Friday, January 29, 2010

Newton's method on your TI, fancier

Using actual programming, not just the "ans" function. TI 83/84 or 89.

Back in the day, we didn't have such things ... it is almost too easy :-)

PH253: Homework 3 is out

Here you go. I'm sure you've been eagerly awaiting it ...

Thursday, January 28, 2010

PH253: Randomness

First, I'll be in Gallalee all day today if you have last-minute homework questions. My office is 110; I might also be in room 322.

"Material particles can be understood as the quanta of various fields, in just the same way as the photon is the quantum of the electromagnetic field.” - Steven Weinberg

“In its mature form, the idea of quantum field theory is that quantum fields are the basic ingredients of the universe, and the particles are just bundles of energy and momentum of the fields.” - Steven Weinberg

Wednesday, January 27, 2010

PH253: stray HW2 hints

#1 - That's not a typo, it really is hc^2, not hc. There is a difference of a factor 4/c when you talk about energy or power, but here we are worried about intensity. The rest really is just math ...

#2 - Still just math ... but note that the constant 'sigma' you find here is not the same as the Stefan-Boltzman constant of number 7. Again there is a factor 4/c to convert between energy and intensity.

#3 - Just the Wien displacement formula, nothing more.

#4 - We'll talk about this in Thursday's lecture if you're having problems.

#5 - Using a fixed wavelength of 641nm, just calculate I(T) for both temperatures, using the formula from #1 and take the ratio.

#6 - Circular motion + electric force gets you velocity. Acceleration on a circular path is determined by velocity and radius (given). Kinetic energy comes from velocity, and power is energy divided by time. I'll field questions on this in lecture, there are a few steps involved.

#7 - The rate of heat loss is just the power emitted as thermal radiation, which you know to be P = A(sigma)T^4, where A is area and sigma is the Stefan-Boltzman constant. Power loss is due to thermal emission by the human, but the human is also absorbing thermal power due to the temperature of the surroundings (over the same surface area). Power lost minus power absorbed is the net power loss, which is the rate of heat loss.

PH253: HW2 #4

For number 4, I've uploaded the raw data if you'd rather process everything numerically. You can find it here. Finding the peak wavelength and area under the curve might be much easier working from the raw data, if you know how to do numerical integration ...

Keep in mind that the intensity for the 60V curve is still multiplied by 2, as in the plot. When you find the area under the 60V curve, you will therefore have to divide by 2 ...

UPDATE: there is an excel file there as well with the data already imported ...

UPDATE 2 (10:25pm): I made a mistake when making the excel sheet and raw data files, and the 80 and 100V data were accidentally scaled to a max intensity of 1. That is fixed now, but if you downloaded the excel sheet or raw data files before ~10:20pm, you should grab them again  ...

Tuesday, January 26, 2010

PH253: Radiation from accelerated charges

A nice qualitative article on radiation from accelerated charges. (On-campus only.) The abstract:
A few conceptual questions on radiation from charged particles moving in circular orbits are answered here in a purely qualitative way without using any mathematics. These relate to the quasicontinuous spectrum of synchrotron radiation, the absence of radiation from current rings and Bohr orbits, and the phenomenon of radiation reaction.


A friend of mine is looking for a math tutor for his daughter once or twice a week (algebra 2 I think). If you'd like to make a few bucks helping a high-school student learn math, let me know ...

Planck & Einstein Nobel lectures

How it happened, in his own words.

Also: Einstein's Nobel lecture, which talks about relativity (last week's material) in spite of the fact that his prize citation specifically mentions the photoelectric effect (Thursday's material).

Newton's method on your TI

Say you want to solve for the root of some equation that has no analytic solution, and you have your TI-8x handy. Should you take the 'shotgun' approach? No! You can easily implement Newton's method, making use of the fact that you have an 'ans' function to use the previous result as part of the next calculation.

