Adventures of the Learning Assistant (Part 3)

(Here is Part 1 and Part 2, in case you missed them).

Sorry for the silence this week… you know how it is.

Before I begin, looks like the MIT physics department is having a few troubles of its own with the new physics curriculum. And, don’t forget to check out the First Excited State for Week 2 of the teaching journal.

I need your help. The practicals are becoming slightly tricky in terms of grabbing students’ attention for tutorial-like situation. As I mentioned last week, the students are vastly more motivated to do the activities than ask tutorial questions because they will be getting graded on the activities. We have the ability to create quiz questions on their workstation computers and we’ve tried creating a quiz question to try to draw out questions from the students. What actually happened was they spent a little while on the question, guessed if necessary (since it wasn’t worth any grades) and then didn’t ask any questions (probably for fear of not having enough time to do the lab activity).

I’ve been toying with a few ideas to try to get their participation in asking questions. The first is instead of asking the whole class a question and going over the solution, to instead go around and ask each workstation one at a time. It would take up the same amount of time for the students. The upside is that they will be much less shy and almost certainly reveal any gaps they have in their understanding. The downside is that any enlightening bit of information will be confined to that table.

In order for the whole class to benefit, I’d have to somehow engage the whole class in problem solving. One general idea I’ve had in that respect is to do away with a multiple choice quiz type question (and eliminate half hazard guesses) and instead ask an involved/conceptual problem. They could then write their answers/ideas on their whiteboards and share their ideas with the rest of the class. Alternately, if they are too shy to speak up, I could go around the class while they are working on the activities and look at the ideas on their whiteboards and discuss with them.

I think the problem here is shyness and time constraints. I’m wondering if any of you have ideas to get students to participate in sharing their conceptual difficulties with the class. Also, I’m wondering if any of you have any ideas for relatively short, interesting questions on the subject of static electricity.

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…

I’m dreaming of a white and sparkling christmas

Canadians know snow. Recently, I’ve been around Toronto and Montreal and I’ve been exposed to a great deal of snow. Delayed street cars; slushy, slippery sidewalks; frosty faces; hail and hazard lights on highways. These are just some of the things I’ve dealt with this past week…

But there’s a warmer side to the white stuff which one of my dearest friends reminded me of two nights ago.  She drew my attention to the fluffy, freshly fallen snowflakes which sparkled under the illumination of the streetlights. She had heard that there was some interesting physics behind the glisten of snow (of which I had no knowledge). She asked me to, one day, explain it to her. I love questions like this, so I decided to do a bit of googling.

…what makes snow sparkle, you ask?

First, let’s take a look at snowflakes in general. They can come in simple hexagonal shapes or complex tree-like crystals. So much could be said about the anatomy of snowflakes, most of which I couldn’t tell you because I don’t know (but here’s a link that might help). The key point I would like to get across is best illustrated by the graph to the left. The graph shows temperature decreasing to the right and humidity increasing upwards. While the more complex, pretty snowflakes tend to form at high humidity, the type of crystals that sparkle are actually the simple ones near the bottom of the graph. These plates and prisms at low humidity have large flat surfaces which act like mirrors reflecting almost all light that hits them. These snowflakes are randomly scattered on the ground and will reflect the dimmed light reflected from the trees, cars, and whatever else happens to be around into your eyes. The majority of the snowflakes will appear to have some average brightness, however, some snowflakes will happen to be at the correct angle to reflect light emitted directly from a light source (like the sun, or streetlights). It is these snowflakes which will be almost as bright as the light source itself; they will stand out and glisten. As you move your field of view, these snowflakes will no longer be properly oriented to reflect the light source and, instead, other snowflakes will stand out. The sparkling will appear to move as you do, in a sort of spectacular specular reflection.

But wait! There’s more!

These simple snowflakes don’t only need to reflect, they can also refract light. Refraction, in case you’ve forgotten, is the bending of light as it enters or exits a different material. The angle of refraction depends primarily on the materials it is entering and exiting, but it also depends on the frequency (color) of the light. Different colors of light will bend different amounts as they enter and exit a snow crystal. White light (coming from the sun, or a streetlight) consists of many different colors of light, these colors will be separated by the snow crystal as it passes through a prismic snow crystal. This is called dispersion. So if you are far enough away from the sparkling snow that the colors have separated significantly, you may see certain snow crystals as being certain colors! The result is something like this:

So on the next dry winter night after a fresh snowfall, take a look outside and see if you can spot some spectacular specular reflection, or even the colorful dispersion of randomly assorted snowy prisms.

Measuring the speed of light with chocolate and a microwave oven

Here’s a great excuse to eat a lot of chocolate in the name of science.

