Monday, August 24, 2015

Locating the Sun Whenever

At around dusk on a recent evening, I came to a logical conclusion while staring up at the half moon in the blue sky.  The Sun was hidden by this time, but I was able to draw a conclusion about its whereabouts.  I just needed to use the Moon as a guide.

First, let vector v1 point from you to the center of the Moon.  Second, let vector v2 point from the center of the Moon to the vertex of the lit up part (as shown below):

Vectors v1 and v2 form a plane.  The center of the Sun lies in that plane.  Think about it.

Thursday, July 9, 2015

Rationing on an Island

I almost never watch television programs other than live sports, and truly never watch 'reality' programs.  However, I made one exception this summer when I tuned in regularly to "The Island".  Over six episodes, the last of which aired this week, a group of men, fourteen initially, were dropped on a hot deserted island with the clothes on their backs, two water canteens, some machetes, and some video camera equipment to record the 28 day experience.  After those 28 days on the island, nine of the men remained, the other five having experienced severe health problems and requiring evacuation.

The first thing that strikes me in a situation like this is just how difficult survival is/was pre-industrialization.  I get that kind of feeling when I go camping, and I 'rough it', you know, with all of my camping equipment and food prepared and packed beforehand.

The enduring thought that stays with me from the show, however, is the idea of limited resources in a group, and the importance of rationing.  The group of men needed to assess their resources and share them fairly amongst them in an amount that would ensure their survival.  Imagine life in a small group on an island where resources are scarce.  If the goal is survival of the group, then rationing water and food is an absolute necessity.

The thing is, mankind as a whole does live on an island - a great big one - the surface of this planet, which trudges along lonely in the solar system.  Our resources are indeed finite, yet we act as though this is not the case.

Thursday, June 4, 2015

The Cohen Condition for Extinction

It is getting harder and harder to make a name for yourself in the science world.  Harder still, if, like me, you would like it to happen without putting forth much effort.

It seems as though it's all been done.  What's left?  The unification of general relativity and quantum mechanics?  That problem, which has stumped all of the greatest minds over the past half century?  I have an engineering background and teach college-level physics - it ain't gonna happen.

But, I had an epiphany recently.  If getting an equation named after you requires something novel, then maybe rather than try to push the boundaries of knowledge, I should think of something that is extremely simple.  There are probably ideas out there so stunningly obvious that academics didn't bother to point them out.

I'm not looking for a unit named after me, nor an element on the periodic table - just something to hang my hat on.  So, without further ado, let me unveil "The Cohen Condition for Extinction"...

Let N = TB - TD,

where TB is the total number of births for a given species throughout all of history

and TD is the total number of deaths for a given species throughout all of history.

If N = 0, the species in question is currently extinct.

If N = 1, the species in question will soon become extinct.

Again, to reiterate, I am not after the Nobel prize.  Ed Witten can keep his Field Medal.  Just having my name in some textbook will satisfy my ego.

Tuesday, March 17, 2015

Magnetism the Most Magical of Forces

Nothing impresses a child more than magnets.  OK, maybe balloons, but magnets are a close second.  Give two magnets to a five year old and that is a solid hour of entertainment right there.  The magnetic force is not like the 'ever-present' gravity in our day-to-day lives.  It seems to be the result of some special, 'magical' force that we observe from time to time.

At the start of my electricity and magnetism course, I usually emphasize that although the electrostatic and magnetic forces are of the same family of forces, they must not be confused as the same thing.  The average person interacts with both of these forces daily and has little understanding of either.  It takes a while to wrap one's head around magnetism, but let's give it a try...

The mere presence of a charge creates an electric field, which can exert an electrostatic force upon another charge.  This is the basis of electrostatics.  In order for a magnetic field to be produced, charge must be in motion.  It then follows that for a charge to experience a magnetic force within a magnetic field, it too must be in motion.  This is the basis of magnetism.  So, whereas all charges produce and respond to electric fields, only those in motion produce and respond to magnetic ones.

The electrostatic force acting on a charged particle in an electric field is quite straight forward:

Here, charge q responds to electric field E.  What makes this force kind of intuitive is that the force points along the same axis or exactly opposite to that of the field (depending on the sign of the charge).  Contrast that with the magnetic force, which acts on a charged particle as follows:

Friday, December 19, 2014

The Physics of "Gravity" and "Interstellar"

Hanukkah is a Jewish holiday celebrating a miracle whereby oil sufficient for just one day burned for eight.  Over this past week, an entirely different miracle took place: I, a father of two young girls watched two movies, none of which contained a single princess.

