Monday, April 29, 2013

What if There Were no Moon?

On one late drive home last week, I looked up at the full moon in the early night sky, and just marveled at its beauty.  And I asked myself the question, "How much different would life on Earth be if there were no moon orbiting around us?"

This may sound like an arbitrary question, but it is a very legitimate one.  Trying to imagine life without the Sun would be a rather pointless exercise, because without a star to govern our orbit and act as a steady energy source, there would be no life.  The same cannot be said for the one celestial body that orbits around the Earth.   

For all of its beauty, the Moon, our singular natural satellite that orbits us roughly once per month, is, for lack of a better word, unnecessary.  Some planets have no moons, some have many (the other night, I looked at Jupiter through a telescope and beheld its four moons) - a moon is, in a way, a planetary afterthought.  If the Moon were to mysteriously disappear tomorrow, the resulting physical changes on Earth would be minimal.

Tuesday, April 16, 2013

Keeping our Heads in the Face of Tragedy

My heart is filled with sadness.  Yesterday's Boston Marathon Bombing is at the front of my mind as it is no doubt for you and everyone you know.  I don't know anyone killed or injured on a personal level, but it is the kind of event that breaks the heart of humanity, and for this reason I feel the need to mourn.

When ugliness becomes so apparent in the world, we feel the need to make sense of it.  I imagine a work of art, so carefully painted by an artist over the course of days or weeks.  The beautiful result can be destroyed in seconds by a vandal with a can of spray paint.  It is so much easier to undo something than to do it.  It is a manifestation of the second law of thermodynamics.  Chaos has a tendency to increase.

When an event that aims to lift the spirits of a city is marked by the sinister act of one or a few rogue individuals, some feel as though we should just give up.  It seems there will always be these bad seeds.  We must remember that such cowards form the tiniest portion of humanity, and in no way represent us.  They succeed in wreaking havoc because it is vastly easier to rain on a parade than to assemble one.

In this dark hour, let us keep our heads, mourn the individuals directly affected, and honour them with our persistence.  We must keep celebrating life despite such acts.  In many ways, life is like a marathon; we must keep running, even when the terrain is so terribly unforgiving.

Thursday, April 4, 2013

Unraveling the Mechanics of Spider-Man's Web

My three-year-old has an obsession with Spider-Man.  She has been putting bad guys in jail for the past week with the help of her Spider-Man action figure.  So, being who I am, I could only resist conducting a mechanical assessment of the fictitious hero's web for so long.

I have deconstructed the physics of superheroes before.  My approach is to ignore the mutation aspect - to accept the background story that gave the hero his or her powers.  My concern is instead, given such powers, is the rest reasonable?  For Spider-Man, I'd like to focus on the web that he shoots from his wrist to the buildings of New York City as a principal means of transportation.  Can a thin web realistically sustain the tension that manifests within it when Spider-Man swings through the city?

Consider the awesome illustration below (mad 'Paint' skills) that shows the famous web-slinger swinging from the top of a building using web length 'R'.

If Spider-Man is initially at rest (at 1), then a simple energy conversion analysis (gravitational potential energy converts to kinetic energy) shows that at the bottom of his swing (at 2), his speed v is given by (2gR)^0.5, where g is the surface gravity.  Here, aerodynamic effects were ignored as were any elastic or visco-elastic effects associated with the web.  A free body diagram for Spider-Man is drawn in the figure at the instant the web is vertical (at 2).  The tension in the web points up while the gravitational force points downward.  Applying Newton's Second Law in the normal (n) direction gives the following (note that there is an upward acceleration associated with this circular path):

Ft - Fg = ma
where m is Spider-Man's mass.  This becomes:
Ft = m(g + v^2/R) = m(g + 2g) = 3mg

Tuesday, April 2, 2013

Do we Really Improve with Age?

There is no debate as to whether a person's physical well-being improves with age: it does not.  When I was ten years old, and I got a cut or a bruise, it was gone without a trace within days.  Now, at the age of thirty-one, small bumps and bruises linger for weeks, even months.  It is as though my physiology has stopped trying.

When adults confront this reality, they may look on the bright side: as we grow older, we gain experience, and get smarter.  But, is there any evidence of this?  I am beginning to notice that the longer we are around, the more resistant we become to change.  And, if this is so, then our age actually becomes a deterrent for self-improvement.  A relative of mine recently pointed out that as adults age, they simply become more exaggerated versions of themselves.  Think of the seniors in your family - you may find that there is much truth to this statement.

Why do we become set in our ways?  Many reasons.  For one, the effort to improve has a smaller return on investment as we age, as there is simply less time remaining.  Another reason is that change implies we have been doing it wrong, and, the longer we have been around, the harder it becomes to face such a reality.  But, the bottom line is that change is hard because learning is hard.  Seeing the world in a new way - accepting that something is not how you always thought it was - is daunting.  It is something that students are asked to do every day, and it is so clear to me which ones wish to accept this challenge and which do not.