The 1994 action thriller Speed introduced America totwo soon-to-be movie stars in Keanu Reeves and Sandra Bullock.  Thefilm contained all of the escapist elements that a summer outing tothe theatre is supposed to: adrenalin-fuelled intimacy between the twoleads, a smart yet mentally deranged villain, and lots of things thatcan and eventually do go boom. 

Yet, after the credits role, and the movie goers make their wayhome, the images that stick with them are not those of kissing,lunacy, or explosions, but rather the exciting set-pieces involvingmechanics that are continuously on display.  From the elevator on whichthe film opens, to the bus, where the majority of it takes place, to the subwayon which it concludes, it feels like a 116-minute mechanics course,albeit an entertaining one.  I don't know this for a fact, but I wouldsuspect that director Jan de Bont took a physics class as a kid and enjoyed itimmensely.

I suppose it is not surprising that the movie features mechanics,as its title is a key term of kinematics - speed is defined asthe magnitude of velocity.  And, when an ex-cop turnedpsycho attaches a bomb to a city bus, he programs it with this kinematicparameter in mind: the bomb is armed once the bus surpasses a speed of 50 mph,and is set to blow should it ever fall below this value again.

If there were more class time in the Mechanics course that I teach,I would actually show Speed in class.  And, after eachaction sequence, I would pause the film to discuss the key concepts ofmechanics on display, and even solve explicitly for some of the unknownparameters.  As this exercise is quite time-consuming, I simply encouragemy students to try this activity on their own.

In the first scene alone, many aspects of mechanics are highlighted whenan elevator filled with innocent people threatens to plummet to theground.  The periods of free fall experienced by both theelevator and those inside begs several questions, like "Shouldthe passengers float upwards?" and "Would they increase theirlikelihood of survival if they jumped just before the cabin hits theground?"  I'll leave readers to consider these on their own.

When the cabin and its contents are supported by a single rope, how muchtension manifests inside it?  Does the rope extend, and if so, by howmuch?  Why does the supporting crane above break?  I'll answer thislast one: the tension in the cord creates a large moment (or torque) about thesupport structure.  The bending moment leads to a local stress that islarger than the ultimate stress value of the material making up the structure.

We could go on and dissect the mechanics of the entire film in thisfashion, but instead, I would like to focus on two particular action sequencesin some detail.  These two sequences occur on the fast-moving bus, and Ialways discuss them with my mechanics classes.

 The Sharp Turn

Midway through the movie, Bullock's character, the stand-in bus driver,must attempt a sharp turn at a high speed.  When a moving vehicle followsa circular path, it has an inherent centripetal acceleration that pointstowards the center of the path.  The magnitude of this accelerationis v²/R, where v is the speed of thevehicle and R is the radius of the circular path.  

Typically, when a vehicle rounds a bend, it reduces its speed to reducethe magnitude of this acceleration.  A car does this to avoid skiddingoutwards during the turn.  This would occur if the inertial term of thecar (its mass multiplied by its centripetal acceleration) were to exceed themaximum static friction between the tires and the road.  To help carsavoid skidding, curved roads are often inclined upwards at some angle - theresult of this feature is that the inertial term must overcome both thestatic friction as well as a small component of the car's weight in order forit to skid.

As our friends in Speed preparefor a sharp turn, their concern is not that they will skid, but that they willroll over.  A typical sedan has a center of mass that is quite close tothe ground, such that it will always skid before it rolls over.  A bus,however, has a center of mass that is fairly elevated, and is at risk ofrolling over on tight turns at high speeds.  A bus may overturn if itsinner wheels (those closer to the center of the circular path) lose contactwith the ground.  It is fairly easy to solve for the minimum radius of turn, Rmin, that a vehicle can undergo at a given speed and not roll over (Let thenormal force under the inner tires go to zero, and set the angular accelerationof the vehicle to zero as well).  Let us also assume that the sharp turnis not banked.  We then find:

R min = (v²h)/(gx)

Here, g is the surface gravity of the Earth, h isthe height of the center of mass of the vehicle off of the road, and x isthe radial distance from the outer wheels to the center of mass of the vehicle. If the bus in the film was travelling at 50 mph (its minimum allowable),then the minimum allowable radius turn it could safely make would be 50(h/x)in units of meters.  It is for this reason that Reeves' character rightlyinstructs every person on the bus to go to the right side of the bus beforeattempting the sharp right turn up ahead.  This shifts the center of massof the entire vehicle (passengers included) from the center to slightlyoff-center, thereby increasing x by a small factor.

How big an effect could this shift in mass have had on their survival? Well, if the bus were 5000 kg and contained 15 people, then the totalmass of the bus and its contents would be about 6000 kg.  If 1000 kg ofthat total mass (the people) were to all pile up on the extreme right side,then the center of mass would shift outward from the center by a factor of onesixth.  If the total width of the bus were 2 meters, then this mass shiftwould allow x to grow from 1 m to 1.17 m.  

