Final exam scores

Your final exam scores are on moodle ...

The final course grade posted is basically correct, but subject to an audit of my master spreadsheet. Very few were on a grade boundary (either +/- or a full grade) as it turns out, so probably nothing will change, but I want to be on the safe side and check everything a few more times.

Now is a good time to check that your HW, lab, and quiz grades seem correct. If you are curious about what grades you are missing (e.g., HW not turned in), send me an email.

Final exam breakdown

Individual final exam scores will be on Moodle imminently. Must make one more check of grading ...

Final course grades will be posted sometime tomorrow afternoon. I need to do a thorough review of everything before I'm willing to posit final final grades, and carefully audit everything. You can calculate from Moodle what you should receive, and there is a 99% chance you will be correct. Keep in mind Moodle does not include random bonus points I have given over the semester, for instance, and for this and other reasons the Moodle grades are not 'official.'

Incidentally, the overall course grade is a very complicated case. You know, a lotta ins, a lotta outs, a lotta what-have-yous. Mostly when you are on the narrow borderline between grades ... there are often some very tough calls to make.

Let it suffice to say that I usually err on your side if there is a chance for ambiguity, but it is rarely (rarely) necessary. Strictly by the numbers in the end.

e-homework chaos

A nice post about how having emailed homework can suck.

Pretty much everything she mentions has happened this semester, and then some ... but it all worked out in the end.

Also, she missed a lot of other chaos-inducing problems, like email addresses that give no hint as to the sender's address coupled with no discernable name within the attachment. Thanks to what I think is better-than-average handwriting recognition on my part and good email search capabilities, this was not much of an issue this semester.

In other news, the finals are graded. I have not tabulated the results yet ... probably in another couple of hours, I will post here when I have results for you to see.

Final Exam

Your final exam is here, if you want to look back at it ...

Also, moodle is now up to date with everything except the final exam. Labs 9, 10, and 11 were from the rocket competition:

L9 = competition performance
L10 = quality / correctness / cleverness of code
L11 = quality / cleverness of the physical setup and measurement system

FYI, the grading breakdown (weighting, number dropped, etc.) can be found here.

Moodle

HW 12 grades are now up on Moodle. The only grades missing are from the rocket launcher project, which counts as 3 lab grades.

Excepting the 3 rocket grades, you have 8 lab grades in so far. I will add in the 3 rocket grades (performance, code, and hardware) and drop the lowest 2 grades overall (for a total of 11 lab grades). I should have this done late Tuesday or early Wednesday.

After you finish the final exam tomorrow, you can check with me to see that your grade distribution is accurate - e.g., missing homeworks and labs. If you don't see this in time, send me a short email and I'll let you know what grades I'm missing from you to make sure everything seems to be correct.

I will probably have final grades done by Friday; I'll post here when I have everything finished.

Formula sheet

Here it is.

Draft anyway; some proofreading remains.

Review Session TONIGHT

Room 203 Gallalee, the usual classrom, 6-7pm.

Come bearing questions ...

Final Exam

One of you asked about the final exam details. Below is what I said.

The review session will be Monday evening, I'll post here when it is finalized. I'll also provide the formula sheets, probably on Sunday, along with more detail. It will be easier than any of the other three exams I gave ...

It is going to be a larger number of much easier problems, much like the example problems in the chapters. Only chapters we covered in class are on the exam, and nothing we covered after exam III is on the exam.

It is going to be something like 8-10 fairly easy problems that you need to solve in about 15 minutes each, rather than the 4-6 hard problems that take 30 minutes you had on the previous exams. You will have a choice of problems, so it is reasonable to skip over a couple of chapters and just not choose problems related to them.

My suggestion would be to try to solve the sample problems without looking at the solutions at first. Basically, the exam will reward knowing the basics really well. I will try to make the problems very similar to the level of practice problems. After that, I would try the problems on the sample tests I posted - mostly easier problems than we have been doing.

You'll get a formula sheet which is fairly comprehensive. I'll try to post it as soon as I can, but it might be Sunday before I get it done. It will be a combination of the formula sheets from the first three exams. You can bring in two sheets of paper with your own notes.

We made the news ...

Video of the contest on the Tuscaloosa News site.

UA News writeup.

And, Mr. Cecil is on the front page of the "B" section of Friday's Tuscaloosa News. Very cool. Try to save him a copy of the paper if you can :-)

Reminder: no recitation today

Also, I will hold a review session Monday evening some time. Still working out the details, I'll post here when everything is settled.

Reminder: code submission

Each team owes me code ... soon.

Don't worry about dependencies, libraries, etc. I'll figure it out.

Rocket Contest

Well, I was pleased, and had a good time :-) I thought it went well, and you all did a great job. The visitors were pretty impressed with what you were able to come up with, and in particular the variety of solutions presented.

By the way: no one will come out of this with a bad lab grade, I was impressed all around. Even if you didn't get as many 'hits' as you would have liked, it was clear you all had solid approaches and took the task seriously, and that's worth a lot.

Currently, I'm uploading many photos and some video from today, but I'm not quite finished yet ... I'll post some links here when it is finished. Keep your eyes on the Tuscaloosa news, they may run a story based on the video and pics they took today.

Also: I've decided you can keep the launchers, sensors, and laser pointers - your lab fees more than paid for them, and at this point you put a lot of work into the customizations. I do need the voltmeters back if you still have them though ...

In the mean time: here is (1) a UA news bit, (2) a short video of a successful shot, thanks to Marcy Huey's fine camera work, and (3) a listing of several other videos, including team Red Scare's propaganda.

(All videos are AVI straight from my camera; editing and conversion to mpeg should happen this weekend I hope.)

Last-minute things for the competition

Last minute preparations and information ....

Things: Tomorrow, I will bring the following items, at least:

• USB extension cable
  
• tape measure (verify ceiling height, etc)
  
• camera
• soldering iron (sensor repairs)
  
• stopwatch (elapsed time between shots)
  
• target

What to bring: The launcher (duh), position sensor, and the computer running your calculations. If you need a computer for tomorrow, you'd better let me know soon. Like right now.

Press: It is not clear if press will come or not - they won't know themselves until the last minute. They have been invited, so we'll see what happens. If they do show up, it would be nice if a few of you were a bit early to the competition so they can ask you a few questions. Obviously this is optional, but the basic point is, 'show up early, and there is a chance you'll be interviewed.'

Visitors: There are going to be a number of random visitors tomorrow. Pay them no mind, go on about your business :-)

Location: Shelby L107. This is not the same as 107, a lecture hall you may have had classes in.

