Sunday, December 23, 2012

The Engineer's Pulse 2012 Year in Review

With the year coming to a close, I'd like to thank my growing number of readers for joining me here during this, the second full year of operation of this blog. 

Longtime readers may have noticed the gradual increase in what can be described as educational content.  Indeed, my favourite aspect of the blog is how the "For Physics Students" page is beginning to get filled up with content.  This site, which began as a place for me to put some science and technology ideas into words, has become an educational resource that I can refer my physics students to.

Monday, December 17, 2012

I'm Starting to Like Chemistry... But Only a Bit

Sir Ernest Rutherford's most enduring quote is: "In science there is only physics; all the rest is stamp collecting."  This may appear bizarre given Rutherford's numerous contributions to the field of chemistry, including his discovery of the tiny nucleus that resides within every atom.  The statement, as I understand it, is less of an insult to chemistry, and more of a declaration of physics as the fundamental branch of science.  Physics lay atop the hierarchy, its laws governing all.  This does not mean that chemistry is useless; it merely asserts that molecular behaviour, for example, obeys the laws of physics (if not, the laws of physics are incorrect).

The usefulness of chemistry is that it conglomerates a lot of physics into one step.  For example, the occurrences during a chemical reaction involve work done by the electromagnetic force, but it is not necessary to analyze such forces in order to predict the outcome of such phenomena.  Making use of trends within the periodic table allows the physics to take place behind the scenes, and saves much time.  One can study the periodic table without regard to why the elements exist as they do (quantum mechanics) and how particular atoms come to be (nuclear physics).  Indeed, stamp collecting is a suitable analogy for the discovery of the elements; like anything else, it is exciting if you think it is.

Thursday, December 6, 2012

NASA Aims for Faster than Light Space Travel

Perhaps you have heard that NASA has recently set its sights on building a spacecraft that can traverse space at a rate greater than 300,000 km/s - the speed of light.  The final product may well arrive a century from now, but at first glance, the very prospect of a spacecraft exceeding the speed of light seems to violate special relativity.  One of the first things we learn when studying relativistic physics is that 300,000 km/s is a cosmic speed limit.

Before investigating this apparent violation of physical law, let us examine what a faster than light speed spacecraft really means in the context of current space travel standards.

Friday, November 23, 2012

Math as a Muse (Part II)

In my previous post, I described a math problem that kept my mind busy during a church service a couple of weeks ago.  For a description of the problem, the link is here.  In any case, I will show the image that describes the problem again below...

As people sang their hymns, I began to think of the trigonometry of the situation - of the right angle triangles that are formed.  By the end of that hymn, I realized that actually, the line of sight to the nth column (pew) forms two right angle triangles which were geometrically similar (same internal angles).  As a result, the ratio of the two triangles' opposite and adjacent sides was the same.

Thursday, November 15, 2012

Math as a Muse (Part I)

I have had an affinity for math for as long as I can remember.  Even in elementary school, when working with numbers or shapes, it always seemed like magic to me.  Now, as an adult, I find this magic hiding in unexpected places, like the relationships between notes in music, and in the geometry of architecture.  It was the latter that called out to me last week.

I was standing in a place of worship.  Admittedly, I do not spend a great deal of time in such places.  On this particular occasion, in a church, my mind was wandering, and I began examining all of the geometry around me: the slopes in the roof, the shapes of the stained glass, and the angle in which the sunlight came through them.  When my gaze returned forward, I began to carefully examine all of the equally spaced columns (known as pews) between me and the front of the church, where the Reverend stood.  Almost immediately, a fun math problem presented itself to me, and I spent the next twenty minutes analyzing it in my mind.

As shown in the figure below, I can see less and less of each column the further they are from me, as each column is obstructed by the one that precedes it.  But, what governs how much of a given column I can see?  I called the column directly in front of me n = 0, and then came 1, 2, and so on.  My aim was to find a function that described the height of each column that I could see for each column, h(n).  I decided that it depended on three other parameters: the column spacing (s), as well as the vertical and horizontal distance from my eyes to the zeroth column immediately in front of me (H and L).

Searching for visible height h as function of pew number n (mad paint skills, I know...)

Wednesday, November 7, 2012

Richard Feynman Comes Alive in Unorthodox Autobiography

I finished reading Richard Feynman's "Surely You're Joking, Mr. Feynman!" last week, and still find myself laughing about it today.  What could have been a conventional autobiography of the Nobel Prize winner for physics is instead a collection of quirky stories, through which one really gets to know the man.  To give you a sense of the tone of the book, Feynman mentions the Nobel Prize he won about halfway through it, as a sort of after-thought - the focus is rather on what he is truly proud of, like, for example, his ability to break into safes that contained top-secret information about the Manhattan project during the second World War.

Friday, November 2, 2012

"Slow Mo Guys" = Great Teaching Tool

"Sir, you're going too fast!" - it is a complaint I hear in my physics classes every so often.  Whether it is the case or not, it is true that there is an ideal speed for progressing through science content in a classroom setting.

Similarly, there is an ideal speed for the viewing of the countless science phenomena that occur in nature.  Often times, events like chemical reactions or travelling waves elapse over too short a time interval to be properly grasped.  This is actually the reason why many scientific phenomena that are now well understood went misunderstood for so long (and why others still go misunderstood).

Take something simple, like an apple falling from a tree.  Five centuries ago, people believed that the fall was at a constant speed, which was governed by the apple's mass (heavy apples would fall faster than light ones).  Of course, this assessment is wrong on many levels, but one can easily appreciate why such a faulty conclusion could be arrived at.  The entire fall of an apple might take one second, which is an insufficient amount of time for a person to gauge an event.

Had mankind invented the video camera a few centuries earlier than it did, enabling it to see the world in slow motion, early science would have evolved more rapidly than it did.  The apple could then be seen to displace more and more with each passing frame, invalidating the constant speed theory.

Some people today may not see how valuable adjusting the frame rate of an event is outside sports and action movies.  Fortunately, a few young people certainly do, and they are responsible for my current favourite YouTube channel: "Slow Mo Guys".

