the Earth itself moved – finally crystallized.
The Copernican Model (aka. Heliocentrism):
In 1503, having finally earned his doctorate in canon law, Copernicus returned to Warmia where he would spend the remaining 40 years of his life. By 1514, he began making his Commentariolus (“Little Commentary”) available for his friends to read. This forty-page manuscript described his ideas about the heliocentric hypothesis, which was based on seven general principles.
These seven principles stated that: Celestial bodies do not all revolve around a single point; the center of Earth is the center of the lunar sphere—the orbit of the moon around Earth; all the spheres rotate around the Sun, which is near the center of the Universe; the distance between Earth and the Sun is an insignificant fraction of the distance from Earth and Sun to the stars, so parallax is not observed in the stars; the stars are immovable – their apparent daily motion is caused by the daily rotation of Earth; Earth is moved in a sphere around the Sun, causing the apparent annual migration of the Sun; Earth has more than one motion; and Earth’s orbital motion around the Sun causes the seeming reverse in direction of the motions of the planets.
Thereafter he continued gathering data for a more detailed work, and by 1532, he had come close to completing the manuscript of his magnum opus – De revolutionibus orbium coelestium(On the Revolutions of the Heavenly Spheres). In it, he advanced his seven major arguments, but in more detailed form and with detailed computations to back them up.
However, due to fears that the publication of his theories would lead to condemnation from the church (as well as, perhaps, worries that his theory presented some scientific flaws) he withheld his research until a year before he died. It was only in 1542, when he was near death, that he sent his treatise to Nuremberg to be published.
Towards the end of 1542, Copernicus suffered from a brain hemorrhage or stroke which left him paralyzed. On May 24th, 1543, he died at the age of 70 and was reportedly buried in the Frombork Cathedral in Frombork, Poland. It is said that on the day of his death, May 24th 1543 at the age of 70, he was presented with an advance copy of his book, which he smiled upon before passing away.
In 2005, an archaeological team conducted a scan of the floor of Frombork Cathedral, declaring that they had found Copernicus’ remains. Afterwards, a forensic expert from the Polish Police Central Forensic Laboratory used the unearthed skull to reconstruct a face that closely resembled Copernicus’ features. The expert also determined that the skull belonged to a man who had died around age 70 – Copernicus’ age at the time of his death.
These findings were backed up in 2008 when a comparative DNA analysis was made from both the remains and two hairs found in a book Copernicus was known to have owned (Calendarium Romanum Magnum, by Johannes Stoeffler). The DNA results were a match, proving that Copernicus’ body had indeed been found.
On May 22nd, 2010, Copernicus was given a second funeral in a Mass led by Józef Kowalczyk, the former papal nuncio to Poland and newly named Primate of Poland. Copernicus’ remains were reburied in the same spot in Frombork Cathedral, and a black granite tombstone (shown above) now identifies him as the founder of the heliocentric theory and also a church canon. The tombstone bears a representation of Copernicus’ model of the solar system – a golden sun encircled by six of the planets.
Despite his fears about his arguments producing scorn and controversy, the publication of his theories resulted in only mild condemnation from religious authorities. Over time, many religious scholars tried to argue against his model, using a combination of Biblical canon, Aristotelian philosophy, Ptolemaic astronomy, and then-accepted notions of physics to discredit the idea that the Earth itself would be capable of motion.
However, within a few generation’s time, Copernicus’ theory became more widespread and accepted, and gained many influential defenders in the meantime. These included Galileo Galilei (1564-1642), who’s investigations of the heavens using the telescope allowed him to resolve what were seen at the time as flaws in the heliocentric model.
These included the relative changes in the appearances of Mars and Jupiter when they are in opposition vs. conjunction to the Earth. Whereas they appear larger to the naked eye than Copernicus’ model suggested they should, Galileo proved that this is an illusion caused by the behavior of light at a distance, and can be resolved with a telescope.
Through the use of the telescope, Galileo also discovered moons orbiting Jupiter, Sunspots, and the imperfections on the Moon’s surface, all of which helped to undermine the notion that the planets were perfect orbs, rather than planets similar to Earth. While Galileo’s advocacy of Copernicus’ theories resulted in his house arrest, others soon followed.