Directions: from the rotunda entrance, go left. Continue down the hallway until you reach the breezway. Go through it and into the next hallway. At the dead end, turn right. L107 is on your right. I will have a few signs up to guide you.

Timing: We might be done by 12:30, it is hard to predict. We will not go beyond the normal class period.

Grading-related: Remember that you need to turn in your source for the trajectory calculations. Please try to do this by the end of Friday.

Ok ... that is all I can think of right now. The contest will be pretty relaxed, but we will have to be efficient - with 5 teams and multiple shots, it will take a while.

Physics Majors on Facebook

Join us.

Quiz 8 & 9 solutions

Well, answers anyway. Almost everyone aced quiz 9 (thermo). Quiz 8 was not quite so great ... but I think now the answers will be clear to you.

Moodle update coming shortly (give me like 30min) so you can see your quiz results.

Exam III solutions

Here you go. Let me know if you find any errors.

Physics Majors event

Just FYI, since a number of you are physics majors ...

---

All PHYSICS MAJORS!!!

Do you actually know other physics majors?? Yeah, that's what I thought. So come to the meet AND greet.

FREE FOOD! Yes, completely free. In fact, it will even be surrounded by nerds. So come.

DETAILS:
Who - YOU....hopefully...
What - Meet the other people who share your uniquely awesome interests
When - FRIDAY, as in THIS FRIDAY of dead week. which is May 1st, just fyi. 3:00-5:00pm
Where - Room 109 in Gallalee (obviously)
Why - because Tara and Ted were upset that we didn't know all of you

So, it'll be awesome, especially once you get there :)

-Your Fellow Physics Majors, Tara and Ted - and kind of the Society of Physics Students, kinda -

Old PH105 Exams

I put up some old PH105 exams for you to look at - some with answers only, some with solutions.

They are easy problems compared to what you've been doing, but good practice nonetheless. For the final it will be advantageous to be able to quickly solve a larger number of straightforward problems, as opposed to our usual exams where you have to solve only a few tough problems.

Tuesday's class

Today we'll go over some review questions, and spend an hour or so practicing for the rocket competition on Thursday.

Also, I had completely forgotten about Exam III solutions until one of you reminded me in the comments ... I'll get on that and have something for you by Thursday at the latest, along with solutions to the example problems from last week. The end of the sememster is proving a bit more painful than expected, so I am a bit behind ... apologies.

I have put up some very silly flyers to advertise our little contest. If you feel so inclined, you can do some of your own advertising as well. A number of faculty and staff members have expressed an interest in coming to watch the competition, mainly because they think what you've been up to is very neat. Probably, they are jealous.

(I may have mentioned this to the University Relations office. There might be local press.)

Finally, I'll post directions to L107 Shelby soon. You can find a handy map here. Note that you are going to L107, which is not the same as plain old 107. (Grab the 'emergency evacuation plan' map, it is actually much clearer. And possibly quite relevant, one never knows.)

Common Misconceptions

Nice link courtesy of Alex.

I liked this bit at the end:

"A telling comment on the issue of fairness in teaching elementary physics: Two students asked if I was going to continue asking them about things they had never studied in the class."

The answer is always this: HAHAHAHA yes.

(I am at least mostly kidding. There won't be any material on the final that we didn't cover in class, but there will be relatively simple situations that are new ... but situations which can be handled straightforwardly with what we covered in class. No surprises.)

Quiz tomorrow (Friday)

Reminder: there is a 5-question multiple-choice quiz on Ch. 18 tomorrow.

The content of the quiz will be restricted to the sample problems in Ch. 18 - if you can do those, you are good to go.

In addition we'll go over some practice problems for the final (the ones I put on the board today).

Today's class ... probably

I am mulling over a change of plans. On one hand, we should do more thermodynamics. On the other hand, you will all end up taking it again anyway ...

So here's my thought: if you agree to do a bit of reading on your own and take a short multiple-choice quiz on Ch. 18 on Friday, we'll spend tomorrow doing final exam review instead. Nothing we covered after Exam III is on the final exam, so this is a reasonable gamble for you to take, I think.

Anyway: tomorrow you have a choice - lecture on heat and thermodynamics, or do practice problems for the final. Since our PH125 Deathwatch is in its final stages, here's what the rest of our time looks like:

This week:
Thurs: practice or thermo + concept test + rocket testing
Fri: pending your vote for Thurs, possibly a thermo quiz. Post-mortem on the concept test (i.e., where are you as a whole having the most trouble). After thinking about Crito's comments & link, I'll also point out the ones I thought were tricky and why ... where does intuition seem to fail?

Dead Week:
Tues: final exam review, dry run for rocket competition
Thurs: rocket competition
Fri: no class

Thursday's class

Thursday, we'll be doing our requisite post-assessment. Remember that concept test you took at the beginning of the semester? Basically, we'll take it again and see if you learned anything :-)

It should take about 20min, and there will be grade-related incentives for doing well.

We'll also go over a bit more thermodynamics (heat and energy), and leave some time for you to do some 'practice shots' for the rocket competition.

Evaluations are today

If you were planning to stay home this morning ... we are doing course evaluations during the second half of class. FYI.

Last HW set

Here it is.

As I noted before, this one is optional - you don't have to do it, but if you do, it can replace your lowest non-dropped homework grade. Also useful for preparing for the final exam ...

Rocket launcher code

Linux kernel module to control the launchers. Should be portable ...

Update: code for OS X here. Pretty readable & hackable. You are not by any means required to include rocket launcher control in your code, this is just in case you're interested in trying it for 'fun.'

Exam III details

(Update: if you checked Moodle within the first ~10 minutes of my posting this, I may have been updating the overall grade calculations at the time. Anything after 02:35 is accurate.)

I finished grading your exams, albeit under somewhat savage time pressure these last days. That means I haven't had time to process the results very much, but your raw scores will be available on Moodle in the next half hour or so. Anyway, the results:

Average: 73%
Std. Dev: 14%
Hardest questions: 2,3,4

Based on these numbers, I will scale it a bit. Probably, this will mean adding something like 5-7% to your test grade, but I haven't decided that yet. I will scale it such that the class average is at the C+/B- border with a favorable distribution. Details of this should be clear by Friday ...

Despite the averge being a little lower than I had anticipated, I am happy with the results, having seen how you went about the problems. By and large, you know what you are doing, and it was mainly time pressure and simple things that tripped you up. We'll go over the solutions in detail today in class. As a peace offering for giving another bastard exam, we will also devote a good amount of time to rocket targeting and such things and less time to lecturing.