By examining the R min equation, we see that the actionhero's intuition to shift the people to the right side brought the limitingcurve radius down by 17%.  If the center of mass of the bus and itscontents was elevated a reasonable 0.75 m off of the ground, then the sharpest turnthe bus could safely undergo at 50 mph without shifting the peopleinside would have a radius of 37.5 m.  Keanu's stroke of geniusbrought this value down to 32 m; the bomb toting bus narrowly averted a rollover, and the film rolled on at 50 mph. 

The Gap Jump

Having survived several dramatic near-death experiences, the passengersaboard the armed city bus now face their greatest challenge yet: a 50-ft gap inthe overpass ahead.   The scene is both "la pièce de resistance"of the blockbuster film and a gross violation of the laws of mechanics.  When Keanu and friends perform the gravity-defying leap above aMario Brothers-like crevice, it is the moment when the film jumps the shark (deBont may as well have completed the metaphor by placing hungry sharks in a poolof water salivating as the bus swoops above their heads).

If we treat the bus as a particle, rather than a rigid body with actualdimensions, we can approximate the motion of the center of gravity of the bususing projectile motion kinematics.  When a body is launched with aninitial velocity in the horizontal direction (zero pitch angle), it losesaltitude as it sails along horizontally.  So, it goes without saying thatno vehicle can jump a gap of any length at any speed unless one or both of thefollowing conditions are met: (1) the landing is lower than the launchaltitude, (2) the launch velocity points above the horizontal axis by someangle.

It makes for two nice mechanics problems to solve for the minimum valuesassociated with each of the two scenarios described above using the data fromthe film.  Recall that the gap is 50 ft (15.2 m) and note that the bus wasmoving at its top speed, 68 mph (30.2 m/s), at the moment of launch.

Using these values, how much altitude would the bus lose if it were tolift off horizontally?  One simple free fall equation shows that it willlose 4.07 ft (1.24 m).  That means that if the landing were at least fourfeet lower than the launch altitude, the bus could strike the surface of thelanding rather than bowl it over entirely.

Alternatively, if the landing were at the same altitude as the launch,what minimum launch angle (road inclination) would allow the bus to reach theother side?  By combining equations of uniform motion along the horizontalaxis and free fall along the vertical axis, we find the minimum angle to be 4.7degrees.  This might not sound like much, but it would be quite noticeablefor a stretch of road.

So, where is the defiance of the laws of physics that I had previously alludedto?  Let us assume that the road was indeed inclined at around fivedegrees.  And let us pretend that a city bus filled with people couldactually reach 68 mph while driving up such an incline.  The real troublewith this scene is how the pitch of the bus varies during the jump.

If this were a real bus, its pitch would begin to decrease the momentthat the front wheels leave the road.  For the brief period of time whenjust the rear wheels of the bus are in contact with the road, the vehicle'spitch would have an angular acceleration in the clockwise (CW) sense. Then, once the rear wheels have also lost contact with the road, the buswould have a pitch angular velocity in the clockwise direction.  It wouldcontinue to rotate with this angular velocity until it lands (although'bounces' might be more appropriate).  The long term orientation of anyvehicle with two sets of wheels that attempts a jump is a nose dive.

I decided to crunch the numbers on this one, and if you are a mechanicsstudent, perhaps you would like to try to as well.  I assumed that thecenter of mass of the bus and its contents was at its center lengthwise, andfound its rotational inertia for pitch by approximating the structure as a thinrod.  I used a bus length of 7 m, and assumed that the two sets of wheelswere 3.5 m apart and that they were spaced symmetrically about the center ofthe bus.  

With these values and those already mentioned above, Icalculated that the bus would launch with an angular velocity of 0.485 rad/s CW(due to an angular acceleration of 4.18 rad/s² CW experiencedwhile only the rear wheels were in contact with the ground).  By the timethe bus reached the other side of the gap, it ought to have rotated through anangle of 14.2 degrees CW.  This means that if the jump were inclinedupwards at 5 degrees, the bus would be inclined downwards at 9.2 degrees whenit reached the other side.  

Those familiar with the scene know that this does not occur.  AsBullock and Reeves leave the launch surface, the bus immediately begins torotate counter-clockwise.  The unjustifiable rigid bodymechanics are so extreme that when the bus lands, its rear wheels strike thesurface first.  A student in my class once suggested that maybe the bushad wings.  The truth is that not even wings could cause the rotationobserved in this scene.  A more likely justification is that divineintervention saved Keanu so that he could one day play Neo in TheMatrix.

In summary, the gap jump in Speed is not impossiblefrom a particle mechanics perspective, but it is impossible from a rigid bodymechanics one.  The center of mass of the bus might well reach the otherside of the gap, but the rotation of the bus about this center of mass wouldensure that its nose would strike the road first.  The collision dynamicsthat would then ensue are very complex, but would likely result in zerosurvivors and an ending that no member of the audience saw coming.

Science is my favourite realm of study.  Although physics is the branch that I am most comfortable with, I find science as a whole very fascinating.  It seems to me that science can be broken down into five categories: physics, chemistry, biology, psychology and sociology – in that order.

