Whatever floats your boat…

Well now. That was a long lasting spontaneous blog hiatus…

Sorry. It’s not that I’ve run out of ideas, it’s mainly lack of time… well, since time is relative, maybe it’s just that I perceive myself as having less time than I actually do. But enough excuses… let’s get back to the physics.

I saw a really neat (3 page!) article on arXiv today called “Google Earth Physics“. I love google, and I love physics, so naturally I had to check it out. The abstract reads,

Google Earth photographs often show ships and their wakes in great detail. We discuss how the images can be used to calculate the velocity of these ships.

Did someone say, do-it-yourself-physics? I knew I had to post this. Naturally, ZapperZ beat me to it… but I’ll go one step further and actually try it out.

The actual article is only three pages long and is very easy to read, so if you want more details I’ll direct you straight to the source. But the main suggestion of the article is that using a very simple formula and making two measurements, you can get a rough estimate of the velocity of a boat. The formula is simply,

boat velocity =  1.25 * Sqrt(wl)/Sin(ang)

; wl is wavelength of wake in meters,

ang is angle between wake and boat direction of motion

The 1.25 comes from some dimensionful constants in front involving Pi and g, but if you use standard units (meters) for the wavelength of the wake, those factors just become 1.25. (The fine print also says this assumes the boat is in deep water. In shallow water this equation isn’t accurate.) You can check out the article for the real formula. To make the measurements you just need to measure an angle and the wavelength shown in the picture up at the top. You can use a protractor for the angle and a ruler for the wavelength and then use the scale given in google maps to convert between your “image length” and the actual length.

I found a boat in my area (toronto) on google maps here. Then I used gimp to measure the wavelength and angle of the wake. I then converted my image length to a real length by measuring the image length of the google scale and a simple ratio:

real distance = wavelength * real length of gscale/img length of gscale

= 76px *  10m / 93px

= 8.17m

And  I measured an angle of around 35 degrees. Plugging that into the equation I get:

boat velocity =  6.23 m/s = 22.4 km/h

I’d say that’s a fair velocity for a boat… but what do I know about boats. Try it for yourself and see if you get the same answer!

Let’s get philosophical: what’s your existential preference?

Quantum mechanics is weird. It gets even weirder when you try to interpret what the theory is telling you about “reality”. In fact, I’m taking a course at the moment called: Interpretations of Quantum Mechanics. I’m hoping eventually I’ll get some blogable material out of it.

For now, I have a question for you all. It will be a purely subjective question (not like last time). I’ve blogged about the random nature of the quantum world before, and I’ve also given an account of an experiment that demonstrated the requirement (under certain assumptions) for an inherently random world, but the nature of reality is still a hotly debated topic in the world of physics. Some physicists reject the notion of a world that is fundamentally random and instead consider the possibility that we’re not seeing the whole picture. They come up with, so called, hidden variable theories that attempt to explain away the randomness by postulating some hidden property in the small world that we can’t directly measure. I’ve also recently come across a paper that hypothesises that the (random) quantum mechanical nature of the very very small could be an emergent phenomenon; that is to say (in pedestrian terms) we aren’t squinting hard enough to see all of the information about a quantum system and this lack of information results in seemingly random behaviour.

I wish I understood these things well enough to explain them here… but I don’t. Instead I’d like to know what your personal preference is for reality and why.

Which description of reality are you (secretly?) cheering for? Are you more comfortable with the completely non-random deterministic view of the world, or are you instead enjoying the idea of a world built on random behaviour? AND WHY?

Physics Riddle — Of Rope and Wood

I thought it was about time I gave you (yes you!) a physics riddle to go with your morning coffee. I’ll state the problem first and then give a few hints below the fold. Readers with a familiarity with ideas in physics can probably solve this without any hints. If you are unfamiliar with physics, don’t be ashamed to check out the hints. Most importantly: this riddle can be solved without any equations. Feel free to post your solutions in the comments. I’ll give the solution as a comment later on.

Okay. Here it is:

Not to scale...

You have two objects:

• A rope of length a given length.
• Two pieces of (let’s say…) wood joined by a bolt. Together these pieces of wood stretch out to be the same length as the rope.

These objects are the same length, same mass and the same mass per unit length. You now hang them by their endpoints so that they hang side by side (as shown in the picture). The horizontal distance between the endpoints on which they hang is the same for the wood pieces as it is for the rope.

Which object has the lower center of mass?

Note: If you are unfamiliar with the concept of center of mass, check out Rhett’s post on DotPhysics here. You don’t need to understand it all for the purposes of this problem, just know what center of mass is.

Have a causally consistent new year

… so what? Another year, another orbit of the earth. What’s the big deal, you say?

Well! I have some New Year’s news for you. Firstly, did you know that this year we get an extra second? To deal with this I suggest counting like a computer scientist; …3, 2, 1, 0! Happy New Year!