Thursday, October 25, 2012

Life is Like a Non-conservative Force

"Mama always said, life was like a box of chocolates..."  Had Mama been a physicist, she may have instead used non-conservative forces as an analogy to depict life's winding roads.  Let us first explore the meaning of a non-conservative force, and then attempt to draw parallels between it and life.

In physics, it is important to understand the distinction between conservative and non-conservative forces.  For one thing, it comes in handy when trying to solve problems using a work/energy approach, which countless mechanics students are no doubt busily doing as I write.

The conservation of energy principle is merely a statement of the first law of thermodynamics, which, for mechanics, translates to: "The change in the total mechanical energy of a system between states 1 and 2 is equal to the total work done on the system by non-conservative forces between states 1 and 2."  The term 'state' refers to a particular position and velocity of the system's components (time does elapse in between states, but the particular amount is not significant for the analysis).

In equation form, these words look like this:

Monday, October 15, 2012

Mechanical Analysis of Baumgartner's Dive (Part II)

(This is the second and final article of the Felix Baumgartner dive saga - click here for part 1)

By now you have no doubt heard that Felix Baumgartner has shattered several records with his successful sky dive on October 14, 2012.  Fearless Felix stepped off of his perch, fell freely for 4 min 18 sec, and then pulled his parachute, coasting safely to the surface about five minutes later.

The lead up to the historic event was similar to that of a rocket launch, complete with weather delays.  This jump was originally set for October 8, but on several occasions, it got bumped.  You know you are involved in something risky when a little too much wind is cause for serious worry.

Imagine you are Felix, and you wake up on October 8, having probably not slept much the night before, ready for the leap of your life.  You down a few red bulls, get your adrenalin up, and then some guy in a lab coat gives you the news that the jump must be postponed.  Repeat this a few more times, and you just might go mad.  I do not know this for certain, but I would imagine that a psychologist was on site with Baumgartner to help him maintain his mental well-being through this go/no-go roller coaster that lasted more than a week.

Many videos of the dive have circulated on YouTube, though most have been yanked by the sponsor (Red Bull).  Here is their 90 second summary of the event.

One can only imagine what it must have been like to look down from 128,000 ft (8,000 ft more than originally planned), and to behold the planet.  From that altitude, one can begin to get a sense of the Earth's curvature.  With a final salute (to his family, and mankind I suppose), Baumgartner stepped off from his pod and quickly vanished from view.

Based on some of the information given in the video, as well as some educated guesses, I have constructed approximate graphs of Baumgartner's speed and altitude as a function of time for the free-fall portion of his descent.

(Note that it is possible to generate theoretical results by solving the governing equation numerically, but as I do not have access to the particular parameters associated with his specially designed space suit, such as mass and drag coefficient, I elected to plot these 'experimentally')

Thursday, October 4, 2012

Mechanical Analysis of Baumgartner's Dive (Part I)

120,000 feet... 

For a normal person, it represents the distance travelled during a fairly long commute to work.  For Felix Baumgartner, the Austrian daredevil, it represents the altitude from which he plans on free-falling towards the Earth this coming Monday, October 8, 2012.

For someone like myself, any height is too high to jump from with nothing but a parachute to save me from death.  However, even sky divers, who are themselves barely sane, see Baumgartner's jump as nothing short of lunacy.

You see, 120,000 feet is 36,576 m - that's more than 36 kilometers!  To put this into perspective, his descent will begin at an altitude that is three times that at which typical commercial airplanes fly.  It is above the troposphere, in the middle of the stratosphere.  So, "How will he get there?" you ask.  Why, he will wait inside a man-sized pod that is lifted by a large balloon, of course.  When the balloon reaches the correct altitude, the pod will open, and down he will fall.

There are literally countless risks associated with this particular sky dive that aims to crush the previous altitude record of 102,000 feet. 

To begin with, the air way up there is extremely cold.  Should Baumgartner's special suit fail even a little, the convection associated with the high speed sub-zero air flowing by him will freeze him almost instantly.

Not only is it much colder up there, but the air pressure is just 1% of that on the surface.  For this reason, the daredevil will have an oxygen tank strapped to him.  And, with this pressure change, comes a change to the most important environmental factor when it comes to aerodynamics: fluid density.

The density of air on the surface of the Earth is about 1.2 kg/m3.  In the middle of the stratosphere, it is more like 0.01 kg/m3.  A quick application of Newton's second law shows that this has a dramatic effect on the terminal velocity of the dive...

Terminal velocity

A sky diver reaches his or her terminal velocity when his or her body ceases to accelerate.  When this inertial term vanishes, we are left with a simple force balance: Drag force = Gravitational force.  The force of gravity can be approximated as mg (even at an altitude of 36 km, using the gravitational acceleration one experiences on the surface of the Earth, 9.8 m/s2, introduces very little error).  The drag force is a bit more complex, and is given by:

Drag force = (1/2)ρCDAv2
In this expression, ρ is the density (kg/m3) of the fluid, CD is the drag coefficient (unitless) of the falling body, which is essentially a measure of how aerodynamic it is (it is greater for objects that are not streamlined), A is the projected surface area (m2) of the body, and v is the relative velocity (m/s) of the body with respect to the fluid.  It is clear that drag is largest when large objects move within dense fluids at high speeds.  This is why we can often ignore drag for, say, a ball that is tossed through the air by a child. 

Substituting these parameters into the force balance and solving for v, we get the terminal velocity equation as follows:

Thursday, September 27, 2012

Ascent Towards a Type I Civilization

As a species that is in the midst of more than a century of massive technological evolution, homo sapiens, with all of their blinking gadgets and other paraphernalia, rarely fancy themselves as primitive.  It comes then as a surprise to most to find out that we have still yet to attain a civilization status of Type I.  That's right!  Take that, fragile collective ego of mankind.  Despite all that you may feel your species has accomplished, you presently belong to a Type Zero civilization, as did your cave-dwelling ancestors.

While we do indeed have access to vastly superior technology than homo sapiens have had in their long history, we do not yet qualify as a Type I.  We are, however, well on our way.

So, what is this civilization classification system, and who established it?