Random plots for your perusal:

Exam III grading

I hope to have the exams graded and back to you by Friday ... I would say Thursday, but I have a visiting grad student coming in tomorrow. 

In any event: you'll have them before the weekend if all goes according to plan. Don't freak out, it looks pretty good so far. I will scale the exams if necessary.

Most likely on Thursday we'll go over the solutions in class.

Exam III

Here it is. I'll try to have solutions out by the end of the week.

Exam III is IN 2 HOURS

Seriously, people have forgotten before.

Bring a calculator. And writing implements. You won't need anything else.

Have some coffee. Bring music (with headphones) if you think it will help.

Don't forget that you can ask me questions during the exam, and I am somewhat likely to give helpful advice.

Today's office hours

Today I have a meeting that cannot be avoided, and it overlaps the posted office hours ...

If you want to come by today, I'll be in my Gallalee office from 5pm until the review starts.

Solutions to Friday's quiz

Here is Friday's short quiz, and a solution key.

Exam review session

How about 7pm, Monday 13th April, in our normal classroom.

I'll go over some example problems and more details on what precisely will be covered. Come with questions.

HW 12 solution

Here you go. Let me know if you find any mistakes or have any questions.

Formula sheet, Exam III

Here you go.

Working on the HW12 solutions now, I'll post here when they're finished.

There will probably be a review session tomorrow (Mon) evening at 7pm ... I'll decide tonight and post details.

Studying for the exam ...

I hope to have the formula sheet for the exam and the solutions to HW12 posted by mid-afternoon tomorrow (if not sooner).

Last problem

the possible modes of the string have

f = (n/2L)sqrt(T/u)

where n is an integer, L is the length of the string, T its tension, and u the density. You know T=mg, tension is provided only by the hanging mass. You also know f is fixed by the resonator attached, f=120Hz. The only variables are m and n.

If the two given masses m1 and m2 work, but nothing in between does, then they must be adjacent harmonics - one is n and the other is (n+1).

Plug that into the above equation separately for both masses, set equal, and you can find n. Once you have n, you know everything in the equation above except u ...

Homework 12

Remember, today's homework can be handed in as late as tomorrow night without penalty.

Checking your code

In case you want to check that your code is working ...

If you use the drag equation

F_d = \frac{1}{2}\rho C A \vec{v}\cdot\vec{v}

with starting parameters

v_x=31\,\text{m/s} \\
v_y=35\,\text{m/s}\\
m=0.046\,\text{kg}\\
A=0.00143\,\text{m}^2\\
\rho=1.225\,\text{kg}/\text{m}^3\\
C=0.25

then you should get a range of 126 meters over level ground (and 221 meters with C=0, i.e., no drag).

16.25

You can find the velocity of a wave at any point along the string if you know the tension and linear density. At any point along the string, the tension is provided only by the rope below that point - you can't push on a rope.

Finding the time is handled just like the last problem in HW10 - t is the integral of dy/v(y), with the limits being the two ends of the rope.

16.34

The latter parts of this question will make more sense after tomorrow's lecture, if they don't from reading the chapter. To get you started:

The average power transmitted along the string is

P = \frac{1}{2}\mu v \omega^2 y_m^2

Here you don't know the velocity, but you can relate it to the tension and linear density.

If you superimpose two equal-amplitude sine waves together of the same frequency (so kx-wt is the same for both), but they differ only by a phase phi, the resulting wave is given by Eq. 16-51:

y(x,t) = \left[2y_m \cos{\left(\frac{\varphi}{2}\right)}\right]\sin{\left(kx-\omega t + \frac{\varphi}{2}\right)}

The amplitude then depends on the relative phase as well as the amplitude of each wave. If the waves are in-phase, the total amplitude is just double, but if they are 180 degrees out of phase, everything cancels.

Thursday's lecture

Ok, continuing with waves (Ch. 16/17) has won the poll ... so that's what I will talk about tomorrow.

That implies you should look over Ch. 16 and 17 before class if you can.

Standing waves in your shower

Important application of waves.

Research Work

If you like coding, and want to pick up some research work, let me know. Prof. Williams is in need of students to help out, particularly those who know some Java (though good coding skills are generally valuable, you can pick up the Java you need).

Cool factor: her experiment is a giant neutrino detector in Antarctica, see link above. (Pun intended.) Very exciting work, and you would have a chance to make a real contribution to a world-class international research project.

Let me know if you're interested, or contact Dr. Williams directly (via link above).

Current Grades

Moodle has been updated, your grades for HW10 and labs 7-8 are now there. Everything except HW11 is now up to date.

HW11 should be added by the end of the week, and HW12 over the weekend so that your grades are current going into next week's exam.

(FYI - Lab 6 = project memo; Lab 7 = sensor calibration; Lab 8 = group talks)

Thursday 9 April 2009

By the way: short quiz on Thursday. It will not present a problem if you have read Ch. 16.

Really, it will be easy. Just a heads-up.

Even-numbered problems for this week

Numerical answers for the even-numbered problems this week:

Due tonight:
15.24 x < 0.23m
15.56 T~2.0s; 18.4 N-m/rad

Due Thursday:
16.34 10W; 20W; 40W; 26W; 0
16.60 0.846 g/m

Random hints:

15.111 First, for the linear acceleration, you can always just apply the center of mass equations:

m a_com = F_net

Even though rotation is involved, the center of mass stuff still works.

For the second part, you want to find the net torque to get angular acceleration. You have a force F applied some distance x from the point at which the bat is held (point O), and that's it. The distance x is 2/3 of the length of the bat, given. This torque must equal the angular acceleration (alpha) times the moment of inertia about the end of the bat (so (1/3)ml^2).

Finally, if the bat is rotating after the hit, the angular acceleration implies that the tips of the bat have an additional acceleration in the tangential direction. If no one were holding the bat (or if it is held lightly, as the problem states), the rotation will just be about the center of mass. The tangential acceleration at the ends of the bat has to be (alpha)(L/2) in that case. In the end, this acceleration due to rotation acts in the opposite direction compared to the acceleration of the impact of the ball itself. At the "sweet spot" these two cancel exactly, and you shouldn't feel anything when you hit the ball - if you hit anywhere else, it 'stings' because of the net acceleration at your end of the bat.