This year will, apparently, be the International Year of Astronomy! Georgia at Earth & Sky Science has found a great way to celebrate: 365 days of Astronomy Podcasts.

If that’s not enough, why not follow your lightcone this year? I found a great site that provides an RSS feed of astronomical bodies you (yes you!) could possibly have influenced since your birth.

… what’s a lightcone, you ask?

A lightcone is the 4-D surface in space and time that a flash of light forms as it travels away from its origin. The name is actually a bit misleading. It’s less of a cone, and more of a hyper-cone; that is a cone in four dimensions. Imagine a flash of light. As it moves forward in time the light will move outwards in all directions. At any point in time the light will be confined to the area of a sphere. As time progresses, the sphere will grow in size at a constant rate. If we think of time as another dimension, and tried to draw a 4-D graph of the flash, it would be a hyper-cone.

If you are still confused, a good way to begin thinking about this is to imagine a very small circle lying flat on the ground. Now, imagine it growing and as it grows you move it upwards. Every time the circle grows one centimeter in radius, it moves one centimeter higher up. This traces out the 3-D cone you know and love. The upward direction represents time and the other directions represent a 2-D space. To generalize to a 3-D space with time, you change the idea of a growing circle to a growing sphere. Et voila: a lightcone.

… ok, so what’s so special about a lightcone, you ask?

Since a lightcone is the boundary on which a flash of light travels, and nothing can travel faster than light, the lightcone also marks the boundary of influence of a certain action. Let’s say, for example, you sneezed. Achoo. At some other time, in some other place, let’s say a book fell over. Could your sneeze have possibly caused the book to fall over? What you could do is mark two points on a graph; one representing the time and place of your sneeze and the other representing the time and place of the falling book. You could draw a lightcone originating at the sneeze point. If the other point is outside this lightcone then it is physically impossible for your sneeze to have caused the book to fall over.

You could also do the same for your birth. Draw a cone originating from earth at your birthday. Now draw points for all the stars in the sky at time: today. Any points inside your lightcone could have been influenced by your birth. The word “could” is in italics because it’s really saying: “sure, the laws of special relativity don’t disagree with you… but… there’s more to cause and effect than lightcones”. Still, it’s a fun way to learn about astronomy!

So this year be aware of your lightcone and keep track of the people and events inside it. The range of influence of your actions is probably a lot more vast than you originally thought…

ExaMarathon

Sorry for the lack of posts. I have lots to write, but no time to type it. I guarantee a bunch of neat posts over the holidays…

…why are you so busy, you ask?

Here’s my week in comic form:

...Except for me it was 270...

... by hour 18 I was feeling pretty sick...

... in my defence: it wasnt goofing off, it was medicinal...

... awake -> sleep. Its kind of like a phase transition...

Intermission

This is a rather non-serious post. You can blame Clifford at Asymptotia for it. His recent post pointed to a site called typealyzer that claims to measure your blog’s “type”. This type classification seems to be based on the Myers-Briggs type indication tests. I thought I’d play along just for fun. Here are the results:

INTP – The Thinkers
The logical and analytical type. They are especially attuned to difficult creative and intellectual challenges and always look for something more complex to dig into. They are great at finding subtle connections between things and imagine far-reaching implications.

They enjoy working with complex things using a lot of concepts and imaginative models of reality. Since they are not very good at seeing and understanding the needs of other people, they might come across as arrogant, impatient and insensitive to people that need some time to understand what they are talking about.

Well, I’m satisfied with that… except for maybe the part about me possibly coming across as arrogant, impatient and insensitive. Oh well. It also gave me a picture of my brain. Apparently there is an abundance of logic, mathematics, imagination and symbols.

Right now my brain is filled with mathematics. I’m doing some of my first TA work; correcting around 300 midterms for a Special Relativity class. I’ll let you know how that goes if I survive…

In the mean time, if you need something to read, I’d recommend checking out this essay by Alfie Kohn about how current grading schemes actually inhibit learning in our education system, and what can be done about it. (Link via: think twice)

McGill physics students: Been there, done that, made the T-shirt.

The physics undergraduate students at my old university, McGill (based in Montreal), have exercised their creative talents and come up with a T-shirt design to unite them all. It portrays the great difficulty that every McGill undergrad goes through on their way to completing a B.Sc. in physics. It, of course, does this all with style, sophistication, and whit.

Here it is for your pleasure:

If you don’t get the joke here, you’re probably not familiar with quantum mechanics. That’s okay. Let me try to explain it a bit. The Greek letters (psi) around the frowny face form the expectation value of … the frowny face (pain). What that is loosely suggesting is that if you asked (measured) a statistically significant number of McGill physics students, the average emotion you would measure would be pain.