German mathematician and astronomer Johannes Kepler (1571-1630) also helped to refine the heliocentric model with his introduction of elliptical orbits. Prior to this, the heliocentric model still made use of circular orbits, which did not explain why planets orbited the Sun at different speeds at different times. By showing how the planet’s sped up while at certain points in their orbits, and slowed down in others, Kepler resolved this.
In addition, Copernicus’ theory about the Earth being capable of motion would go on to inspire a rethinking of the entire field of physics. Whereas previous ideas of motion depended on an outside force to instigate and maintain it (i.e. wind pushing a sail) Copernicus’ theories helped to inspire the concepts of gravity and inertia. These ideas would be articulated by Sir Isaac Newton, who’s Principia formed the basis of modern physics and astronomy.
Today, Copernicus is honored (along with Johannes Kepler) by the liturgical calendar of the Episcopal Church (USA) with a feast day on May 23rd. In 2009, the discoverers of chemical element 112 (which had previously been named ununbium) proposed that the International Union of Pure and Applied Chemistry rename it copernicum (Cn) – which they did in 2011.
In 1973, on the 500th anniversary of his birthday, the Federal Republic of Germany (aka. West Germany) issued a 5 Mark silver coin (shown above) that bore Copernicus’ name and a representation of the heliocentric universe on one side.
In August of 1972, the Copernicus– an Orbiting Astronomical Observatory created by NASA and the UK’s Science Research Council – was launched to conduct space-based observations. Originally designated OAO-3, the satellite was renamed in 1973 in time for the 500th anniversary of Copernicus’ birth. Operating until February of 1981, Copernicus proved to be the most successful of the OAO missions, providing extensive X-ray and ultraviolet information on stars and discovering several long-period pulsars.
Two craters, one located on the Moon, the other on Mars, are named in Copernicus’ honor. The European Commission and the European Space Agency (ESA) is currently conducting the Copernicus Program. Formerly known as Global Monitoring for Environment and Security (GMES), this program aims at achieving an autonomous, multi-level operational Earth observatory.
On February 19th, 2013, the world celebrated the 540th anniversary of Copernicus’ birthday. Even now, almost five and a half centuries later, he is considered one of the greatest astronomers and scientific minds that ever lived. In addition to revolutionizing the fields of physics, astronomy, and our very concept of the laws of motion, the tradition of modern science itself owes a great debt to this noble scholar who placed the truth above all else.
This week, scientists with the Dark Energy Survey (DES) collaboration released the first in a series of detailed maps charting the distribution of dark matter inferred from its gravitational effects. The new maps confirm current theories that suggest galaxies will form where large concentrations of dark matter exist. The new data show large filaments of dark matter where visible galaxies and galaxy clusters lie and cosmic voids where very few galaxies reside.
“Our analysis so far is in line with what the current picture of the universe predicts,” said Chihway Chang from the Swiss Federal Institute of Technology (ETH) in Zurich, a co-leader of the analysis. “Zooming into the maps, we have measured how dark matter envelops galaxies of different types and how together they evolve over cosmic time.”
The research and maps, which span a large area of the sky, are the product of a massive effort of an international team from the US, UK, Spain, Germany, Switzerland, and Brazil. They announced their new results at the American Physical Society (APS) meeting in Baltimore, Maryland.
According to cosmologists, dark matter particles stream and clump together over time in particular regions of the cosmos, often in the same places where galaxies form and cluster. Over time, a “cosmic web” develops across the universe. Though dark matter is invisible, it expands with the universe and feels the pull of gravity. Astrophysicists then can reconstruct maps of it by surveying millions of galaxies, much like one might infer the shifting orientation of a flock of birds from its shadow moving along the ground.
DES scientists created the maps with one of the world’s most powerful digital cameras, the 570-megapixel Dark Energy Camera (DECam), which is particularly sensitive to the light from distant galaxies. It is mounted on the 4-meter Victor M. Blanco Telescope, located at the Cerro Tololo Inter-American Observatory in northern Chile. Each of its images records data from an area 20 times the size of the moon as seen from earth.
In addition, DECam collects data nearly ten times faster than previous machines. According to David Bacon, at the University of Portsmouth’s Institute of Cosmology and Gravitation, “This allows us to stare deeper into space and see the effects of dark matter and dark energy with greater clarity. Ironically, although these dark entities make up 96% of our universe, seeing them is hard and requires vast amounts of data.”