In other words, there is (say) a forward acceleration due to the force of the ball hitting the bat, and a backward acceleration at the hands due to the resulting rotation. You'd like the two to exactly cancel for your force to be used most efficiently, which is just what happens at the sweet spot.

Thursday's class

So I'm torn about what to do on Thursday. Therefore, I'm going to let you vote - we can continue with what's in Ch. 16 & 17 (which is probably easier) or do one of two other topics which are a bit more challenging. All three are very relevant topics you *will* see again, so in that sense there is no wrong answer ...

We should continue on with wave motion, but we did cover enough that we could pick up the missing bits during dead week - what is left is mostly pretty straightforward. I suspect that if you read the rest of Ch. 16 and parts of Ch. 17 you can pick most of it up on your own - there is not a huge amount of depth there.

We could also go a little deeper into resonance, which we only touched on. This would involve looking at driven oscillations and expanding our investigation of damping. I think this option is more challenging, but probably a bit more fun.

A third option is to look at coupled oscillations. This is not unrelated to the outstanding material on standing waves, and would get into things like synchronization of oscillators, the speed of sound in materials, and Fourier analysis of complicated waves.

Only the first option is really covered in the textbook; none of these three would show up in any serious way on the final. Vote in the poll at right if you have a strong interest one way or another; I'll lecture on whichever topic has the most votes as of Wednesday evening.

Hint on the 2nd homework problem

When you have the torsion spring connected to the pendulum, you don't have any sort of simple equation you can use any more ... you have to just add the torques up.

First, you have a torque due to the weight of the hanging deal, something like (weight)(radial distance)(sin of inclination angle) if you're not into vectors. That pulls the thing back to equilibrium.

The torsion spring provides a little 'kick' in the opposite direction to keep it going. The torque provided is just proportional to the angle, (kappa)(theta)

In total you have then (weight)(radial distance)(sin theta) - (kappa)(theta) = net torque. The net torque must be the moment of inertia times alpha, the second derivative of angle with respect to time. If you use the low-angle approximation sin(theta)~theta, you can recover an equation for simple harmonic motion: angular acceleration is (omega)^2 times angle.

Twitter

The poll indicates that you are not wild about Twitter ... which I can buy.

For that reason, I won't post anything on twitter that isn't also posted here. That doesn't mean I won't post anything to twitter, just that you won't miss anything essential by not following it.

Today's bit of randomness

Physics is good for anything. Anything.

Exam III

As it turns out, you have an exam one week from today. The format will be much like the last exam - you will have a choice of problems (e.g., solve 5 out of 8), you can bring a formula sheet, you have 2 hours.

The exam difficulty will be somewhere between the homework problems and the example problems in the book (see below) - not as difficult as the homework (though similar to the non-bastard problems), but harder than the example problems. More details, including sample problems, will follow.

The topics covered are:

• 10.6-10 Rotation
• 11.2-4,6-11 Rolling motion, Angular momentum, torque
• 13.2-8 Gravitation (excluding central force laws, only the stuff in the text)
• 15.2-9 Oscillations and simple harmonic motion
• 16.2-8 Waves, pt. 1

Basically, chapters 10, 11, 13, 15, and 16, but not all sections are included. Owing to Honor's day this Friday (no class!), there will not be much time for review. Studying the homework solutions and example problems in the text will serve you well. I'll be online most of the weekend and available Monday before the exam (13 April) most of the day for questions.

There will be roughly 2 questions from each from:

• Ch. 10-11
• Ch. 13
• Ch. 15
• Ch. 16

If you have been understanding the homework problems, you will probably be fine.

Tomorrow's class

(1) Waves: read chapter 16 (or at least skim it)
(2) Problem-solving: homework for this week, more harmonic motion
(3) More rocket madness

Numerical answers

Preaching to the choir.

HW 11 Solutions

Here you go. They need some proofreading, but they are basically complete.

Note that for the first problem ScienceWorld already has a great solution up, so I just linked to it.

HW 12

Homework 12 is out.

Problems due Tues 7 Apr: 15.24, 15.56, 15.111
Problems due Thurs 9 Apr: 16.25, 16.34, 16.35, 16.60

We'll spend plenty of time during the week going over these problems before they are due.

Keep in mind that there is no class on Friday for Honor's day.

Homework via email

FYI, I've created a separate email account just for homework ... since my inbox tends to get flooded when homework is due.

I mostly plan on using this for next semester, since we are already nearly done and old habits die hard. It is active right now, and I will be checking it ... and it would make things more efficient for me if you sent your homework to this address.

However, you can keep using the normal email address for the semester if you would rather, it isn't a problem.

Today's recitation

Today, we'll have one more presentation, if all the group members are around ...

After that, we'll work on homework problems - both the ones from last night, and the ones due tonight.

HW10 solutions

Here you go, all but the last one. Hope to have that solution out over the weekend ...

HW 11: 15.106

Problem 15.106
a) Translational - 1/16
b) Rotational - 1/32
c) it is a proof ... show that acceleration is proportional to -(const) times position.

HW 10 solutions

Sigh, I only have the first two problems done so far ... I will be working on them tomorrow and hope to finish them up. Here you go.

At the very worst, I will scan my hand-written solutions tomorrow

Following twitter updates, if you're in to that sort of thing

I am putting out some homework hints via twitter now, just as an experiment. You do not need a twitter account to follow these updates.

(1) the twitter updates will also be mirrored as my facebook status. You can look at my wall on facebook and see the same stuff.

(2) go to http://twitter.com/pleclair periodically

(3) get an RSS feed of my twitter updates, then you can read them in your aggregator of choice. You can get a facebook application to bring RSS feeds to your facebook homepage, fyi.

(4) (update:) follow the little twitter-box on the right side of this page ... type "pleclair ph125" in the box and hit "set."

One obvious question is why bother with this. I don't know, actually - it may not be worth the trouble. My thoughts:

(a) it is easy to follow twitter updates on a mobile device (if you have enough text messages in your plan). this means you can get HW hints and stuff without having to be near a computer.

(b) it takes me like 5 seconds to make a twitter post, whereas even on the blog I tend to spend 5-10min or so composing a post. If it is easier for me, I am likely to do it more often (even under savage time pressure), and the more help you get. (The reason I switched to a course blog in the first place was speed & frequency over static web pages.)

(c) On the other hand, having this blog is probably plenty already. I may be overthinking this problem, or going toward too many channels of information.

Physics scholarships

If you are a physics major, it is not too late to apply for a scholarship.

Specifically, the E. Scott Barr scholarships have not yet been awarded. Tell your friends.