How do these five pillars relate to one another?  What is their connection?  Consider the following simple organizational chart.

A Scientific Road Map

The scientific road map shown above is organized in terms of causality and complexity.

Although my physics students would disagree, physics is the simplest science, as there are only a few key relationships to consider.  There are only four kinds of forces that affect the way in which matter interacts in the universe.  Conversely, there exist hundreds of known elements and millions of known chemicals, each with their own unique properties.  Chemistry is indeed more complex than physics.  Bring the chemistry to life, and you have biology.  The most baffling aspect of biology is the brain of an organism, which is the least understood organ in the human body by far.  The only thing more complicated than psychology would be how many psyches interact: sociology.

Let us now follow this chart in the reverse sequence.  Why do people act the way they do?  This is the root question in sociology.  Well, the answer may be found in the study of psychology.  What controls our psyche?  It is most certainly biological.  Biology is simply chemistry, and the way in which chemicals interact is governed by the laws of physics.

The neat thing about the scientific road map is that it is chronological from left to right.  What arrived first in the universe after the big bang?  For the first 5 billion years, the laws of physics were sufficient to describe everything in the universe.  After all, there were only two elements in existence (hydrogen and helium undergoing fusion within stars).  When stars burn out, they release many new elements, and the study of chemistry becomes necessary.  Perhaps 10 billion years after the big bang, life begins to emerge, and biology is born.  Evolution then runs its course, such that biological complexity increases from bacteria to organism.  Once organisms become sentient, the study of psychology pops up.  Finally, when groups of sentient beings begin to interact in large groups, the branch of sociology comes into existence.

It makes sense that the complexity of the universe should grow with time.  This is what the second law of thermodynamics predicts: entropy (chaos) can never decrease with time.

One final conclusion I take from this picture, which comes as no surprise, is that physics governs everything.  If you continuously ask “Why?” for any problem within the scientific realm, you will eventually arrive in physics territory.  Physics is where the why ends.  In truth, physics is the how, and the rest of science from chemistry on down is the what.  Physics is the king of the scientific jungle, sitting atop the scientific food chain.

 

This is what Rutherford meant when he said, “Physics is everything – the rest is stamp collecting.”

In the month of June, as most students are beginning to think about summer camp, or a temporary job, some students are beginning a new semester of school.  Whether they are retaking a failed class or trying to get ahead in their studies, summer school is not how most adolescents would like to spend their summer.

I have an unusually high interest in the notion of summer school this year because, for the first time, I will be teaching a class during these hot months.

Summer courses are much like fall or winter courses.  The classrooms are the same, but tend to have fewer students in them, and are filled with much hotter air.  Most institutions I know of, mine included, have no air conditioning.  I plan on wearing sandals to work. 

I suppose the main difference between regular semester courses and summer ones is that students sitting in class during the summer do not want to be there.  Let me rephrase that ... However much a student wants to be in a classroom under normal circumstances, they want to be there in the summer less.

Summer is supposed to be a time to relax.  In our childhood, it is the time to play outside.  It is typically less structured than the rest of the year.  It is a time that is conducive to slacking.  And, I must admit, I have done my share of summer slacking over the years.

Where does that leave me?  This coming Monday, I will be faced with twenty or so adolescent students who want to be sleeping or tanning or both.  They do not want to be learning about vectors, circular motion, or the conservation of energy.

 

In a typical semester, my classroom is composed of three roughly equal groups.  The first third have chosen a path of science, and want to learn physics.  The second group of students are pushed into science by their parents and are willing to try to appease them.  The last group wander into the classroom as though they are lost and maintain a lost expression on their face throughout the semester.

I expect my class this summer to have a similar student makeup, but for everyone involved, myself included, to be itching to leave, go sit by a lake and enjoy some soft ice cream.

 

I am open to suggestions as to how to make the upcoming five-week intensive physics course as enjoyable as possible for my students.  I am content to talk about physics for three hours each day, but I am also a nerd who operates a science blog.

 

Is it possible to make the classroom experience so positive that the majority of students actually want to spend their precious summer time there?  That is my goal, but I am not sure it is an achievable one.  Any advice?

The distance between the average person and their tools has grown a great deal over the past century.  There was a time when the average adult was fairly independent: they could grow and catch their own food, build their shelter, and manage their own health, albeit for their forty-year lifespan.  When the tools that were used in society were primitive, it was not difficult to understand how they worked, in a general sense.  Today’s tools are not primitive, and they continue to advance exponentially.

That being said, aircrafts have been taking flight for over a century.  The latter half of the twentieth century saw the friendly skies open up to even middle class passengers.  Air transit is now a typical form of transportation.  It is normal for a new technology to appear mysterious, even magical, to the common man.  However, one would expect the common man to comprehend the basics of a relatively old technology such as aviation.

I am fairly positive that more than 80% of the passengers aboard a given flight today haven’t a clue as to how the airplane is flying.  Perhaps they feel better chalking airplane travel up to magic.  I have news for you: the pilot is not a magician – he or she is just an operator of a well-tuned piece of engineering hardware.