The telescope and its instruments enable precise measurements utilizing a technique known as “gravitational lensing.” Astrophysicists study the small distortions and shear of images of galaxies due to the gravitational pull of dark matter around them, similar to warped images of objects in a magnifying glass, except that the lensed galaxies observed by the DES scientists are at least 6 billion light-years away.
Chang and Vinu Vikram (Argonne National Laboratory) led the analysis, with which they traced the web of dark matter in unprecedented detail across 139 square degrees of the southern hemisphere. “We measured the barely perceptible distortions in the shapes of about 2 million galaxies to construct these new maps,” Vikram said. This amounts to less then 0.4% of the whole sky, but the completed DES survey will map out more than 30 times this area over the next few years.
They submitted their research paper for publication in an upcoming issue of the Monthly Notices of the Royal Astronomical Society, and the DES team publicly released it as part of a set of papers on the arXiv.org server on Tuesday.
The precision and detail of these large contiguous maps being produced by DES scientists will allow for tests of other cosmological models. “I’m really excited about what these maps will tell us about dark matter in galaxy clusters especially with respect to theories of modified gravity,” says Robert Nichol (University of Portsmouth). Einstein’s model of gravity, general relativity, could be incorrect on large cosmological scales or in the densest regions of the universe, and ongoing research with the Dark Energy Survey will facilitate investigations of this.
We have no idea what it dark energy is, so how are we pretty sure it exists?
I’ve talked about how astronomers know that dark matter exists. Even though they can’t see it, they detect it through the effect its gravity has on light. Dark matter accounts for 27% of the Universe, dark energy accounts for 68% of the Universe. And again, astronomers really have no idea what what it is, only that they’re pretty sure it does exist. 95% of the nature of the Universe is a complete and total mystery. We just have no idea what this stuff is.
So this time around, lets focus on dark energy. Back in the late 90s, astronomers wanted to calculate once and for all if the Universe was open or closed. In other words, they wanted to calculate the rate of expansion of the Universe now and then compare this rate to its expansion in the past. In order to answer this question, they searched the skies for a special type of supernova known as a Type 1a.
While most supernovae are just massive stars, Type 1a are white dwarf stars that exist in a binary system. The white dwarf siphons material off of its binary partner, and when it reaches 1.6 times the mass of the Sun, it explodes. The trick is that these always explode with roughly the same amount of energy. So if you measure the brightness of a Type 1a supernova, you know roughly how far away it is.
Astronomers assumed the expansion was slowing down. But the question was, how fast was it slowing down? Would it slow to a halt and maybe even reverse direction? So, what did they discover?
In the immortal words of Isaac Asimov, “the most exciting phrase to hear in science, the one that heralds new discoveries, is not ‘Eureka’, but ‘That’s Funny’” Instead of finding that the expansion of the Universe was slowing down, they discovered that it’s speeding up. That’s like trying to calculate how quickly apples fall from trees and finding that they actually fly off into the sky, faster and faster.
Since this amazing, Nobel prize winning discovery, astronomers have used several other methods to verify this mind-bending reality of the Universe. NASA’s Wilkinson Microwave Anisotropy Probe studied the Cosmic Microwave Background Radiation of the Universe for 7 years, and put the amount of dark energy at 72.8% of the Universe. ESA’s Planck spacecraft performed an even more careful analysis and pegged that number at 68.3% of the Universe.
Astronomers know that dark energy exists. There are multiple lines of evidence. But as with dark matter, they have absolutely no clue what it is. Einstein described an idea he called the cosmological constant. It was a way to explain a static Universe that really should be expanding or contracting. Once astronomers figured out the Universe was actually expanding, he threw the idea out.
Hey, not so fast there “Einstein”. Maybe just one of the features of space itself is that it pushes stuff away. And the more space there is, the more outward pressure you get. Perhaps from virtual particles popping in and out of existence in the vacuum of space.
Another possibility is a phenomenon called Quintessence, a negative energy field that pervades the entire Universe. Yes, that sounds totally woo-woo, thanks Universe, Deepak Chopra crazy talk, but it might explain the repulsive force that makes up most of the Universe. And there are other theories, which are even more exotic. But mostly likely it’s something that physicists haven’t even thought of yet.
So, how do we know dark energy exists? Distant supernovae are a lot further away from each other than they should be if the expansion of the Universe was slowing down. Nobody has any idea what it is, it’s a mystery, and there’s nothing wrong with a mystery. In fact, for me, it’s one of the most exciting ideas in space and astronomy.