Twitter

So, I am on the twitter (@pleclair). I was thinking lately it might be useful for posting quick updates for class, e.g., HW hints or notifications of new assignments. (Though I joined for other reasons, mainly because all the cool kids were doing it).

Would this be a useful way to disseminate small bits of course-related info?

(N.B. - it is easy to use twitter to update your facebook status and vice versa. Joining is not the time sink I thought it would be.)

HW11

A little later than hoped, but here is HW11. Based on what we covered today, and sections 15.1-15.4 in the textbook, you should now enough to do all but 15.63 already. We'll go over some of the first ones in class on Thursday. Text-only version of HW11 below.

Problems due by the end of Thursday, 2 April: 15.26, 15.37

Problems due by the end of Friday, 3 April 15.55, 15.63, 15.106

HW11

Homework 11 will come out some time later today (Tues). They will all relate to Ch. 15 in your textbook. If you want to get a jump, read through Ch. 15 and study the example problems. This week's homework will not be quite as bad as last week's ...

As I mentioned earlier, there are no problems due this week until Thursday, since I'm asking you to give talks later this week.

Talks for Thurs/Fri

Thursday and Friday of this week, I would like each group to give a short oral presentation on their progress with the rocket project so far. A few formal details:

• It is a group presentation - designate a speaker, or take turns. Either way.
• Minimum 10 minutes, maximum 15 minutes per group
• Powerpoint/etc are not required but may be used if you like.
• We will start on Thurs and finish these on Fri. Pseudo-random numbers will choose your presentation order on Thurs.
  

As for the content, I would mainly like to see you present your basic approach to the assignment, where you are now, and what you think you still need to do.

• What is required for the project?
• What experimental quantities must be determined, and what is your progress?
• What parameters must be controlled, and what is your approach?
• What are the relative errors & their sources?
• How will you determine the trajectory/angle at launch time?
• What problems are still outstanding?
• What solutions are you still working on?

I'll discuss this a bit more tomorrow, but hopefully you get the idea. This is really just meant to be a reasonably informal (but not too informal) status report, like an oral version of your memos, updated with all your recent progress.

You can keep the talk fairly general in some respects - I am not asking you to give all your secrets away to the other teams, but I do expect you to give concrete statements about what you have done. For example - quoting your launch velocity and error or discussing the algorithm you are using for your calculations is fairly general. Giving away your trick for highly accurate positioning of the turret or optimizations to basic algorithms is not necessary.

Grade-wise, this will count as a lab.

Tomorrow's class

Tomorrow, we will begin Ch. 15, "Oscillations," and continue with this material for the rest of the week. Start reading :-)

We will defer Ch. 14 on fluids until the end of the semester, for two reasons. First, the material is a bit fluffy at the level presented in the text. It will be nicer to cover this during our last week, when the PH125 Deathwatch begins. Second, I think it is more logically consistent to move on to oscillations now that we have covered all the core topics in Mechanics.

Next week, we'll begin Ch. 16, "Waves I" ... and the week after that is Exam III (April 14).

HW11

HW 11 will come out later today, but there are no problems due until thursday.

That is, I'm giving you the day off from homework tomorrow so you have some time to work on your presentations for Thursday & Friday. I'll post details about the presentation requirements later today to help you get started.

Friday's class

We'll delay harmonic motion until Monday. Tomorrow we will spend some time solving homework problems, and a little bit of time discussing the rocket project and your (informal!) presentations for next week.

For the rockets, I'll sketch out some algorithms and pseudo-code you can use to get the trajectory and then find the launch angle (some of you have already done this). There will be extra points for particularly clever solutions, so it is worth some time to optimize your calculations. I heard talk of pointers today, and it pleased me :-) I should mention that spiffy user interfaces and graphics are not necessary, we would rather focus on cleverness of calculation and efficiency for now.

I will also introduce you to the position sensors you'll be receiving next week (one per team) that you can use to determine the target's range and height.

Homework due at what time?

So I have said that the homework is due at the end of the day formally, i.e., 11:59pm on the day in question. That is still true. There are 'grey areas,' however.

Less formally, it will not be considered "late" if I am still awake after that time. Tonight that means you have about another hour or maybe 90 minutes. In general, 1-2am is a reasonable bet. If you're staying up until 2am doing homework, that is hardcore, and I'll give you some leeway ;-)

Minimal points are taken off for submissions arriving before I begin grading the homework, usually a day or two after the due date. Things happen, you get busy. Don't make it a habit.

Submissions after I have already posted the solutions online are taken on a case-by-case basis, but will receive some credit for at least bothering to copy the solutions. Learning by osmosis can work sometimes.

The message here is again: always turn it it. It is never given zero credit.

HW 10 question 9

Updates to the hint to fix the glaring error. (with the proper link this time)

I might try to revise it a bit more to make it less terse ... I'll post here if I get that done.

Even-numbered problems for this week

13.16 3e-10 N
13.68
a : 92min
b : 7.67e3 m/s
c : 5.77e10 J
d : -1.18e11 J
e : -6.0e10 J
f : 6.64e6 m
g : new period ~89min; difference ~150 sec. Since Picard was initially behind by 90s, this means he is now ahead by about a minute or so.

I should double-check my numbers on #68, since I did it a bit quickly ... but I believe they are correct. Update: they are correct after a double check, except g) is closer to a minute.

Problem 9 / HW10

There is a mistake in the beginning of the hint ... the first expression for velocity v(y) is inverted.

I will fix that and clean it up a bit in the next hour. The proper expression for velocity is

v(y) = (const)*sqrt[y/(R+y)]

where "const" involves G's, M's, and R's. Possibly even a 2.

Keep an eye out here for the revision soon.

Constraints vs. real forces

It is confusing sometimes to realize what is a real, live force, and what is not. For instance, circular motion. You draw a free-body diagram, and sum up the forces. This is one side of the equation. The other side is your constraint on the motion, namely, that for a circular path a net force of mv^2/r is required. Sometimes, we call this "centripetal force," and that is highly misleading. It is not a real force, but a fictitious force, which basically means that if you impose the requirement that the motion is circular, an specific constraint is placed on your force balance.

When you think about it, your force balance always has a constraint, namely, that the net force has to result in mass times the acceleration required to produce the observed path. For a straight line path, zero acceleration, the force balance is zero: equilibrium. For a circular path, the required acceleration is v^2/r, so if circular motion is observed then the net force divided by mass must give v^2/r - if not, then you don't have circular motion. For generic paths, it is more complex: an observed path constrains the force balance, but it depends on the speed along the path and the local radius of curvature.