The system measures the technological advancement of a civilization by assessing the amount of space it takes up, and the extent to which it utilizes the energy resources within that space.  It is known as the Kardashev scale, and can be expressed in terms of the order of magnitude of power that a civilization extracts for its personal use.  This very forward-thinking and pragmatic scale was proposed in 1964 by Soviet astronomer Nikolai Kardashev.  A civilization that has attained a certain level of technological development is described as follows:

Wednesday, September 12, 2012

Universal Gravitation (Journey to the Center of the Earth)

Having seen parts of the original film and the previews for what must have been a horrible remake, I can assert with confidence that the physics behind a Journey to the Center of the Earth are of much greater interest than any film that goes by that name (from the preview of the latter, it appears that dinosaurs currently reside somewhere within our planet, where they are safe from all the pesky breathable air up here).

While we usually think of the gravity due to planets when we reside on their surface or orbit around them, it is intriguing to consider the role that gravitation plays inside a large body.

Newton's law of universal gravitation states that all bodies having mass emit a gravitational field and thereby attract all other masses to them.  The magnitude of the attractive force (which, by Newton's third law, acts on both bodies) is governed by the mass of each body, as well as their proximity to one another.  The force is stronger for more massive bodies, and increases as the gap between them reduces.  In equation form, the magnitude of the gravitational force, Fg (in Newtons), that acts on both bodies is given by

Fg = GM1M2/r2    (refer to figure below)

Here, G is known as the universal gravitational constant (6.673 × 10-11 m3/kg s2), M1 and M2 are the masses of each of the bodies (kg), and r is the distance that separates them (m).

Thursday, September 6, 2012

Extremes in Engineering and Politics

As I watch the election season unfold in America, I am constantly stunned at how far to one side each party and their supporters are and seemingly must be.  It is, by and large, Republicans to the right, Democrats to the left, and no middle ground in sight.  When we categorize ourselves as one of these two extremes, we may enjoy the apparent sense of community that comes from it.  After some time, we begin to identify with one extreme.  However, as a whole, such categorization has the net effect of polarizing a nation.

In the twenty-first century, it seems that so many of us are unimpressed by an optimized solution.  There is nothing sexy about a calculated compromise.  On YouTube, it is the biggest this and the fastest that which tend to garner millions of views.  We simply are not interested in anything average.

I think that politicians ought to replace their segragating rhetoric with a middle of the road approach.  But the fault lies not only with them.  The voting population must recognize the value of a moderate approach.  Why do we tend not to award those who are steady and balanced?  Is it related to our fascination with outlandish personalities like those of the Kardashians?

Tuesday, September 4, 2012

Vive le Québec Intolérant

Today, for a change, I write of nothing scientific.  You may find it to be educational nonetheless, particularly if you do not reside in Canada, as it concerns the provincial election of its most diverse and bizarre province: Quebec.  As the majority of my readers reside in the United States, where an election with global impact is on the horizon, I will continue on.

Let's begin with some geography.  Canada has ten provinces and three territories.  Quebec is one of the bigger provinces in terms of both land mass and population, and is located towards the East.  It is rich in terms of water, and, as a result, is one of the only North American states whose energy production is primarily sustainable (hydro power).  The population of Quebec is concentrated along the St. Laurence river, which flows from West to East.  The city of Montreal, the second most populous in all of Canada, is an island along the St. Laurence towards the western side of the province; it happens to be my home.

Monday, August 27, 2012

Neil Armstrong's Legacy

The recent passing of Neil Armstrong at the age of 82 has caused many of us to stop what we are doing and consider man's past and ponder its future.  This is not an obituary for the first man to have ever set foot on the Moon or any surface not called Earth.  This is simply a commentary on the significance of that momentous step in July of 1969.

The lunar landing was, for mankind, the defining moment of the twentieth century.  In a century that contained countless events that we would like to forget, Armstrong's steps onto a distant world will be forever remembered and cherished as a supreme achievement.  If ever one feels cynical about life, or is experiencing a mundane stretch in one's day to day activities, one can simply imagine the realization of the Apollo 11 mission.  It exemplifies man's desire to explore and ability to achieve.

Friday, August 24, 2012

On Free Post-Secondary Education and Lifelong Learning

Much ink has been spilled in recent months - particularly in the province of Quebec - as to whether a post-secondary formal education is a privilege or a right.  After reflecting on this question over the summer, and listening in on several debates on the matter, I have not been swayed from my initial stance: it is a privilege.

A prosperous society should ensure that its citizens have access to a high quality elementary and high school education.  While some students benefit from this environment more than others, all high school graduates leave with a basic body of knowledge.  More importantly, after more than a decade of interacting with roughly fifty different educators, these young men and women, some more than others, have learned how to learn.

Learning is a right in the sense that no one should be prevented from doing so.  But learning is not limited to a school setting.  Educational institutions do not hold a patent on learning.  Someone who is not enrolled in University is still welcome to visit the library, to have discussions with friends and family, and to peruse the internet, which contains an unimaginable wealth of useful information amidst an endless supply of videos of cats eating their own vomit (the user gets to decide what content is more beneficial to them, and judging by hit counts on YouTube, society tends to favour cat puke).

Thursday, August 9, 2012

Curiosity: How NASA Got its Groove Back

If NASA were a prize fighter, few would have been lining up to place bets on it in recent years.  The American space agency suffered a metaphorical TKO in 2011 as its shuttle program came to an end.  From that point onward, in order to send American astronauts to the International Space Station, the US government would need to rent some seats aboard a Russian spacecraft.  This position of dependence that the one time unrivaled space faring nation found itself in seemed to indicate that NASA had lost its mojo.

Well, what a difference a year, and a trip to Mars, can make.  This week, NASA's one ton rover suitably named Curiosity began cruising around Mars following an eight month long voyage through the solar system.  As the first pictures of the red planet reached our blue one, it became clear immediately: NASA was back.

Tuesday, August 7, 2012

What Makes Usain Bolt so Fast?