What justifies the time lag between the introduction of a new technology in society, and the public's comprehension of how it works?  Well, I would like to do my part, and help the public catch up to the relatively old technology of aviation.  What follows is a quick summary of the way in which an airplane cruises through the air without plummeting to the surface of the Earth...

There are four external forces acting on an airplane as it maintains altitude and pushes forward at constant velocity.  The forces are shown in figure 1, and are described below:

(1) Thrust: the engines on the wings cause a forward force by exhausting air out the back at extremely high velocities.

(2) Drag: the air that the plane’s surface must displace poses a resistance, and its force opposes the direction of motion.

(3) Weight: the gravitational force pulls the airplane down towards the Earth (the value of this force in Newtons is the mass of the plane in kilograms, multiplied by 9.8 m/s²). 

(4) Lift: the pressure gradient on the wings of the plane counteracts the weight force – the lift force is dependent on the airplane’s speed, as it is responsible for the pressure gradient.

Figure 1: Basic Free Body Diagram for an Airplane

For a plane to maintain altitude, the lift force must be equal to the weight force.  The lift force occurs because of the ingenious design of the cross-section of the airplane wing.  When the air is cut by the wing, it meets up on the other side of the wing.  However, the air molecules that choose the top path of the wing have a longer distance to cover than do those that choose the bottom path.  As a result, the air on the top must travel at a higher velocity than those on a bottom.  The lower velocity of the bottom path causes it to have a higher pressure than the air on top. 

The difference in pressure (pressure gradient) on either side of the wing causes the lift force, which is proportional to the bottom surface area of the entire wing.  As the velocity of the plane increases, the air pressure gradient increases.  This is why a plane suddenly takes off as it accelerates – it occurs when the lift force exceeds the weight force.  The generation of the lift force is depicted in figure 2.

Figure 2: Lift Generation for a Subsonic Aircraft Wing

The rest of the aircraft motion story occurs in the horizontal direction of the airplane.  The thrust pushes forward, but the drag pushes back; drag pushes back harder the faster the airplane travels (roughly proportional to the square of the speed).  The plane finds an equilibrium velocity for a given thrust force.  The situation is akin to a sky diver that reaches a terminal velocity (constant velocity in the area of 200 km/hr) because the upward drag is equal to the downward weight force.  An airplane differs from the diver in that it can control the force that is pushing it along.

Aircraft dynamics are actually less simplistic than presented here.  For example, the wings can make certain mechanical adjustments to their shape, affecting lift and drag forces.  Also, the atmospheric medium that is being flown through is not static.  The air is always in search of equilibrium, and fluctuations of this atmospheric environment causes what is known as turbulence for airplanes navigating through it.

So, why don’t airplanes flap their wings?  To make a long story short, biomechanical structures like birds trump mechanical ones any day of week.  In any case, can you imagine the passenger discomfort if aircraft dynamics resembled bird dynamics?  The up and down motion would force even the most seasoned air travelers to resort to the vomit bags.

Airplanes do mimic the flight of birds when birds stop flapping and simply glide.  However, airplanes are much less aerodynamic, and require constant thrust to maintain velocity.  Among other advantages, birds can dramatically modify the shape of their wings at will.  As “smart” materials advance, airplane wings will be given this ability as a means of saving fuel.  Decades from now, commercial aircrafts will have wings that can bend across their length like falcons.

If President Obama really wants American citizens to be more educated, he might insist that the passengers flying in planes learn how they work.  A physics manual outlining the basics of aviation would allow the average flyer to appreciate the complexities of airplane design.  Passengers might even complain less about turbulence if they realized that it is an act of science and not an act of God. 

The physics manual could sit in the back flap of the seats next to the mandatory safety tip illustrations (of impossibly calm passengers sliding out the plane) and magazines selling only the most ludicrous items (what is it about high altitudes that make a $500 robotic dog toy seem like a good purchase?).

I hope that the next time you are in an airplane you will appreciate the lift force that keeps you in the air.  Maybe you can educate the passenger sitting next to you.  Together, we can begin to appreciate the tools we use as well as the concepts behind them. 

There was a time when the secrets of aviation were just for the birds.  Today, these secrets are common knowledge for aeronautical engineers, who build more and more efficient airplanes every year.  A basic understanding of aviation will never be a prerequisite for being a passenger.  However, if people would get their heads out of the clouds, they would find that the fundamental principles governing aviation are simple and accessible.

In the sixties, a band called “The Zombies” sang: “It’s the time of the season for loving.”  Now that December has rolled around, it’s the time of the season for freezing if you live north of the equator, and reasonably far from it.  Those of us who actually experience four distinct seasons usually agree that it is good for the soul to see our environment change.  Still, as we dump cat litter under our snow tires before giving the car yet another push, many of us would like to skip over winter.  We curse its arrival every year, and even vacation far from it when the opportunity presents itself.