The confusion is, in my opinion, largely an unfortunate artifact of history and terminology. There is no centripetal force, it is just a boundary condition on your force balance that enforces circular motion.

Anyway: here's what I wrote to one of you earlier. We'll touch on this again in class tomorrow.

In the middle of page 336, in Equation 13-12 (F_n - m*a_g = m(-(omega^2)R)), why do we have a negative sign on the right side. I feel like gravitational acceleration (weight) and centripetal acceleration, both being directed toward the center of the earth, should have the same sign. Here, if you put them on the same side, they have opposite signs.

It is a little bit confusing because the centripetal force is not a true force in its own right, but only the *result* of all other forces. The language in the text is confusing in this regard.

What it is saying is that there are two real forces acting: the normal force acting upward, and the gravitational force acting inward. Since the box follows circular motion by virtue of being on the earth's (rotating) surface, we know that the *constraint* on the force balance in magnitude is that it must sum to mv^2/r. The constraint on direction is that it must be directed radially inward to result in a circular path.

Saying that "centripetal force points toward ..." or "the centripetal acceleration points ..." is misleading. The left side of the force balance contains all the real forces; the right side contains the constraints on the motion from the known path:

(1) straight line: constraint is that forces sum to zero
(2) circle: constraint is that forces give mv^2/r to be consistent with the path, pointing radially inward.
(3) general: what we derived a while back; sum of forces relates to the rate of change of speed and the local radius of curvature of the path.

So it is OK that they have the same sign - it says that the net force balance comes out in favor of gravity, and the net force (which we call the centripetal force, misleadingly) points in the same direction ... we stay on the surface and don't fly off.

Thursday's class (26 Mar09)

Today, we will focus on applying the general ideas I presented on Tuesday. This will start by motivating the full form of Newton's general law of gravitation, and the principle of superposition. This will allow us to handle the gravitational force between arbitrary (non-point-like) objects like spheres and disks and so forth, as well as the gravitational force above the earth's surface. You should have read most of Ch. 13 by now ...

As a side bonus, we'll figure out what really happens if you drill a hole through the earth.

This will lead us to gravitational potential energy, which will reduce to mgh close to the earth's surface, and lead us to the energy required to achieve stable orbits around a planet/star/etc. From there, we already derived Kepler's laws, and that is that.

I hope to spend a good amount of time on the homework problems for this week and some other examples, at the expense of what is normally reserved for lab time. In what time is left, I want to see your progress on rocket calculations and what your next plans are.

Friday, I will announce another small rocket-related project ... next week, each team will have to present a short progress report.

Problem set 10, number 9

Having worked it out myself last night, I realized that problem 9 is a bit more ... punishing than it really ought to be. The physics is easy, but the integral you need to solve is somewhat pathalogical.

Thus, the MASSIVE HINT, which sets up the integral for you and gives you the basic result. Note that I said "Use any means necessary to evaluate the integral required." This means you can look it up, perhaps with the Wolfram Integrator.

If you read the hint carefully, there are bonus points for solving the thing the hard way, and further bonus points for proving that it reduces to our usual expression for small heights.

Further hint: don't reinvent the wheel. What are the odds I made this problem up, and what are the odds that it comes from any number of advanced mechanics books?

Turning your homework in late ...

If I haven't started grading it yet, it isn't late. If the solutions are not posted yet, the grade reduction is likely to be minimal.

This is something of a gamble ... but always turn it in. It is highly likely that even disgustingly late and incomplete homework will merit some credit, which is better than nothing.

Sigh.

Snipped from an article on wired.com:

Toyota's bland bar graph makes saving gas about as much fun as a physics lecture.

Sigh. Having attended my fair share of physics lectures, they do make a good point ... you can only aspire to be an occasional exception to the rule.

One more hint

11.13

On 11.13, we managed to find alpha, but we can't find how long the ball slides because we don't know omega at that point. We know we can solve for the rest of the problem, but we're stumped right here.

Ah, but you do know omega at the point that slipping stops - at that point, it is pure rolling motion, and v = r * (omega). That's what you found in the first part.

You know that the linear velocity starts out at v_i, and ends up at v at the moment t that the sliding stops. That means

v(t) = v_i + at

where a is the acceleration you already found. For the angular part, you know that the ball starts out *without* rotation, so (omega)_i = 0. At the moment rolling without slipping starts, you know (omega) = (omega)_i + (alpha)t = (alpha)t. You also know what when rolling without slipping starts, v = r(omega). Put that together ...

v(t) = v_i + at = r(omega) = r*(alpha)*t

Now you know everything but t in the equation above ...

compiled HW hints

This is stuff that I sent to various people this afternoon ... just so you all get the same info. Forgive the lack of useful typesetting on the math, this is cut & pasted from plain-text emails.

11.13 (#3)

for number 3. i doesn't give us a mass of the ball, so are we supposed to calculate exact values or just symbolic solutions?

in the end, you shouldn't need it ... the mass should cancel everywhere.

for instance, on part b, you want the acceleration. the only force is friction, f = (mu)mg. acceleration is f/m, or (mu)g.

for part c, you want angular acceleration, which is (torque)/(moment of inertia). The force is the same f as above, acting at a distance r. the mass occurring in the torque will cancel with the factor occurring in the moment of inertia.

the other parts are similar - you only need velocities and so on, and since the accelerations are independent of mass, so are they. Let me know if you get stuck on a specific part. The answers of this one are in the back of the book too.

10.67 (#2)

We've pretty much figured out that our tangential acceleration is not
constant, which is pretty obvious since we're told to find it at 35
degrees, but we have no idea how to derive it. We managed to solve for
omega, but that really only gave us a single number, and there's not
really another way to solve for alpha, and therefore tangential
acceleration, since it isn't constant.

you are on the right track ....

the radial acceleration is just a_r = l (omega)^2, since the radial distance is l. That's half of it.

You can differentiate omega, but you want to use the chain rule when you get to the thetas - theta *is* a function of time.

actually, its easier to differentiate (omega)^2 implicitly and avoid the square root:

d(omega^2)/dt = 2*omega*(d omega/dt) = 2 * omega * alpha

Now if you know (omega)^2 = 3g(1-cos(theta))/l, then you also know

d(omega^2)/dt = (3g/l) * d(-cos(theta))/dt = (3g/l)*(sin(theta))*(d theta/dt) = (3g/l)*sin(theta)*omega

Here you have to use the chain rule when you differentiate sin(theta) with respect to time:

d(sin(theta))/dt = [d(sin(theta))/d theta] * [d theta/dt]

Thus, 2*omega*alpha = (3g/l)*sin(theta)*omega. This gives you alpha, which relates to the tangential acceleration via a_t = r*alpha = l * alpha.