The quintessential Summer Olympic event has yet again come and gone, and as was the case in Beijing in 2008, Usain Bolt of Jamaica has captured the gold medal in the 100 m dash in convincing style.  True, fellow countryman Yohan Blake has the ability to run with Bolt, and a few others in the field can compete with him on their best day, but for half a decade, Usain Bolt has held the coveted title of 'world's fastest man'.  The question I would like to address is "Why?"

Let us begin with a quick kinematic assessment of the 100 m dash, using Bolt's 2009 World Record setting run in Berlin as an example.  Starting from rest, Bolt ran 100 m in 9.58 seconds - a feat that will likely not be matched for a long while.  Bolt's average speed (distance over time) on this occasion was 10.44 m/s.  He reached his top speed at around the 65 m mark of about 12.27 m/s.  That is 44 km/hr, which carries a hefty fine for a car in a school zone.

Saturday, July 28, 2012

Stephen Harper Hears a Who - but Ignores it

I sat down to watch the movie, "Dr. Seuss' Horton Hears a Who!" with my three-year-old daughter the other day.  The only Seuss books that I recall from my childhood are "Green Eggs n' Ham" and "Hop on Pop", but I was very impressed with this 2008 animated film from top to bottom.  While my daughter was very entertained by the many jungle animals, I gradually became quite focused on the real world symbolism that is not so subtly embedded within it.

Tuesday, July 17, 2012

Happiness Not a Consequence, Merely an Assertion

Science is all about measurements.  Scientists try to determine the model that best fits the data to gain insight into the behaviour of the world around them.  They measure everything, from temperature to charge to chaos.  These measurements are dependent upon a number of things.  In thermodynamics, an engineer may like to measure the temperature of a body as a function of time for a specific set of conditions.  Here, temperature is a dependent variable, and time is an independent variable.

It is appropriate to consider the measured temperature of a body to be a consequence of several factors.  It may seem sensible then to apply this approach to assess our state of mind on a given day.  I aim to show that this is a misguided way to perform a self-assessment.  That is, it is nonsensical to attribute our mental state to a given set of conditions that is present in our lives.  The measured variable that I wish to focus on is happiness.

Happiness... That state of being that we are all encouraged to pursue from a young age.  But, how does one measure it?  How does one know when one has achieved it?  Whatever the answers to these questions, it is certain that the assessment is anything but absolute.  I would even take it one step further.

Saturday, July 7, 2012

Domesticating our Kids

I heard today on the radio about how more and more pet owners are abandoning their pets on moving day.  This is negligent, because domesticated animals are ill-prepared to fend for themselves in the wild.  While such negligence may be punishable under the criminal code, and is, of course, morally wrong, it seems to me that there is a more general issue at play here. 

On some level, there is an inherent disservice in the practice of domesticating animals at all.  By sheltering them and feeding them, we undermine all of the instincts they have developed over the long adaptive road of evolution.  This article will not explore this debate any further, but will use it as a backdrop for a discussion on how we raise our kids.

I am about to become a parent for a second time, so, naturally, the question of what constitutes effective parenting is on my mind.  If one were to summarize the role of a parent in one sentence, it might look like this: "To ensure the safety of your child, while empowering him or her to take on life independently upon reaching adulthood".  Though parenting is anything but a bland activity, it can be viewed through an engineer's lens, as an optimization problem.

If one hovers too close (helicopter parent), one's child will never attain the level of independence that is needed to tackle life on his or her own.  On the other hand, a completely 'laissez-faire' parenting attitude at too young an age can place a child in an unneccessarily risky situation.  Thus, the parent must find the sweet spot, where their child is free to explore the world, but with reasonable boundaries imposed on them.

Saturday, June 16, 2012

Career Advice for New Grads

A few days ago I was describing my old engineering job to one of my physics students.  I summarized the role I played as a structural engineer for an astronautical space company, ensuring that satellites that were launched into space would not break during rocket launch or during the thermal cycling of Low-Earth orbit.  I would optimize the parts for cost and mass, and then know that these multi-million dollar hunks of metal and composite fiber would encircle our planet relaying electromagnetic signals for years to come.

Then came a question that I get asked a lot: "Why did you leave?"

I left a few years ago, and had a difficult time answering this question clearly and accurately at that time.  Now, having practiced my response to "Why did you leave engineering to teach physics?" about a hundred times, I am beginning to better understand it myself.  While major career decisions are seldom one-dimensional, the ultimate reason that I left my 'cool' job tinkering with high-tech space equipment is quite straight forward.

Tuesday, June 5, 2012

Carl Sagan: The Greatest Storyteller of Science

When I mention the name "Carl Sagan" in my physics classes, only a small minority of my students recognize it.  It is a shame, as in my view, he is the greatest author of science non-fiction of all time.  It is also surprising, as he was the leading physics rock star of his time: His masterpiece, The Cosmos, has amassed an audience in the area of five hundred million (it exists as a TV series and an accompanying book).  A leading astrophysicist and genial communicator, Sagan inspired wonder, and helped to attract a generation of scientists to their field.

Sagan has been on my mind over the past month as I made my way through what has become my new favourite non-fiction book: The Demon-Haunted World, Science as a Candle in the Dark.  It happens to be the last book that Sagan wrote.  Published in early 1996, it was his love letter to science and his parting message to us all; he died later that year at the relatively young age of 62 after a long battle with myelodysplasia.

Unlike much of his previous work, The Demon-Haunted World deals less with the behaviour of nature and more with the practice of science.  He details the importance of critical thinking among all members of society and methodically rips apart the practice of mysticism and pseudoscience through detailed analyses of ghost mythology, astrology, witchcraft and, in particular, UFO 'encounters'.

What makes this work so special is the complete treatment that each of these diverse topics receives.  While most readers of science non-fiction are skeptical of alien visitors, they rarely go the extra step, and ask why a non-negligible proportion of people claim to have been abducted by green extraterrestrials.  The conclusions presented in this book enter the realms of psychology and psychiatry, and the discussion follows  fascinating directions that I did not see coming.  For example, I had not considered the fact that most alien abductees claim to have been taken advantage of sexually in a space ship, and most of them also have a history of being sexually abused.