Let's say we want to solve for the roots of f(x) = x^2 - 2. We know the roots are the plus and minus square roots of 2, but we need to start with an easy example. Newton's method, in short, asks you to guess a solution to f(x)=0, and calculate an improved guess using f(x) and its first derivative f'(x). The algorithm:
x_{n+1} = x_{n} - \frac{f(x_{n})}{f^{\prime}(x_{n+1})}

For our function, this means
x_{n+1} = x_n - \frac{x_n^2-2}{2x_n}

So, you first guess at the root, and that is your starting x. The next guess for x is calculated from the formula above. Let's say we guess 1 for the root. It is a bad guess, but it doesn't matter too much.

x_0=1 \qquad \Longrightarrow \qquad x_1 = 1 - \frac{1^2-2}{2\cdot 1}=1.5

Our next-best guess is then 1.5. We plug 1.5 into the equation above, and the next-next-best guess is 1.417. Not bad! After 3-4 iterations, you'll see the numbers start to converge.

How to do this on the TI? First, type your guess and hit [enter]. That makes the current value of "ans" equal to the number you just typed. Now type this as your formula:
(ans) - ((ans)-2)/(2*(ans))
Don't forget the parentheses. Hit [enter], and you've found your second guess, which is now the new value of "ans." Keep hitting [enter] until the result starts to converge, and that's that! You've implemented an iterative root-finding algorithm.

Doing this for a more complicated function, like the one on the homework, is not much harder. You just need to know the function and its derivative, otherwise you follow the same procedure.

Monday, January 25, 2010

PH255: primer on errors

From the MIT advanced lab course (8.13/8.14), a nice primer on errors.

In general, the open courseware for 8.13/8.14 and its current incarnation are fantastic resources that should be a big help this semester.

PH255: lab procedures

Just a reminder, bring the lab procedures you used last time with you to lab today. For the first few weeks, you'll pass the write-ups from group to group, marking them up each time you find errors/improvements/etc. After a couple of weeks, I'll collect them all and fold the changes back in to the master copies. Continuous quality improvement.

Along those lines, don't forget to use the instrument log books (beside each apparatus) to note any details that might not be in the writeup, the status of the equipment, and date and operations you performed on the apparatus. These logbooks will serve as guides to the next group to use the apparatus, as well as crucial information for troubleshooting should anything go wrong. They are meant to be a 'living record' of how and when the equipment has been used.

Also, don't forget your lab notebooks ...

Sunday, January 24, 2010

Saturday, January 23, 2010

HW1 solutions (mostly)

Here they are, except for problem 4. Hope to finish that off tomorrow ...

HW2 Bugfixes

Homework 2 has been updated (minor) - in particular, #4b was redundant and has been removed, along with a few typos.

Friday, January 22, 2010

PH253: HW2 #1

If you're a programmer, this may help with the first problem, as will this.

At some point in the problem, you have to find the root of an equation numerically. You can do this by any means necessary, including a graphical solution. Code solutions will please me though.

PH255: atomic spectra lab

If you are in PH255 (only), it is worth your time to check out the post below and read through the second PH253 homework set. Particularly problem 4, since it covers the same data analysis you'd want to do for your atomic spectra report ...

Of course, if you are in both PH253 and PH255, this is a rare chance to kill two birds with one stone.

PH253: Homework 2 is out

Homework 1 solutions will come out Friday afternoon some time; for now here's homework 2.

It should be shorter than the last one, but two things to note: there are a couple of nasty mathematical bits which I'll point out in lecture, and question 4 involves some basic plotting and data analysis, so it may take a little longer. Here is a copy of the plot needed for question 4. As for the plotting required: it can be a hand-drawn plot on graph paper if you like, or a fancy Excel/Matlab/Origin graph, whatever is easier for you. I'll give you the raw data used to generate the plot if you wish.

Tuesday I'll run through all the questions in case you're having trouble, and probably before that I'll post some hints here.

Thursday, January 21, 2010

Physics help desk / Textbooks

Free, and staffed by physics grad students. Basically, all of the 100-level physics tutors pool their office hours together to have a help desk of sorts staffed most of the day. Though it is nominally for PH10x, most of them will not mind if you come by with PH253 questions.

Also, straight from the senior purchaser at the supply store:
As of right now, we have 6 books at our Ferguson Center location. We do have another 12 books on order. They are scheduled to be delivered Monday the 25th.

Other ways to ask questions ...

So far, you have all figured out the email/SMS option quite well :-)

Another option: AIM, username
I'll try and keep the IM client fired up when deadlines are impending. I also usually keep a facebook tab open if you prefer that.