Alternatively, you can find alpha by using torque (even though the problem tells you not to, bah!) ... the total torque is moment of inertia times alpha.

10.54 (#1)

For 10.54, is part (b) talking about directions in terms of x- and y-
coordinates or in terms of clockwise/counterclockwise? I'm a little
confused about that because the forces are represented as vectors in the figure.

Just clockwise or counter-clockwise is enough. It wants the direction of the angular acceleration for (b). The angular acceleration is an axial vector, so it has a direction, but also specifies the direction of rotation about an axis. You can specify either one and that is enough, but it is just simpler I think to say clockwise or counter-clockwise ...

So basically, write down which way should it rotate, that's enough.

Tonight's even-numbered question

10.54: 9.72 rad/s^2

The other two problems due tonight are odd-numbered, and therefore have answers in the back of the book.

Special lecture TONIGHT

Something I forgot to mention in class today that I just found out about:

At 7pm tonight Dr. Nathan Smith, UAB School of Medicine's assistant dean for admissions (and professor of Psychology) will be speaking at the AED meeting in 30 ten Hoor.

If you are interested in medicine, and contemplating medical school, this is a great chance to hear from someone who actually evaluates medical school applications for a living ...

More action photos

Rocket launchers in action.

Coding for fun and profit

By the way: if you enjoy coding, I can probably find you an independent study in the department doing it for a real, live research project. Seriously - there are really not many students around who 1) enjoy coding, and 2) are any good at it. If you can answer yes to even one of those criteria, there is a job for you ...

In particular, the astronomers are always looking for someone, as are the condensed-matter theorists. The particle physicists also do a serious amount of numerical work, and could probably use your skills.

If you think you would be interested, let me know. You have the possibility of getting 400-level physics or astronomy credit during the semester, and actual cash during the summer. There is also no reason why it couldn't be a CBH project, that is not hard to arrange.

N.B. - Fortran is still in common use in physics, as are things like C/C++, python, etc.

Tuesday's class / Gravitation

For better or worse, there will be much mathness tomorrow. Two things that can help either before or after the fact:

• Skim Ch. 13 of your text (gravitation)
• Remind yourself about motion on generic curved paths.

The idea is that we're going to "derive" Kepler's laws of planetary motion and Newton's law of universal gravitation from some basic principles and one astronomical observation (viz., the existence of orbits described by conic sections).

In the end, you will not be responsible for the derivations, only the main results. You will see the derivations again in PH301 or PH302 (and possibly MA227). The hope is to show you that the main points of Ch. 13 can be derived with a bit more work, which will ideally help you appreciate them a bit better. Also, all that scary math at the beginning of the semester will pay off again, which is nice.

Once that is out of the way, we'll work on some of the homework problems. Thursday, we will make use of our shiny new results, and be able to show that the remainder of Ch. 13 is a bunch of special cases.

Anyway: tomorrow will be a lot of 'I derive stuff not in the book and you watch' than usual, but not without good reason.

HW 9 solutions

Here you go.

HW 10

Yes, the spring break is over. Sigh.

Homework 10 is out, first problems are due Tuesday following the break. The first problems are more angular momentum and torque, after that you will need to read Ch. 13 in your text.

Final exam

Wouldn't this be fun?

Kidding. Good practice though, they are not all easy questions ... some of them do require Physics II stuff you haven't seen yet. Note 80% is considered a 'pass' by the Diesel Technician Society.

By the way: Moodle is now up to date, I spent quite a while grading over the break catching up. One thing I have noticed: the rate of missed (or partially missed) homework seems to be increasing ever so slightly lately. This is not shocking, being near the end of the term and all ... but be careful. It is not a large percentage of your grade, but the practice is crucial.

Finally: next week is the last week of advising. I am the undergraduate adviser for physics and astronomy. If you want/need to take more physics and astronomy courses, I'd be happy to talk with you about your options and give some friendly advice (that is, in addition to your regularly-scheduled advising sessions if you are not a physics major).

Homework 9

If you are stuck so far ... don't fret too much yet. Tomorrow we will spend most of the first hour of class on problem solving, specifically setting up the homework problems.

What we did Tuesday was very general and high level, what we missed was putting it all into practice ... and the homework problems are not easy ones. I think by the end of class tomorrow you'll be able to burn through the homework problems pretty quickly.

Photos

Here are a few cell-phone-camera photos of you sciencing today ...

(If for any reason you object to having your photo online, let me know and I will remove it.)

(Probably should have warned you that I was taking photos ... and I should bring a real camera next time.)

Homework 8 solutions / Tues class

Here you go.

They are a bit more terse than I would like, in the interest of getting them out quickly (and as a result of it being late). Hopefully they are still somewhat readable ...

For Today' class, we'll begin to discuss angular momentum and torque, which we will finish up on Thursday. Please read/skim Ch. 11 before class if you haven't done so already. We will devote about an hour to the rocket launcher project.

Homework 9

All problems are due by the end of Friday (meaning, realistically, before you leave for break). With one exception, they are not too bad. Here you go.

In the end there 6 questions on angular momentum and torque, and one odd math problem that somehow found its way to your problem set. You will need to know what a geometric series is ...

The even-numbered H&R problems have the following numerical results, for reference:

• 11.14: 1.34 m/s
• 11.16: 0.25
• 11.66: 32 degrees (this is the bastard problem, FWIW)

Homework this week

For the record: there are no homework problems due tomorrow. There will be problems due on Thursday, which will come out this evening.

Physics Advising

This week begins the advising season for the F09 semester, which will continue through the week following spring break. If you are a physics major, thinking about a physics major, or plan on taking more physics in the near future, I would like to meet with you.

Individual meetings only take 15-30 minutes, please let me know if you are interested, and when you would have some time either this week or the week following spring break.

One new thing I should mention is our new seminar course, PH111. It is a 1-credit seminar course with no prerequisites, meeting once per week, and it is devoted entirely to discussing neat topics in physics at a completely introductory level. In the fall, it will meet on Mondays from 4-5:30. Anyone interested in physics is encouraged to take the course, it should be a lot of fun. A tentative syllabus can be found here.