Wednesday, May 30, 2012

Peer Instruction Beats out Lecturing by Factor of Two

In the early 1990s, Harvard physics professor, Eric Mazur, was teaching advanced physics courses to bright students. He gave exciting lectures, complete with compelling, thought-provoking demonstrations.  He was praised by students for his clarity in delivering the material.  Then, something unusual happened.

Mazur set out to gauge the effectiveness of his teaching scientifically.  He employed a standardized test known as the Force Concept Inventory (FCI) to assess his students' conceptual understanding of mechanics, before and after teaching his courses.  The results surprised him.

He was not surprised that most students entering his class came in with a relatively weak understanding of mechanics.  He was, however, astounded that after having taken his mechanics course, his students performed only marginally better on the FCI.  Mazur was dumbfounded.  In the years that followed, he set out to determine, scientifically, what constitutes effective pedagogy for science education.

Traditional lectures, where a teacher communicates information to students who dutifully take note of the content, are fairly useless.  At its best, such an approach can be entertaining, but not cognitively stimulating for students.  In fact, cognitive function in students while attending a lecture (even a good one) has been shown to be lower than while sleeping.  In this context, who can fault a student for sleeping through a lecture?

Tuesday, May 22, 2012

Mechanics in an Elevator

Though the title of this article is less catchy than the Aerosmith classic rock tune that it alludes to, an elevator is, nonetheless, an excellent place to solidify one's understanding of mechanics.

I rode up an elevator from the ground level to the eighth floor of a condo building long ago with my daughter, who was three at the time, to visit her great-grandmother.  As we approached our destination, and the elevator began to slow down, my daughter asked, "Daddy, are we going down?"

"Amazing," I thought, "kids can sense acceleration, and have already developed the same false preconceptions about it that they bring to their introductory mechanics courses."

It makes sense that people, and all animals for that matter, can sense acceleration, as we live in a dynamic world, and acceleration, which is the rate of change of velocity, may be thought of as the forecaster for motion.  If one can detect one's own acceleration, then one can accurately predict one's future position (provided one knows one's own current position and velocity with accuracy).

Thursday, May 10, 2012

Hybrid Cars Finally Worth Considering

Until recently, I harbored mixed feelings about hybrid cars.  On the one hand, they decreased fuel consumption significantly, while on the other, they were very expensive, and entailed more parts than a standard combustion engine car, which translates to more maintenance costs down the road.  I would never have recommended that anyone buy one.  At best, an environmentally conscious consumer could undertake a lease, pay a bit more in total costs, but feel they'd done a small service for the atmosphere.

In 2012, it seems to me that hybrids have rounded the bend, and crossed a very significant threshold.  In some cases, it appears that the purchase of a hybrid is, in addition to environmentally considerate, cost beneficial.

A new technology like hybrids had a lot going against it in the early going.  Purchase prices were high since production quantities were low and R&D costs were significant.  Also, new technologies are less reliable than tried and true ones; they have not been through the iterations that come through multiple generations of development.

Wednesday, May 2, 2012

Life is Just One Big Experiment

This coming Friday, a friend and I will be performing music at a bar (pop, rock, reggae).  It will be our first show together.  Our band is shamelessly called, "The Acoustic Love Explosion."  We have been practicing together for a few months.

I will be playing the drums, he the guitar, and we will both be singing.  I have never witnessed a performance having this musical arrangement before, and am curious to see how the audience will react to it.  In particular, I wonder if the lack of a bass guitar will be noticable, and whether the sound will feel empty.  This first show really feels like an experiment - one that, if successful, will spawn similar ones in the future.

Sometimes, life, from the moment we are born until the moment we die, feels like a giant series of experiments.  Some might prefer to substitute the word "experiments" with "experiences", but really, the difference is quite subtle.  An experiment is possibly even more accurate, as it implies that some lesson will be learned, and retained in our memory.

Thursday, April 26, 2012

Airplanes That Seem to Hover

Last year I posted an article about the fundamental principles behind how a subsonic aircraft works.  In summary, an airplane takes off once a critical speed is reached: the greater the speed of the wings relative to the air being cut by them, the greater the pressure difference between the air on the top and bottom of the wings, and the greater the lift force.

Now, I would like to address a particular concern about airplanes that some of my students have had.  Have you ever looked up at an airplane, and had the impression that it was barely moving?

Helicopters, hot air balloons, and some supersonic aircrafts possess the ability to hover, but subsonic aircrafts do not.  As already mentioned, the only reason that a commercial plane can maintain a given altitude is because it is moving horizontally with respect to the air around it.

So, what is going on here?  I too have looked up at aircrafts as they descend and have remarked, on occasion, that the plane seems to be moving at a snail's pace.  Sometimes an airplane flies above me as I cruise along the highway, and my impression is that I am in fact moving faster than it relative to the ground.  Is it an optical illusion?  Let us investigate.

Friday, April 13, 2012

The Wondrous Night Sky

When my daughter recites twinkle, twinkle, little star, I am tempted to answer her question regarding what they are: "Giant collections of particles moving in all directions colliding into one another at high speeds forming larger particles in fusion reactions that give off heat and light..."  And then I remember that she turns three this summer.

I got to thinking about stars when a couple of callers rang me up the other day on my call-in show.  OK, I don't have a call-in show.  It was just a couple of friends calling me at home with questions about stars.  They were either genuinely curious about these glowing masses or were poking fun at my passion for all things science.  I am going to assume it was genuine curiosity, and answer their questions below.

Monday, April 2, 2012

Pushing the Boundaries of Science Like Pushing a Vacuum

As far as division of labour around the house goes, my wife and I each have our own respective duties, and one of mine is vacuuming the house.  I kind of enjoy mindless activities like this one, because it allows me to shut off my brain for the better part of thirty minutes.  But with the mind unfocused, it is at once free to wander; I find that I do some of my deepest thinking while under the hypnotic trance of the vacuum's purr.

Once, while seeking out lose dirt and dust-bunnies with my trusty dust-sucker, my mind began to wander even further than normal.  I began to see clear parallels between my search for dust around the house and humanity's pursuit of science in general.  Before I go any further, let me assure you that I realize that only one of these two endeavours is of great importance, and it is not the one that involves me pulling out the couch, cleaning behind it, and pushing it back.