Winter is very particular.  You can examine a picture of downtown Montreal in mid-February, and know with absolute certainty that you are looking at the winter season.  Snow is the symbol of winter, and after a quarter of a metre of the stuff got dumped on my walkway and driveway last week, I set out at 6:30 am to displace it.

The first thing I observe every winter as I dig my shovel into the fresh snow is how quiet it is.  I live less than one kilometre from a highway, and yet I hear no car engines as I stand outside.  The reason for this is that the ground surface is covered in snow, which absorbs more sound than pavement otherwise would.  I really like the quiet.  After five minutes of intense work, if I listen carefully, I can actually hear my heart beating.  The next thing I remark is that the air is so fresh.  Again, it is the snow that has covered the surface, normally teaming with dust particles.

Later, as the sun rises, the intensity of light striking my eye is nearly blinding.  I am not staring at the sun, but bright light is attacking my eyes from all directions.  While the snow absorbs the sound, it actually reflects the light.  The colour white actually contains the entire colour spectrum; it is a linear combination of the three primary colours, red, blue, and yellow.  The black pavement represents an absence of colour.  It absorbs the photon energy from the sun and heats up, but does not reflect much. 

The snow, with its white colour, has no need for the wavelength of the Sun’s light and so it reflects it.  One can spend a long morning skiing on a clear day without sunglasses on to appreciate just how reflective a surface the snow is.  If you were to then enter a chalet for lunch, you would think someone forgot to turn the lights on, as it would seem so dark by comparison, and the human eye takes some time to adjust.

Oh, and did I mention it gets cold?  It gets very cold, particularly at night, when the Sun’s radiation does not reach us.  The temperature of the air can be as low as -30 degrees Celsius, and even colder if you are somewhere that is essentially uninhabitable like Winnipeg.  But even minus 30 C is beginning to approach absolute zero temperature, the minimum allowable value for matter to exist.  Absolute zero corresponds to 0 degrees Kelvin (-273.15 degrees Celsius).  I suppose it could be worse than Montreal.  The temperature of satellite components in orbit can be as high as 300 C, and as low as -250 C, depending on whether the Earth is blocking the Sun or not, and the direction that the satellite is facing.  The surface of the Earth avoids these giant temperature fluctuations thanks to the atmosphere, which acts as a spongy, protective barrier.

We must note however that the -30 C mentioned above may not include wind chill.  What is the wind chill factor anyway?  In the absence of wind, the warm skin exposed to the cold air loses its heat due to conduction, the most basic method of heat transfer.  Conduction is what happens when your warm bare feet cool as they step along the colder kitchen floor.  If the air is moving with respect to your exposed skin (i.e., wind), then conduction’s evil cousin, convection, will take effect.  Depending on the wind speed, -30 C can quickly feel like -45 C.  The precise decrease in apparent temperature depends on the surface area of exposed skin, but this can be approximated.  Safety tip: mittens will prevent frostbite for a longer period of time than gloves, since gloves force each poor finger to fend for itself.

While we are on the subject of freezing, have you ever noticed that the sunniest days are also the coldest?  This occurs because, in the absence of clouds, the snowy surface reflects the Sun’s radiation back to where it came from; we don’t keep as much of the heat.  The beautiful blue sky is then a tease as you stare outside your window in the morning.  Only your furnace, which is currently in overdrive, is aware of the cold recurring smacks in the face that await you as you head to your car on this morning, cursing that your garage is full of junk and that your automatic starter battery died last winter.

Speaking of driving, the winter roads require their own specific survival guide.  If you can manage to see through your windshield, which is affected by changes in temperature and humidity, and once you regain feeling in your fingers, then the real challenge of winter driving begins.  In the best of cases, where one can see and be seen (Clean the snow off of your car ... Yes, all of it!), all drivers must contend with surface irregularities.  During the course of a one hour drive, the road conditions can change a fair bit.

Traction in a car is directly related to the friction coefficient between the car’s tires and the surface itself.  A lot of friction is a good thing in a car, as it allows you to speed up or slow down much faster.  When the friction coefficient reduces to near zero (as it does when driving over black ice), one’s speed and direction is left mostly in the hands of God.  The force of friction is dependent on the contact force between the surface and the friction coefficient, or abrasiveness of contact.  We can maximize the coefficient by installing winter tires, but it will only take us so far; reducing speed is a necessity for safe driving in winter on icy or snowy days. 

The contact force between road and tire should be maximized for the wheels responsible for breaking and accelerating.  The engine is directly above the front tires, making for a high contact force for front-wheel-drive cars.  Though not good for gas consumption, rear-wheel-drive cars should have about 50 kg of bags of dry cement placed in the trunk above each rear wheel to increase traction during the winter.