PH253: Next Tues class

We went through the quantum thermal radiation derivation very quickly today. On Tuesday, we'll start from the energy quantum hypothesis and derive Planck's result again, in a more methodical manner, and discuss its main features & implications.

For that, read up on black body radiation, e.g., Sect. 2.1.1-2.1.5 in the textbook.

Also, a new homework set will appear tonight some time.

Turning in HW or lab reports

You have a few options.
  1. If it is before ~6pm, drop it off at my Gallalee (110) or Bevill (228) office. You can slide it under the door if I'm not in. After 6 you can't get in Bevill without special access, and after ~8 you (probably) can't get in Gallalee.
  2. If it is before 4:45, put it in my mailbox in the main physics office, Gallalee 206. The staff leave and closet the office at 4:45.
  3. Scan it or take a digital photo and email it to me before midnight. Make sure you have the technology straightened out before, e.g., 11pm or chaos will ensue. Essentially any electronic format is acceptable, it is unlikely you'll pick one I can't read (and that is not a challenge ...).
The same goes, roughly, for PH255 lab reports. For those, electronic copies (PDF, Word, PPT, etc) are vastly preferred. Nearly any electronic format is acceptable.

PH253: Thursday's class

Thursday, we'll discuss thermal radiation, i.e., the black-body spectrum. Basically, we want to figure out why stuff glows when it is hot, how much it glows, and at what color. It is surprisingly tricky to do so.

We'll follow a little different approach than that outlined in the textbook, but with the same result in the end. If you have the textbook, it will be useful to have read sections 2.1.1-2.1.5 ahead of time. If you don't have the book, this will help for now (better links to follow).

I will deviate from the book's derivation and discussion mainly to tie in to what you've covered in PH105-6 already and to try to make the flow a bit more logical and useful for later chapters. In the end, we'll cover all the same material, just not quite in the same order. In particular, we want to start out by emphasizing the necessity of considering energy to be discrete and its consequences, since that is the bulk of the course material in the end.

For now we are done with relativity, but don't forget it -- it will come back again, and sooner rather than later.

Wednesday, January 20, 2010

PH253: Supe store fail

I realize the supe store is still out of the textbook, and that really sucks. They have more copies on the way. In the mean time, just about everything you need to know for relativity can be found in Ch. 1 here. That is ... you have all you need to do the current homework set already. Also, this.*

If you still do not have a copy of the book, see me after class. I will either give you a loaner or make photocopies to get you through the next days, i.e., quantum behavior.

*You should always assume that professors recycle questions, and see if you can find content they used in previous semesters. Just use it wisely, or the exams will eat you alive.

PH253: HW1 #9

You should end up with something like this:
x(t) =  \left(\text{prefactor}\right)\left[\sqrt{1 + \frac{F_o^2t^2}{m^2c^2}}-1\right] 

PH253: Thursday's class

Thursday, we'll tie up a few loose ends in from the relativity chapter and move on to quantum phenomena. In preparation, please read 2.1.1-2.1.5 in Pfeffer & Nir for Thursday. Note that if you click on 'event details' in the google calendar, the reading assignments are already there.

PH253: Homework 1 hints

Mostly this is what I ran through quickly at the end of Tuesday's class, but here you go. A bit more extensive help on the tougher problems. The weekly homework hints will not always be this extensive (hey, it is like the first week), but they will typically come just a couple of days before the due date to encourage you to mull them over on your own first. Technical note, this may look weird in an RSS feed due to my use of an equation typesetting plug-in in a few places.

Thursday, January 14, 2010

PH255: no class on 18 Jan 2010

As you may be aware, this coming Monday (18 Jan 2010) is MLK, Jr. day. PH255 will not meet on 18 Jan, and you will have until the following week (25 Jan) to turn in your first lab reports.

Even though you're given the extra time ... don't put it off. It is a slippery slope.

PH255 e/m experiment

Relevant relativistic considerations. (Note: this link will probably only work on campus.)

PH253: Homework 1 is out.

Here you go. It is due a week from today (21 Jan 2010) by `the end of the day.' Take that to mean 11:59pm if you like.

We'll set some of these up next week Tuesday to help you get started, and I will be posting some hints here as well.