Dust around the house tends to accumulate in the places we encounter the least.  Sections of the home in plain sight are relatively free of such particles, as these areas are well-travelled.  The dust gets displaced to a new spot due to the relative motion of air around it.  If this new spot also sees regular activity, the dust will inevitably move yet again.  It will only settle permanently in a quiet, unused spot within the room (usually behind something heavy, to the vacuumer's chagrin).  The phenomenon is much like snow on a high-traffic ski slope, which tends to build up on the two outer edges.

How then is vacuuming like scientific advancement?  Imagine that each piece of dust to be collected is like a scientific mystery to be solved.  Much like the loose dirt that we wish to suck up, the vast majority of the mysteries associated with the physical world are well-hidden - that is, unless we search for them explicitly, we will not even know that they exist.

Each room within the house may be thought of as a scientific pillar, each with its own particular sort of unsolved mysteries waiting to be uncovered.  We could have physics in the family room, chemistry in the kitchen, biology in the bathroom, and so on.

In the early going of modern science, the house was a complete mess throughout.  As almost no one was taking part in scientific research, dirt was evenly distributed.  When Isaac Newton decided to begin to clean the house, he began with what he interacted with most on a daily basis - that which was the most visible.  In the late seventeenth century, he uncovered the basic principles of mechanics (the motion of bodies) and geometric optics (the behaviour of visible light).

As the study of physics moved along, research in other fields of science began.  Before long, each room in the house was being cleaned in parallel.  The science research landscape was a busy one indeed during the twentieth century. 

As the dust settles, and the twenty-first century soldiers on, we may look at the house and conclude that it is clean.  Scientific principles may be invoked to explain just about everything we typically interact with.  That which was most obvious, that which presented itself, has been sucked up by the scientific research community.  All that remains to be discovered in the present science landscape is that which is not in plain sight.

Sunday, March 25, 2012

Ender's Game, The Movie

You know that uncomfortable feeling that you get upon learning that your absolute favourite novel will be spun into a Hollywood film?  I am currently dealing with such a feeling in regard to my favourite sci-fi novel, Ender's Game, which will hit the big screens in the spring of 2013.  On the one hand, I am excited to experience this wonderful story through a new medium, but on the other, I fear that the movie will not live up to the book. 

It is strange for one to have such strong feelings for a story that one takes offense to a lacklustre portrayal of it.  After all, I am not Orson Scott Card, the author of the Ender's Game series of novels, of which Ender's Game was the original publication.  But, that is what is special about a novel: the reader has the freedom to make the story their own, and in so doing, develops a much more intimate relationship with it than can be established through film.

I first read Ender's Game (I have read it twice since) in 1999, as part of a college English class.  The 1985 novel may be summarized as follows: Star Wars meets Harry Potter without the hocus pocus.  The story examines two advanced species, mankind and formics (commonly referred to as "buggers"), for whom this neighbourhood of the universe is not big enough.  The story unfolds almost entirely on a military base in space, where young boys and girls are trained in space war.  Harry Potter fans will draw comparisons between this training facility, known as Battle School, and Hogwarts, but to be fair, J. K. Rowling's fictional world was created after Card's.

Monday, March 19, 2012

The Art of Presenting

As part of my physics courses, my students are usually required to perform a powerpoint presentation about a course-related topic that they find interesting.  As harmless as it sounds, the very idea of speaking in public induces fear in many of my students.  While I do sympathize with them, these presentations remain a part of my courses because (1) oral communication is an important skill, and (2) I feel that if you cannot communicate what you have learned, you have not learned it.

Jerry Seinfeld once observed that the number one fear of most people is public speaking, while number two is death.  He went on to muse that, at a funeral, the majority of people would rather be inside the casket than giving the eulogy. 

What is it about giving a presentation that is so scary?

Friday, March 2, 2012

Engineering Firms Can be a Drag

I had the great privilege of taking in a 45 minute long keynote speech by Canadian astronaut, Dr. Robert Thirsk, at a teacher's workshop last month.  The speech was about inspiring students to pursue the sciences, and also included an inside look at the incredible career that Dr. Thirsk has enjoyed.  To be clear, the overall message was not "Inspire young students in science and math and they will all become astronauts."  While the presentation did include awe-inspiring visuals of Dr. Thirsk floating in low Earth orbit, the take home message was grounded in reality: science is interesting and can lead to a wide spectrum of promising careers.

But, let's be honest.  No engineering career stacks up against what Dr. Thirsk and his handful of colleagues do. Not more than two years ago, the man at the microphone took part in forty unique science experiments over a six month period aboard the International Space Station.  He ate space food and exercised on specialized zero-g cardiovascular machines for two hours per day (to minimize bone density loss).  For every engineer that can boast about a work experience as rich as this, there are literally thousands who spend their days deciding whether to use three bolts or four bolts to connect parts at interfacing flanges.

What, in the first place, draws engineers to pursue a career in engineering?  Usually, possessing strong math skills and having a comfortable understanding of physics can sway a young student towards the direction of engineering.  However, the desire to work on ground-breaking projects - the first lunar mission, the first nuclear reactor - this is what budding engineers envision for themselves.  Engineers want to have a hand in shaping the technological landscape of the future.  The sad reality is that only so many hands have the opportunity to take part in such shaping.

Sunday, February 26, 2012

You Cannot Eat Money

When all the trees have been cut down,
when all the animals have been hunted,
when all the waters are polluted,
 when all the air is unsafe to breathe,
 only then will you discover you cannot eat money.

- Cree Prophecy

The economy is based on an imaginary entity; it is a currency called money.  While it makes sense to have a currency whereby goods and services can be easily exchanged, this modern method of trade allows us to forget that money, in and of itself, is worthless.  The quotation above illustrates this notion with absolute clarity.

Modern society is so far removed from a time when one's needs to survive and prosper were met through direct action (the collection of one's own food and shelter).  To be clear, I have no desire to turn back the technological clock to a time when societies did not enjoy the benefits of divided labour.  But it is helpful to consider the hunter gatherer way of life, if only to allow us to correctly identify what matters.