First of all, you need to understand that microwaves are just electromagnetic waves with a certain frequency and wavelength just like visible light. Wavelength is the length between consecutive peaks of the wave. It’s a very intuitive name. You can see it labeled in the picture to the right as the Greek letter “lambda” (λ). Since waves propagate (move), we can also define a quantity called the frequency. Frequency is the number of peaks of a wave that pass a certain fixed point per second. Wavelength is a measure of distance, and frequency is a measure of one divided by time. So to find the speed (“c“) of the wave, you just need to multiply these two quantities together:

c := speed = (distance) x (1/time) = (frequency) x (wavelength)

…but why the chocolate and the microwave, you ask?

What you need to do is use a microwave oven and a piece of chocolate to measure the frequency and wavelength of microwaves. Then you can find the speed of light! Fortunately, microwaves usually have the operating frequency written on the back. Check the back of your microwave. Mine says the frequency is 2450 MHz ( = 2,450,000,000/1 second).

Now that we have the frequency, all we need is the wavelength; this is where the chocolate comes in handy… You might have a microwave with a spinning dish inside. You can probably guess what that’s for. It’s to help heat things up evenly (like stirring a pot of soup on the stove). Whereas on a stove the heat is concentrated on the bottom of a pot, the energy (and thus heat) that microwaves give to food is concentrated at the peaks of the microwaves (which are standing waves in a microwave oven). If we take out the rotating dish then we can find these peaks, measure the distance between them, and find the wavelength. So we just need to heat the chocolate up a bit, find some soft spots (where the peaks of the microwave standing wave are) and measure the distance between them with a ruler.

Here’s what you’ll need:

• Large chocolate bar (bigger than 5 inches)
• Ruler (to measure distances)
• Microwave oven (with rotating dish removed)
• Coffee (optional… it goes well with chocolate)

Place the chocolate bar (unwrapped) in the microwave oven and heat it up (without moving it) until you can see soft spots forming. If I were to hazard a guess for the timing, I’d say heat about thirty seconds… but that’s a guess. It really depends how powerful your microwave oven is.

When you have at least two soft spots forming in the chocolate, take it out and try to measure the distance between them with a ruler. (I had to prod the chocolate lightly with a spoon to find the soft spots). My chocolate didn’t turn out very nicely, but I was able to make a very rough measurement of about 4.5 inches between the centers of the soft spots. Edit: when I made this measurement I forgot that I was measuring peaks of a standing wave which are half the wavelength of the microwave. So really, you should find the distance between the soft spots and multiply by 2 to get the wavelength. Thanks, Lord Axil. Somehow I must have missed a soft spot when measuring, which automatically corrected this factor of two.

Now we can use the wonders of Google to do the calculations for us. I can just type the following right in Google and it will calculate the speed in the proper units: “2450MHz*4.5inches“.

Google says:

(2450 megahertz) * 4.5 inches = 280 035 000 m / s

…but how close are we to the real answer, you ask?

We can check our answer with Google again. Just type “c” into google and it will give you the speed of light!

Google says:

the speed of light = 299 792 458 m / s

For a measurement made with a ruler and a chocolate bar, it’s not too far off. It works!

But don’t take my word for it, listen to this amateur scientist explain the experiment.

How to float a frog in a magnetic field.

Some who read this (if anyone actually reads this blog) will probably thing there are a lot of things wrong with the title of this post. First of all, in high school you probably have learned that only other magnets or metallic objects (containing iron, nickel or cobalt) are attracted to magnets. Frogs aren’t metallic (aside from the traces of iron in a frogs blood) nor are they magnetic. Secondly, if you’ve ever tried to take two magnets, put one on the ground and try to float the other above the first using magnetic repulsion, you know this is impossible. So floating a frog in a magnetic field seems very unlikely. No, not unlikely, unphysical!

Well, if it weren’t for quantum mechanics, it would be unphysical. I assure you, however, floating a frog is very possible and has been done! A small group in Norway used an incredibly powerful magnet to float a frog. Not only a frog, but water, a strawberry and a grasshopper! Here’s the link to their site which has videos.

So, how did they do it? Firstly, you need to know a bit of electromagnetic theory. Specifically the fact that moving charges create magnetic fields. For example, if you run a current through a wire, you are sending billions of electrons through it per second. This actually causes a small magnetic field around the wire which you can “see” by putting a compass next to it.

Next you need to know that atoms, the building blocks of matter, are made of a positively charged nucleus and negatively charged electrons which orbit around it. That’s right, moving electrons means moving charge, which means a magnetic field associated with every atom. The atoms in materials called diamagnetic materials (like water, carbon, graphite…) have a strange property which makes their atomic magnetic poles oppose the magnetic pole of a nearby magnet. What I mean by this is that if you put a diamagnetic material, like water, near the north pole of a magnet, the water atoms will line up so that their north poles point towards the magnet. The north poles of the atoms and the magnet will then push each other away, so, theoretically, the water will repel the magnet.

In reality effect is so small that it counts for almost nothing. It’s probably pointless to get your heavy duty magnet and try it out. It won’t work. If you are a physicist, however, with a magnet 200 times stronger than a regular store-bought magnet, the effect is noticeable, very noticeable, and you can actually get a frog (maybe even a person) to float in mid air.