With all of the above precautions taken, applying the break can still cause the entire car to rotate, which should surprise anyone new to driving.  Why does this occur?  If the friction coefficient is high on one side of the car, where the surface is pavement, but low on the other, where the surface is snow, then the force on one of the braking tires is greater.  The difference in applied forces about the center of mass of the vehicle and its passengers causes a moment or torque in it, which then causes a corresponding angular acceleration.  In lay terms, if your left wheel has better traction than the right, your car will spin about this tire (it will involuntarily turn counter-clockwise).  If, in the same scenario, you tried to accelerate, a clockwise rotation would occur.  Driving a four-wheel drive vehicle can ease winter driving, though not fully eliminate the "car = bull riding" phenomenon.

Considering the additional challenges that winter imposes on drivers, it is not surprising that half of all car accidents in Montreal occur during the three winter months of December, January, and February.  I would not be surprised if these stats extended to other snow-covered cities.  The stat implies that the frequency of car accidents increases by a factor of three during winter.  To keep our safety constant, we should all drive three times more carefully in the winter.  So, put down the cell phone, stop texting, and eat your sandwich later.

Why don’t we all just move away?  It seems that some retirees smarten up and move to Florida, where snow is a figment of one’s imagination.  The joke may be on the Floridians, as their climate will become too hot during certain months by the year 2050 if global warming trends continue.  By that time, snowbirds that fly south will be replaced by sweathogs that stampede north.  Who knows, Montreal’s climate may become agreeable year round.  Consider this carefully before putting your northern property up for sale.

Hopefully these tips and insights into winter have been helpful for you.  I will end this commentary with a look at why we have seasons at all.  For this, as with most big, important questions concerning the Earth, the answer lies with our immediate master: the Sun.  If the axis of Earth’s rotation were exactly perpendicular to the plane of our orbit around the Sun, we would have no seasons.  January and July would be indiscernible for any given location on Earth.  Thankfully, Earth’s axis of rotation is inclined by about 23.45 degrees; this is its angle of inclination.  This angle changes ever so slightly over time, but the effects of this minor wobble on our seasonal oscillations are negligible.

Why is the Montreal winter so different from the Vancouver winter?  After all, the two cities are roughly the same distance from the equator.  The main reason for this is due to their proximity to two very different large bodies of water.  Large bodies of water distribute heat around our planet, functioning like massive conveyer belts.  An oceanographer or atmospheric scientist could offer a more detailed description on these dynamics than I.  As much as I would like to research this topic right now, I cannot, because I need to start scraping the sheet of ice covering my car if I plan on arriving to work on time.

There are not that many parallels one can draw between Keith Richards and Stephen Hawking.  They are both British, they are both in their sixties, and, uh, they are both from England.  One is a theoretical physicist, and the other uses his body as an ongoing experiment, in a cause and effect sort of way.  Keith Richards is a legendary rhythm guitar player, while Stephen Hawking is today’s leading Physicist, in terms of accomplishment and reputation.  Though you could not find two more different specimens, I would argue that both are rock stars.

Stephen Hawking is not a rock star in the traditional sense.  Sometimes, this term is used to describe someone at the top of his field, and Professor Hawking most certainly is.  What is more, the story of his life is intriguing, and he is world famous.  He has suffered from a neuro-muscular dystrophy known as amyotrophic lateral sclerosis since his early twenties.  He has spent the majority of his life confined to a wheelchair, and much of it without the ability to speak.  Despite the inevitable physical difficulties associated with his disease, Hawking used his mental prowess to have a profound effect on the world.  He is no James Brown, but he is, without a doubt, the Godfather of Black hole. 

What is perhaps more impressive than his long list of scientific distinctions, is his unique foray into pop culture.  He is openly proud of himself for having sold more books than Madonna; Hawking has sold more books than just about anyone not named J. K. Rowling.  Through what scheme has this theoretical Physicist managed to reach such a vast audience?  It turns out, there’s no scheme.  He simply takes what might be the most important and fascinating subject known to man, science, and makes it accessible to all who are interested.

There is only one Physicist that is on par with Hawking in terms of twentieth century fame, and that is Albert Einstein.  Indeed, these two Physics legends put their stamp on the science world with so much ink that it spilled into a much wider audience.  Even those who cringe at the subject of science can easily imagine Einstein’s wild white mane of hair, and are actually familiar with the equation: E = mc².  Such folks are also likely to have heard of black holes, and are aware that the physicist who wrote the book on them communicates with a robotic monotone.   Einstein was the leading Physicist for the beginning of the twentieth century and Hawking carried that torch through to its conclusion.  What the two share, among other things, is a less than exceptional academic record; an encouraging fact for students who are struggling.

Stephen Hawking has interesting views on aliens: he suggests that we should avoid them at all costs.  Should they arrive here, they will likely be technologically superior to us.  It would be like when Columbus landed in America; an event that did not end well for the Native Americans.

Much more controversial are Hawking’s views on Religion.  He has stated that the laws of science may have been written by God, but that God never intervenes to break these laws.  Most recently, in his book, “The Grand Design,” Hawking states that God did not create the Universe.  A scientific law such as gravity shows that a Universe can grow from nothing.  Then, to leave no doubt as to what his viewpoint is, he said the following in an ABC newscast in 2010: “There is a fundamental difference between religion, which is based on authority, and science, which is based on observation and reason. Science will win because it works.”  Even when bands crank their amps to eleven, they do not cause the Earth to shake as much a statement such as this.