Going on a camping trip is a great way to briefly escape the economic landscape, and to accurately reflect on what we truly value.  I actually tried ice fishing for the first time this past weekend, and in my group of four, we caught three small fish collectively over the course of many hours.  Without modern agriculture, and environmental conditions in which it can thrive, we would all be screwed.

Saturday, February 18, 2012

Vanier College Robotics Club Gives me Hope

I tend to keep the college at which I teach and this blog on which I write as separate entities, as there is no actual affiliation between the two.  But I am a mentor for the Vanier Robotics Club "Build Team", and today, I really want to praise them and the entire Vanier Robotics Club for their accomplishments over the past four months.  I urge adults who fear that today's youth have become lethargic to read on.

Vanier College hosted Profuga 2012, the 11th edition of the CRC Robotics competition, inside its Sports Complex over the past three days (Thursday, Feb 16 to Saturday, Feb 18).  The annual provincial competition is run by a company called CRC Robotics.  On their website, they describe themselves and the competition as follows:

"CRC Robotics is a non-profit organization offering high-school and CÉGEP students a quality multidisciplinary competition in an entertaining, high-intensity environment to counter school dropout rates by inspiring tomorrow's leaders. Students are challenged to build a robot and to produce a video, web site, and kiosk presentation, where all tasks are entirely student-run."

This year's robotics challenge was ultimately a series of two-on-two capture the flag heats, where schools alternate who they compete against as well as alongside.  The terrain on which the robots did battle had ramped surfaces.  Designing a robot that can not only manipulate objects, but do so while translating up or down a 20 degree incline is no easy task.  However, the tech-savvy students composing the Vanier Build Team and those of tens of other schools were up to it.

It may surprise you to learn that the goal in this competition was not to chop other robots to bits with buzz saws or axes (I must admit that this was the particular image I used to associate with robotics competitions). But there are a couple of reasons why, in my view, a relay-race or capture the flag is a much better choice than a battle to the death for this particular competition:

(1) The event is longer when robots don't get sawed in half.
(2) Canada in general (and the province of Quebec in particular) has a fairly pacifist mindset.  

Sunday, February 12, 2012

"Speed", Featuring Keanu Reeves and Mechanics

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

Yet, after the credits role, and the movie goers make their way home, the images that stick with them are not those of kissing, lunacy, or explosions, but rather the exciting set-pieces involving mechanics that are continuously on display.  From the elevator on which the film opens, to the bus, where the majority of it takes place, to the subway on 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 would suspect that director Jan de Bont took a physics class as a kid and enjoyed it immensely.

I suppose it is not surprising that the movie features mechanics, as its title is a key term of kinematics - speed is defined as the magnitude of velocity.  And, when an ex-cop turned psycho attaches a bomb to a city bus, he programs it with this kinematic parameter 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 each action sequence, I would pause the film to discuss the key concepts of mechanics on display, and even solve explicitly for some of the unknown parameters.  As this exercise is quite time-consuming, I simply encourage my students to try this activity on their own.

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

When the cabin and its contents are supported by a single rope, how much tension manifests inside it?  Does the rope extend, and if so, by how much?  Why does the supporting crane above break?  I'll answer this last one: the tension in the cord creates a large moment (or torque) about the support structure.  The bending moment leads to a local stress that is larger 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 this fashion, but instead, I would like to focus on two particular action sequences in some detail.  These two sequences occur on the fast-moving bus, and I always discuss them with my mechanics classes.

Friday, February 3, 2012

Guinness Book of World Records a Useful Resource

One of the first books I ever bought, The Guinness Book of World Records - 1992 edition, is still, in my mind, the most informative and entertaining among those that sit on my book shelves.  Where else can one turn to when they want to know the height of the tallest person (8' 11", Robert Waldo), the maximum combined length of finger nails on one hand (181 inches, Shridhar Chillal), and the maximum g-force experienced by any bird (10g's, when the red-headed woodpecker strikes a tree)?

Well, I suppose one could turn to Google, but performing such searches would be much more arduous.  Also, no one would even think to search for most of the endeavours described in the Guinness Book.  In fact, much of the fun in flipping through this record book is had by marveling at some of the most bizarre records it contains, such as the longest leapfrogged distance (888.1 miles by 14 members of a high school class during a 189-hour and 49-minute span).   

From business to the arts, science to sports, anything that has a maximum or minimum is likely captured within those 833 pages.  And, I would go so far as to say that The Guinness Book of World Records is a vital tool for all engineers.  Let me explain...

Saturday, January 28, 2012

Why Does Lightning Appear Blue and Cause a Rumble?

Fans of the film Rocky are very familiar with the character played by Burgess Meredith.  While Mickey, Rocky's lovable, old, grumbling boxing trainer has a lot of memorable lines, I particularly enjoy the one he uses to motivate Rocky during his training: "Kid...You're gonna eat lightning and you're gonna crap thunder!"  This hilarious line, delivered ferociously by Meredith, is not without educational merit: the sound of thunder always follows a lightning event.    

While everyone has observed the awesome phenomenon known as lightning, most do not know what they are seeing, nor the cause for what they hear afterwards.  Still, most are aware that one precedes the other (Rocky would never, for example, eat thunder and then crap lighting).

The reason for the order is simple: a lightning bolt causes a flash of light, which travels at 300,000 km/s (the speed of light), and the sound it produces, thunder, travels through air at about 0.34 km/s (the speed of sound in air).  So, the light from a flash of lightning that strikes one kilometer from you reaches your eyes almost instantly (1/300,000 of one second), while the sound it produces reaches your ears three seconds later.  We cannot easily fathom a ratio of one million, but in our atmosphere, that is just how many times faster light travels than sound.

Thursday, January 19, 2012

Earthquakes and Emotions

While watching a Nova documentary about earthquakes, I could not help but notice the many parallels between the huge releases of energy by the Earth's crust and the huge releases of rage that people experience when they suppress their negative emotions for too long.  We have all witnessed somebody having a personal meltdown, and most of us have snapped to some degree at some point in our lives.  The results are not pretty, and can leave those around us distraught.  While keeping one's feelings withheld for extended periods of time is a tendency that should be avoided, it serves as a fitting backdrop for a discussion on seismic activity.