PH255: error analysis example

A short post about analyzing the motion of a Focault pendulum, with error analysis.

Things you should know about

Wolfram integrator.
Derivative calculator.
Wolfram functions.
Google calculator one, two, three.

PH253: Example relativity problems

You can find some example problems & solutions: here, here, here, here, and here (Ch. 1).

Since these are all questions I've asked in the past, it is a good bet I'll ask similar stuff in the future. For instance, in the first homework set that will come out on Thursday some time.

PH255: lab notebook

An excellent guide to the care and feeding of a lab notebook, courtesy MIT's open courseware.

Wednesday, January 13, 2010

PH253: philosophy & relativity

Interesting notes from NYU-Poly on the philosophy or relativity. I highly suggest looking at the second set of notes, discussing why relativity was more or less inevitable.

Tuesday, January 12, 2010

PH253: MIT open courseware

Some of the MIT open courseware related to relativity might be useful. We'll only spend a short amount of time on relativity (rather than a whole course as they do), so obviously we won't cover everything they do. Still, some useful bits.

PH255: tutorials on lab writeups

Here's a good site with example lab reports, tutorials, and all sorts of goodness.

PH255: lab manual

It turns out that I had set some permissions incorrectly, and the password protection for the lab manual was not working correctly for a while yesterday.

Rather than messing around with linux permissions and .htxxx files (it is not 1990 anymore), I've just password-protected the PDF for the lab manual itself. All of the links at right are now unrestricted, but when you download the lab manual, you'll need a password to open it.

Same password I gave you yesterday in class ...

PH253: slides I'll use on Tuesday 12 Jan

Here are the slides I'll use in class. Partly official course intro stuff, mostly figures to aid in relativity explanations.

PH253: relativity notes

We'll be starting out with relativity for the first 3-4 classes (Ch. 1 of your text), and you might find some notes I wrote [23Mb PDF] useful as a supplement. The first chapter of the notes covers relativity; the rest should be review, but might still be helpful. The notes are for PH102, but that class actually covers relativity in about the same way (albeit a little less 'mathy').

There are also solved problems at the end of the chapter, which might look a lot like the first homework set ...

PH253: Syllabus and important information

You can find your syllabus here, which contains important information about grading and such things. You will probably also want to check out the course calendar, which you can subscribe to if you wish.

By the time you read this, we will have had the first class already, so you probably know what's going on by now. For Thursday's class, please read through Ch. 1 in Pfeffer & Nir, at least as far as section 1.3.6.

The first homework set will appear on Thursday, so rest easy for now ...

Monday, January 11, 2010

PH255: Lab safety

Something you might want to peruse: a lab safety/etiquette orientation talk I've given a few times at the MINT center here on campus. Most (but not all) of the things apply to PH255. I should have a PH255-specific version by next week's class ...

PH255: Lab manual / error analysis

The PH255 lab manual is a work in progress, but I will be keeping the current version online here. The lab manual includes the course syllabus and schedule.

You will need a password to access the PH255 lab manual (which I will give you in class today). It is annoying, but necessary for me to restrict access to class members due to my (temporary) use of copyrighted material.

You might also find the lab report templates useful, there will be more of these in the next week.

Also, an interesting introduction to error analysis, courtesy a UA Physics alum. His site is highly recommended, a lot of good physics discussions to be found.

Finally, some resources you might find useful. Not all of them will work at UA (we don't have subscriptions), but enough do that it is worth checking out. You may also want to have a look at the rest of the MIT 8.13-14 course content, there are some good laboratory procedures, explanations, and related documents. We'll be doing some of the same experiments in PH255.

Friday, January 8, 2010

PH255: Why keeping good lab records is important ...

Actually, there are many reasons. Here's another good one - the authors were forced to retract a high-profile paper after they lost their laboratory notebooks and could not reproduce earlier experiments. From the retraction:
"Regrettably, through no fault of the authors, the lab notebooks are no longer available to replicate the original experimental conditions ..."
 Another good reason is that dated & signed laboratory notebook entries can be critically important in patent cases, should you discover something useful.

Tuesday, January 5, 2010

Welcome to PH253 & 255!

This is where you will find all the information you need for PH253 and PH255 this semester.