Professor Hawking is an inspiring man.  My students may find it hard to relate to, say, Isaac Newton, who did crucial work in the seventeenth century.  Hawking, who against all odds is still ticking today, has popularized Physics for this generation of students.  He is without question, a rock star physicist – just don’t ask him to carry a tune.

The vibrations that the Beach Boys were singing about were probably the kind felt emotionally for something or someone else.  Vibrations, however, exist in many forms.  Engineers are often concerned with the mechanical kind, which manifest in all kinds of structures, such as bridges and tall buildings.  These vibrations are caused by an external excitation, such as an earthquake or high winds.  Musicians are interested in transmitting sound waves, and causing vibrations in their listeners’ ear drums.  In the most general sense, a vibration can be thought of as something that moves back and forth repetitively, such as a buoy bopping up and down in a lake, a stock price during the course of a week, or a person’s mood during the course of a day.

Vibrations occur around a specific ‘average value’.  In science, this value is known as equilibrium.  If left untouched, all mechanical items find and stay in their equilibrium positions.  If a spectator at a Tennis match is twisting his head back and forth to follow the ball, his equilibrium position occurs when he is looking straight ahead.   The vibration from side to side can be thought of as the search for equilibrium. 

It is interesting that this search exists for living and non-living things alike.  When a guitar string is pulled on and then let go, it then vibrates back and forth hundreds of times per second (its frequency) until the vibration subsides, and the string returns to equilibrium.  A person can also be stretched out of his or her comfort zone.  When some external stress is applied to someone, the natural tendency for this person is to seek out the balance that existed before the stress occurred.  This search for balance is what most people struggle with throughout life – some succeed, others do not.  And the funny thing about succeeding in this balancing act we call life is that it is so fleeting; there is always a new challenge around the corner threatening our personal equilibrium.

If you hit a bump when driving along in your car, the car’s chassis will bounce due to this external excitation.  The job of the car’s shocks is to cause this bounce, or vibration, to dissipate, or dampen.  Nearly all vibrating systems have some kind of damping associated with them.  The more damped that a system is, the quicker the system will return to equilibrium.  I would argue that people too have a damping coefficient associated with them.  Some people bounce back quickly from an insult and resume their day, while others brood over it for a long time.

Another property that vibrating systems have is a specific natural frequency.  This value defines the rate of vibration.  The natural frequency of a simple pendulum is governed by its length and the surface gravity of the Earth, whereas that of a block of wood is governed by the wood’s elastic Modulus (material property), geometry, and how it is constrained.  If a system is purposely vibrated at its natural frequency, a special phenomenon known as resonance occurs.  Resonance can be devastating to a structure, as it causes the amplitude of its vibration to grow a great deal (the extent to which the amplitude increases depends on how damped the system is).  If a metallic structure is excited at its natural frequency, the input vibration can be amplified up to one hundred times, so that a slight input vibration can quickly output a disaster (YouTube the famous collapsing Tacoma Narrows Bridge for an illustration). 

Returning to our people analogy, I believe that they too have a natural frequency.  When a person is stimulated in just the wrong way, we often call it ‘pushing their buttons’.  This specific code that ticks off a person can be thought of as their natural frequency.  It is unwise to stimulate someone’s natural frequency... I’ve seen insufficiently damped individuals stuck in traffic – they are on the verge of snapping.    If you wish to see resonance manifest within a person, just attend a sporting event, and watch them lose it on a referee that makes a few wrong calls.

You can only stretch a spring so far and expect it to return to its equilibrium.  An airplane’s wing can only vibrate so many times before it cracks due to fatigue.  People are equally fragile.  We can be taken far out of our comfort zone due to some outside stimulus.  If we are stretched too far from our personal equilibrium, we risk never finding it again.  Sometimes these stimuli are simply bad choices we make that lead to an addiction like drugs or alcohol.  Sometimes we are being stretched by something internally, as in many cases of mental illness.  Such changes can cause our equilibrium position to shift.  In more unfortunate cases, such changes can cause exponentially increasing vibrations in our lives: the very definition of instability.

We must remember that vibrations are a very natural part of life.  Without some kind of stimulation from the outside, life would be boring.  A tree never wishes for a day without wind so that the incessant swaying will stop.  When confronted with a problem, we can accept it, roll with it, and we can return to equilibrium afterwards.  With enough damping in our system (patience), we can even learn to enjoy challenges, and take on more than one at a time.  We are more in control of our destiny than we may think.  A pendulum does not get to choose its natural frequency, but people do.  We can choose whether or not to be bothered by external excitations.  Our response is not predetermined.

When a structure remains static, without any external excitation, its motion (or lack thereof) is sometimes referred to as ‘the trivial solution’.  Such a designation is equally fitting for a person who coasts through life without any challenge at all.