Another of their potential designs uses the idea of spherical cows (metaphor for approximations):

I especially love the insight that you can set the tail to zero here. It really simplifies things.

Busy

Posting has been slow this week. I have excuses all lined up for you. Firstly, I was a judge at the Canadian Undergraduate Physics Conference (CUPC) which was hosted at the University of Toronto last weekend. All in all, it was fun. I listened to many undergrads presenting their research in a cold dark lecture room. Very few showed their fear of public speaking (and who could blame them, really). If that wasn’t interesting enough, several prominent physicists were invited to give talks to the massive group of undergraduate students from around the country. My personal favorite was Lawrence Krauss, who gave a very similar talk to one I attended (and blogged about) at McGill. This time, however, he prepared it so that an undergrad could fully benefit from the information.

While at the CUPC, much to my surprise, I bumped into a fellow science blogger, Chris Ing of Jacks Of Science. I remembered his blog once he mentioned his fantastic post of science Valentine’s Day cards.

Apart from that, I’ve been learning the Lindy Hop, and catching up on assignments and sleep. I’ve also been catching up on my rss feeds. Here are a few things I found that you shouldn’t miss:

• X-Rays produced from peeling scotch tape! Seriously. Enough to even take an X-ray photograph. It comes with a great video of the researchers too.
• Ever wonder why atheists don’t publicize their views like christians do? Well, wonder no longer. They’ve gone and done it! Atheist bus adverts.
• You also might find it interesting to read Bee’s Eleven steps to improve the world.

Our elevators are more awesome…

I’m a fan of the University of Toronto physics department’s elevators.

…is it because they’re fast?

…do they telepathically know which floor you want before pressing a button?

…do they transport you by moving in more than one dimension?

Nope. Better. Let’s take a look inside…

Hmm… looks pretty standard so fa — but wait! What’s that in the far left corner? It looks like a glass cylinder. Let’s go in for a closer look…

<ghasp>It’s a force meter attached to a 750g weight!</ghasp>

A force meter is a type of measuring instrument that enables you to measure the amount of force acting on the object it is attached to — which in this case is a 750 gram weight.

If you don’t understand why this interesting, you need to understand the following: physicists like solving problems, and at least once in every physicist’s life (s)he wonders “what is the acceleration of this elevator, and what g-force am I experiencing?“. This question, of course, bothers us for the whole 30 second elevator ride, and we wish we had a measuring apparatus to figure it out. Eventually the curiosity subsides and we carry on with our daily lives… but now in the U of T physics department, we don’t have to.

Let me show you how it works. The top of the force meter is attached to the elevator and the bottom is attached to a hanging weight. The force meter will measure the force between the elevator and the weight. If the elevator is not accelerating (even if it is moving at a constant speed) the force between the elevator and the weight will be that of gravity. As the elevator speeds up to move to a higher floor it will have to pull on the weight with a greater force so that it not only counteracts gravity, but also pulls the weight upwards. Newton tells us that the net force acting on an object is its mass times its acceleration. So if we know the force acting on the weight and what its mass is, then we can find out the acceleration. I took a quick reading and noticed that the difference between the force when the elevator was not moving and when the elevator was accelerating upwards was approximately 1 Newton. So we can take this, divide it by 750 grams (using google calculator) and find that the result is an acceleration of: ~ 1.33 m / s².

Great! Now let’s get some context on this. Comparing it to gravity (which is 9.81 m / s²) we can say that an elevator accelerating upwards is equal to a g-force of: 1.14, which is small considering that fighter pilots can withstand a g-force of 9. Taking the elevator downwards will initially give you a g-force of: 0.86, which is roughly comparable to standing on Venus (0.904).

So, yes… very awesome. It makes me wonder how many other universities’ physics departments have little things like this. What kinds of neat publicly accessible physics toys are in your physics department?

Speaking of geckos…

… what’s that? Nobody mentioned the word geckos?

Oh.

Well anyway, I just discovered a neat article on Physicsworld describing a new wonder material made of carbon nanotubes that mimics the sticky padding on a gecko’s foot… the interesting thing is: the imitation is ten times stickier! Carbon nanotubes are exactly what they sound like; they are very thin tubes made of carbon. What you can’t tell from the name is that the walls of carbon nanotubes are just a single atom of carbon thick.

Somehow, physicists have been able to coax the nanotubes into a fiberous forest similar to that on the pads of a gecko’s fingers. Just like a gecko’s fingers, this material interacts with surfaces creating forces between the molecules of the material and the surface (aka: Van der Waals Forces) that resist motion parallel to the surface. If you pull the material away perpendicular to the surface, the nanotubes peel off fairly easily.

Apparently they are trying to (and I quote) “optimize the structure and scale it up so that they can make ’spiderman’ gloves“.

Could those physicists’ research be any cooler?

Edit: Arg. Why does boingboing always beat me to it.