As you compress a spring from its equilibrium position, its coils store what is known as potential energy.  If the spring is released, this stored energy will be converted into kinetic energy and a vibration will ensue.

Imagine now that instead of a spring or elastic band, it is a less malleable substance that is being compressed, like a steel rod.  Although a steel rod is much sturdier than a typical spring, it can actually be deformed ever so slightly by a large compressive force.  In this compressed state, the steel rod stores potential energy also known as strain energy (energy due to deformation), and would snap back if released, just like the spring.  While the rod deforms less than the spring, it actually stores more potential energy since more work was required to compress it.  What this means is that a compressed rod will rebound more violently once released.

Earthquakes occur when the strain energy stored in the Earth's crust is released over a very short duration of time.  The period of time over which this crust deformation accumulates is usually a number of years.  Inch by inch, adjacent sections of crust move with respect to one another.  The boundaries in the Earth where such tectonic plates meet are known as fault lines.  Unlike the steel rod, whose cross-section is measured in square inches, these tectonic plates are measured in square miles.  A bigger cross-section is linearly related to the amount of strain energy stored for a given displacement.  So, whereas a rod may store many kilojoules of energy, the amount of energy stored in a section of displaced rock may be measured in how many Hiroshima atomic bombs it is equivalent to (note that a 9.0 on the Richter scale is roughly equivalent to one thousand of them).

This massive amount of energy is only dangerous if it is released over a short period of time, as this constitutes a powerful energy release (P = E/t).  All quakes are powerful, as the time of release, t, is always small.  This massive power is spread over a reasonably large surface area, and this ratio describes the intensity of the seismic activity (I = P/A).  Finally, the Richter scale is a logarithmic (base ten) scale that measures the intensity of the tremor.  As such, an R = 7.0 is ten times greater than a 6.0, and one hundred times greater than a 5.0.

Still, it all comes back to the amount of energy that is stored, and this is directly related to the amount of relative slip across fault lines.  The vast majority of earthquakes are so minor that we do not notice them (R < 3.0).  They are the result of a small amount of deformation that builds up over a relatively short length of time.  The mechanism for release is the same for both small and large earthquakes; the difference is that small earthquakes release their stored energy before too much accumulates.

These small earthquakes are an illustration for how we should all manage our emotions.  It is healthy to vent our negative feelings every so often.  When you have a bad day, it may suffice to play some sports and let off some steam.  This is like a harmless 3.0 earthquake.  When several bad experiences pile up over the course of a week, and you haven't had a chance to discuss it with someone close to you, it can all come out in a minor fit on Friday night.  Your spouse may not appreciate being subjected to a 5.0 on the Richter scale, but the dust will settle, and the extent of the damage will be minimal.

Tuesday, January 10, 2012

Hollywood Films Get Space Travel Wrong

As the space ship in the 1986 film Aliens moves towards a mysterious planet, the cosmonauts aboard gaze suspiciously at the foreign body with their feet firmly pressed against the ship’s floor.  The sci-fi adventure has barely begun, and already, the laws of physics have been ignored due to a common imbalance in Hollywood: too much fi, too little sci.

I want to be clear about something: I am an avid fan of science fiction movies, whether or not they are set in space.  In fact, I was thoroughly entertained by Aliens, the sequel to Alien - so much so that I watched it recently for the second time. 

As the film is set in the distant future, it is sensible that several technological leaps have been made by mankind.  I am comfortable with the intelligent robot that is a part of the crew.  I am intrigued by the sensitive motion detection equipment that they use.  What makes me queasy is when the most basic law of motion is inexplicably defied.

When advances in technology occur, they lead to more robust tools.  However, these tools, no matter how fantastic they are, must operate within the constraints of the universe.  Otherwise put, technology is dynamic, but exists within an operational framework that is static.

When a space travelling Sigourney Weaver stands up on the surface of a ship, this implies that there is a set of contact forces between her feet and the surface.  A force, commonly referred to as the normal force, is pushing up onto her feet.  Unless you are currently undergoing a vertical loop on a jet airplane, or happen to be reading this article while in a space orbit, the normal force is currently acting on you.

Friday, January 6, 2012

No, the World Will Not End on December 21, 2012

Let's begin this year by, as the oracle put it to Neo, getting the obvious stuff out of the way.  The widely held prediction that the world will end on this year's winter solstice holds about as much water as a shot glass.

The claim, which stems from the Mayan calender reaching its end, is like many other pseudo-scientific ones that float around the virtual ether: it lingers because it cannot be proven false.  Well, not until the end of 2012, that is.

The end-of-the-world claim can, however, be deemed baseless with relative ease.  I  think that any reasonable person realizes this.  If today's best meteorologists equipped with modern technological tools cannot accurately predict the weather some weeks into the future, how could the Maya accurately predict the "End of Days" moment thousands of years prior?  The obvious answer is that the Maya could not and did not.  But then, I suppose that any devout believer of the silly prophesy would not be swayed by a scientific argument.

Truthfully, I would rather not pay any attention to a debate that cannot be won.  Unfalsifiable statements like, "A flying saucer passed over my house last night," amount to nothing more than noise.  It is a waste of my time and yours to worry about bogus prophesies (is there another kind?) when there is so much richness to be found in real science.  Yes, interpreting actual science requires some logic and a certain degree of effort, but unlike mysticism, it is rewarding.

You know, some "End-of-the-worlders" have modified the terms of their prophesy recently.  They now claim that the world as we know it will end on December 21, 2012.  Well, this is the same sort of cop-out as we are accustomed to seeing in horoscopes, which provide loose predictions that are open to various interpretations.

Every now and then, when horoscopes try to get too precise, they risk exposing how fraudulent they truly are.  For example, my horoscope has alerted me that I will meet the love of my life countless times in recent years.  If the stars really knew me, they would know that I met the love of my life thirteen years ago.

So, I am happy to get this little bit of Hocus Pocus out of the way now.  I will not bring up the implications of the Mayan calender again before the fateful day.  And then, on December 22, I will post the following tweet: "I told you so."