In the Waves Physics course that I teach, the students regularly enter the lab to perform a fairly rudimentary experiment that aims to prove a certain law introduced during a lecture.  Today, for example, the students will be playing with thin, converging lenses, and proving that the image of an object may be real or virtual, depending on whether the object is located inside or outside the focal length of the lens.  This simple Optics experiment involves light, but it surprises my students to learn that man, even today, with all its fancy gadgets, does not know the true nature of light. 

We know a lot more about light than our ancestors did two hundred years ago.  We know that it behaves like an electromagnetic wave, travelling through the void of space at about 300,000 km/s.  Light was Albert Einstein’s lifetime muse, and led to his most important discoveries: special relativity, E = mc², and general relativity.  Einstein was disturbed by quantum physics, and wished to quantify light without it.  Today, physicists are struggling to connect Einstein’s general relativity to the accepted, but incomplete study of quantum physics.  They wish to develop a “Unified Theory,” or, one equation for everything.  In order to do so, they need to find and determine the behaviour of all of the elementary particles that make up the matter in the Universe.

Although the Universe is composed of the elements in the periodic table, these elements are not elementary particles.  An elementary particle, by definition, is not composed of smaller building blocks.  All atoms are composed of protons, neutrons and electrons.  Scientists today believe that electrons are elementary particles, but do not believe that protons or neutrons are.  Today, thirty-eight countries and three thousand scientists are working together, wishing to study the dozens of theoretical elementary particles, like those that may comprise a proton, by means of the most expensive Physics experiment ever developed: The Large Hadron Collider (LHC). 

Built in 2008, one hundred metres below the surface in Geneva, a circular pipe, two inches in diameter, and twenty-seven kilometres long, contains particles that are accelerated by magnets to nearly light speed in opposing directions.  The inevitable collisions of these particles have an inherent high energy density associated with them.  The energy is so great, that mass is created as a result of them.  How much mass is created?  E/c² kilograms are synthesized, as predicted by Einstein.  What does this mass consist of?  It consists of elementary particles, which seem to come from nowhere.  In fact, they do come from nowhere: it is believed that the Universe expands freely over time.  With this in mind, the Big Bang may be viewed as a natural occurrence.  At the LHC site, a one-billion-dollar camera, the ATLAS Detector, takes 3D pictures at a specific location along this pipe where collisions are orchestrated.  The camera is designed to detect elementary particles that are created due to the collisions.  The ATLAS is the size of a six-storey building.  The camera is at the current forefront of engineering technology, but will no doubt come standard with the iphone 6.

By studying these photographs and understanding the particles involved in the collisions, physicists are beginning to extend their understanding of life’s building blocks.  If we learn more about the building blocks, we can learn more about the nature of life during the early stages of the Big Bang, and answer important questions, like what is dark matter composed of?  The world’s most prominent physicist, Stephen Hawking, believes that we may develop a Unified Theory during the twenty-first century.  If this comes to fruition, it will be man’s crowning achievement to that point.  It will be the final answer to “What is the Universe?” and “How does the Universe behave?”  The unified theory may become common knowledge to the public, taught in High Schools across the Planet.  Then, the public can, with a more solid foundation to stand upon, ask the most compelling question of all, “Why?”

Before getting ahead of ourselves, we must examine the current state of the LHC experiments.  Nine days into operation, the LHC had to be shut down for maintenance.  Some magnets were repaired and others were replaced.  Today, the experiment is operating smoothly at 50% of its maximum designed capability.  To date, the greatest detected collisions have generated 7 TeV (seven million million electron-volts).  Many collisions have been photographed, and many elementary particles have been observed, though in an incomplete sense.  That is to say that while such particles have left an “energy trail,” they have not been observed in an up close static sense.  Thus far, the experiment results have agreed with current theories in quantum mechanics.  In about two years, the LHC will be run at its maximum capacity.  Higher energy collisions will likely allow physicists to observe never-before-seen particles.  If you are a physicist involved in research today, the LHC site is the place to be.

In addition to being a very expensive project (ten billion dollars to construct, and a massive monthly electric bill to operate), the LHC is one of the most ambitious and intriguing projects currently ongoing.  By comparison, the lens lab that I am helping my students conduct today feels more than a little dull.  Still, these budding science students need to start somewhere.  The physicists of tomorrow will be working with the Large Hadron Collider and other groundbreaking experiments.

It is interesting that our most important discoveries may come from smashing stuff together.  It is quite a leap from our ancestors smashing two rocks together and observing the sound. It is also rather telling that the LHC, our coolest project ever, is buried one football field length below the surface.  It is akin to a squirrel burying its most treasured nut.  The choice to bury it was made out of feasibility, as a 27 km track above the surface near any civilization would interfere with roadways and be unnecessarily exposed to the outdoor elements.  Still, its location has a certain irony.  It appears that the maker of our Universe has hidden its most compelling secrets very well.  It follows that our search for answers, our attempt to unravel life’s mysteries, should be spearheaded in a remote and hidden location.  Man may yet uncover what truly lies below the surface.