The spring is a marvel of human engineering and creativity. For one, it comes in so many varieties – the compression spring, the extension spring, the torsion spring, the coil spring, etc. – all of which serve different and specific functions. These functions in turn allow for the creation of many man-made objects, most of which emerged as part of the Scientific Revolution during the late 17th and 18th centuries.
As an elastic object used to store mechanical energy, the applications for them are extensive, making possible such things as an automotive suspension systems, pendulum clocks, hand sheers, wind-up toys, watches, rat traps, digital micromirror devices, and of course, the Slinky.
Like so many other devices invented over the centuries, a basic understanding of the mechanics is required before it can so widely used. In terms of springs, this means understanding the laws of elasticity, torsion and force that come into play – which together are known as Hooke’s Law.
Hooke’s Law is a principle of physics that states that the that the force needed to extend or compress a spring by some distance is proportional to that distance. The law is named after 17th century British physicist Robert Hooke, who sought to demonstrate the relationship between the forces applied to a spring and its elasticity.
He first stated the law in 1660 as a Latin anagram, and then published the solution in 1678 as ut tensio, sic vis – which translated, means “as the extension, so the force” or “the extension is proportional to the force”).
This can be expressed mathematically as F= -kX, where F is the force applied to the spring (either in the form of strain or stress); X is the displacement of the spring, with a negative value demonstrating that the displacement of the spring once it is stretched; and k is the spring constant and details just how stiff it is.
Hooke’s law is the first classical example of an explanation of elasticity – which is the property of an object or material which causes it to be restored to its original shape after distortion. This ability to return to a normal shape after experiencing distortion can be referred to as a “restoring force”. Understood in terms of Hooke’s Law, this restoring force is generally proportional to the amount of “stretch” experienced.
In addition to governing the behavior of springs, Hooke’s Law also applies in many other situations where an elastic body is deformed. These can include anything from inflating a balloon and pulling on a rubber band to measuring the amount of wind force is needed to make a tall building bend and sway.
This law has had many important practical applications, with one being the creation of a balance wheel, which made possible the creation of the mechanical clock, the portable timepiece, the spring scale and the manometer (aka. the pressure gauge). Also, because it is a close approximation of all solid bodies (as long as the forces of deformation are small enough), numerous branches of science and engineering as also indebted to Hooke for coming up with this law. These include the disciplines of seismology, molecular mechanics and acoustics.
However, like most classical mechanics, Hooke’s Law only works within a limited frame of reference. Because no material can be compressed beyond a certain minimum size (or stretched beyond a maximum size) without some permanent deformation or change of state, it only applies so long as a limited amount of force or deformation is involved. In fact, many materials will noticeably deviate from Hooke’s law well before those elastic limits are reached.
Still, in its general form, Hooke’s Law is compatible with Newton’s laws of static equilibrium. Together, they make it possible to deduce the relationship between strain and stress for complex objects in terms of the intrinsic materials of the properties it is made of. For example, one can deduce that a homogeneous rod with uniform cross section will behave like a simple spring when stretched, with a stiffness (k) directly proportional to its cross-section area and inversely proportional to its length.
Another interesting thing about Hooke’s law is that it is a a perfect example of the First Law of Thermodynamics. Any spring when compressed or extended almost perfectly conserves the energy applied to it. The only energy lost is due to natural friction.
In addition, Hooke’s law contains within it a wave-like periodic function. A spring released from a deformed position will return to its original position with proportional force repeatedly in a periodic function. The wavelength and frequency of the motion can also be observed and calculated.
The modern theory of elasticity is a generalized variation on Hooke’s law, which states that the strain/deformation of an elastic object or material is proportional to the stress applied to it. However, since general stresses and strains may have multiple independent components, the “proportionality factor” may no longer be just a single real number.
A good example of this would be when dealing with wind, where the stress applied varies in intensity and direction. In cases like these, it is best to employ a linear map (aka. a tensor) that can be represented by a matrix of real numbers instead of a single value.
If you enjoyed this article there are several others that you will enjoy on Universe Today. Here is one about Sir Isaac Newton’s contributions to the many fields of science. Here is an interesting article about gravity.
There are also some great resources online, such as this lecture on Hooke’s Law that you can watch on academicearth.org. There is also a great explanation of elasticity on howstuffworks.com.