I really got my nerd on: I rented "Gravity" and then went to the theater to see "Interstellar".  Both films feature a lot of physics, but they could not be more different.  "Gravity" is a ninety minute expedition featuring orbital mechanics, while general relativity weaves its way through the three hours of "Interstellar".

You are probably expecting me to dissect these two films and expose all of their scientific inaccuracies.  In truth, I enjoyed both of them immensely, but would like to address one major problem with each one.

Wednesday, December 10, 2014

Deep Breaths During Exam Time

Over the past weeks and months, I have witnessed some distraught students.  Young adults who walked into the semester cool as a cucumber are hitting the finish line exasperated - not all of them, but many.  A few have asked me for advice, and all I can seem to muster is "Breath".

I thought that I would strive here for something deeper and perhaps more helpful than this.  At the same time, I'll toss in a science metaphor, cause that is sort of my thing.

We are all aware of the need to manage our stress level.  Everyone has their own coping mechanisms for this, so I won't say "Go to the gym" or "Get more sleep" - it's good advice, but I want to focus instead on the bigger picture.

One thing that has been important for me is setting reasonable expectations.  I was not always good at this.

Thursday, November 13, 2014

Rosetta Mission and Noodle Bridges

A couple of unrelated engineering feats occurred yesterday, and I'd like to address them.

First off, the European Space Agency (ESA) succeeded in landing a probe (Philae) on a comet (67P) for the first time in history.  The level of difficulty of accomplishing such a thing is truly off the scale.

A comet is tiny, 'celestially speaking'.  The mass of 67P is about 10^13 kg.  That's a one with 13 zeros attached to it.  But that makes its mass about 100,000,000,000 times lower than that of a typical planet.  Another aspect that makes docking with such a body tricky is its irregular, peanut-like shape.  It is far from a sphere (largest dimension about 5 km, and smallest about 2 km).  Still, regardless of where you land on this comet, the surface gravity is on the order of 0.001 m/s/s (about one ten-thousandth that of the Earth).  So, if you want to dock, you'd better hang on, because escape velocity is only about 1 m/s (jump, and you now orbit the Sun).

Wednesday, November 5, 2014

My Halloween Costume: A Free-Body-Diagram

Last week, on Halloween day, I came to work dressed in a costume...

As you can possibly tell, I was dressed up as a free-body-diagram.  All the forces acting on me were identified by force vectors (large red arrows) at their respective points of application.

I had the gravitational force, mg, acting at my center of mass, and then a reaction load at each foot.  In the picture above, I also posed with a reaction coming from the wall I was leaning against.  Hanging around my neck is a list of assumptions (this costume is valid under the following conditions...).

So, there you have it.  If you were wondering if I'm a nerd, you now have your answer.  I think even my physics teacher colleagues found it slightly nerdy - that speaks volumes.

I got some nice reactions from my students that day, though as I walked through the halls, non-science folks gave me some strange looks.  I spared my family any embarrassment by removing my costume before I returned home.

Thursday, October 2, 2014

IAC 2014 - Day 4: My Presentation

Today, I give my presentation about the static deformation of the space elevator tether due to the presence of a climber.  I have decided to open the talk with a picture of the CN tower.  You see, its been a foggy week of weather in Toronto, and I have taken some time to stare up at the tower from its base.  The top of the tower disappears into the fog - no end in sight.  The sight appeals to me for obvious reasons, so I have to mention it to the other space elevator aficionados in attendance.  Imagine a time, decades from now, when there will be no end in sight to such a structure, even on the clearest day.

I present a summary of my most recent research.  One of the most surprising things is that this fundamental mechanical analysis had not been documented yet.  You station a climber at some location on the tether, and what will the new equilibrium state of the tether be?  Will it stretch more or less and in what locations?  What are the changes in stress and tension throughout the tether?

The results are as follows:

Wednesday, October 1, 2014

IAC 2014 - Day 3: An Independent Review of the Mars One Proposal

I know I should be writing about day 3 here, but yesterday, after submitting my day 2 entry, I attended perhaps the most compelling symposium of the conference; it was all about manned missions to Mars.  I can say with some confidence that nothing today will top it, so this entry will focus entirely on the exciting presentations that took place yesterday afternoon.

Most of the conference rooms hold about 150 people in it, and it is rare that a room is more than half full.  But I had a feeling that this symposium about Mars missions would draw interest, and sure enough, it spilled out the back of the room.  The first few talks were rather benign: A plan to land on Mars by 2030, recommendations by several experts in the field on planning the first mission, and a commentary on the social and legal structure of the first Martian society (nothing more compelling than reading the novel Red Mars).

The fourth presentation was introduced by the session chair as 'something special', and he was right.  Five students from M.I.T. wrote a paper challenging the proposal for Mars One.