Finally, I would like to point out that all physics majors are eligible for E. Scott Barr scholarships, and we could use some more applicants ... it is not too late to be considered for a fall scholarship! Details here.

Project memos

By the way: you can submit your project memos in whatever electronic format is convenient. PDF, Word, Pages, Tex, etc., or something more exotic. The odds are very good I can read it.

Trajectory calculations

Here's a quick snippet of C code that illustrates the algorithm I was talking about today. Some key bits are missing, but it should give you an idea of what to do.

You start with the initial velocity and parameters, and from that calculate everything a time increment dt later. Repeat for many (many) such dt ...

If you don't read C, I can translate it to some other language upon request. If you request something odd like postscript or the like it may take longer ...

Note also that this only calculates the trajectory given some initial inputs. What you want is the launch angle that gives a certain range ... calculating the trajectory is only a portion of that problem.

while (y>=0) {

v = pow((vx*vx)+(vy*vy),0.5);
theta = atan(vy/vx);
ax = ... ; // get these from your force equation
ay = ... ;
vx = vx + ax*dt;
vy = vy + ay*dt;
x = x + vx*dt+0.5*ax*dt*dt;
y = y + vy*dt+0.5*ay*dt*dt;
if (y<0)
y=0; // negative y means we hit the ground
// store various values here
t+=dt;

}

Error propagation

A nice little post on error propagation, which may be useful for your trajectory calculations ...

Next Friday

Next Friday - the day before spring break - we will not have a formal recitation. One must be realistic about these things ...

If you are still around, you can optionally show up and we will do some more work on characterizing the rockets and launchers. That is, you can use the time to make some measurements or work on your trajectory calculations and I'll be there to help.

Theory

This loosely sums up how I feel about theory & calculations. At the end of the day, someone still has to go and look. A reality check, if nothing else.

Also, it is a thin excuse to link to XKCD. Be sure to read the mouse-over text.

Commentary.

More succinctly, and in t-shirt form.

Rocket launcher progress

Before the end of tomorrow, I want you to write me a memo regarding your plans. About 2 pages (max), one per group, due by the end of tomorrow.

The details will become more clear after today's class, where we will spend a good amount of time on further characterizing the rockets.

Exam II results in more detail

Here are a few more details on the exam results. First, a plot how how many of you chose to answer each question, and a second showing what the average score was among that group.


Basically, this tells me you perceived questions 2 and 4 as far more difficult than the others. This was borne out by the average score for number 2. It is a difficult problem, mainly because it seems like you should be able to solve it by energy conservation, but you can't. Number 4 on the other hand was not so difficult as it seemed - those who tried it did quite well. Compare this to the poll at right; most of you thought question 3 was the most difficult, but you did well.

The second set of plots is just a histogram, with the second plot having more narrow bins. Broadly, it is very good - the average was much higher than I expected, and there are not a lot of people on the left-hand 'tail' of the distribution.

Looking at the finer-grained plot doesn't tell me much more, except that the large majority of you have no cause for worry - you should consider 75 or above on this exam to be a good score, it was very tough. Those of you that were at 90 and above did truly outstanding work, and I was quite impressed.

Those of you on the lower side have absolutely no cause for worry yet. No one has below a C average in the course now. This exam is only 10% of your grade; homework is worth 12.5%, the final is worth 25% of your grade. If you scored (say) 20 points lower than you would have liked to, this is only a (roughly) 2 point change in your grade - barely enough to change a + to a -. The message is: keep at the homework diligently, and work hard at the 3rd exam and the final.

(By the way: there is an 80% correlation between homework grades and overall grades ... the highest of any segment of your grade. Meaning, I like to think, there is some sense in slogging through the homework each week.)

(Also: the last poll option seems to roughly correlate with the tail of the distribution, which makes sense to me. At least one of you should have picked the first option though.)

Problem 10.42

Right .... so I screwed up a unit conversion myself.

The numerical answer to 10.42a should be 8.32e-6, not 8.32e-3.

(I missed that the mass was in mg, not g ... my bad.)

Exam II grades are on Moodle

Check it out.

Average: 82% / std. dev.: 13%

Details to follow.

(UPDATE: details in the next post. Homework 6 and Lab 5 are also on Moodle now. The only outstanding grades right now are those from HW7.)

Tomorrow's class

Thursday, we will devote about an hour to more measurements of the rockets and characterizing the launchers. This, as opposed to the rotational dynamics lab previously scheduled.

Remember your end goal: predicting, for a given angle of launch, where the thing is going to land. Keep in mind the target may not be at the same level as the launcher. Tomorrow or Friday we'll also discuss in more detail how to use your data to model the drag force empirically and use that in your trajectory calculations.

Exam II solutions

Here you go. All problems except the first have solutions; I'll post an update on that one later today I hope, as well as adding some better double-checks to the other problems.

Exam II problem 2

The boy sliding on the hemisphere is trickier than it seems.

An energy balance will not tell you when he leaves the sphere ... finding the normal force as a function of position and finding when it is zero will.

As I grade more of the problems I'll put little comments here on what seemed to trip you.

PS - this was a graduate school qualifying exam (i.e., a comprehensive test of undergrad physics) a few years back.

Problem 1, exam II

Read the question text very carefully.

A block of mass m is released from rest at a height d=40cm and slides down a frictionless ramp and onto a first plateau, which has length d and where the coefficient of kinetic friction is mu_k=0.5. If the block is still moving, it then slides down a second frictionless ramp through height d/2 and onto a lower plateau, which has length d/2 and where the coefficient of kinetic friction is again mu_k=0.5. If the block is still moving, it then slides up a frictionless ramp.

Where is the final stopping point of the block? If it is on a plateau, state which one and give the distance L from the left edge of that plateau.

There is one crucial difference between this problem and the practice problem you did on HW7. One key word, in fact.

Put another way: can the final stopping point be on a frictionless ramp?

Tuesday's class

We'll begin rotational motion today, starting with angular equations of motion and working our way up to rotational kinetic energy. I'm presuming you've skimmed Ch. 10 a bit; if not, be sure you have read through it by Thursday certainly.

We will also go over a few of the exam problems. Probably not all of them, some will have to wait until Thursday in the interests of time. Solutions to the exam will come out tomorrow after class.

After that, we'll work on the ballistics project for 45-60min. If the parts come in, we can start with that already ... if not, we will work on ballistics calculations and determining drag forces. The order for our rocket launchers has been placed, it is only to be seen if they show up tomorrow or not ...

There will be a project-related assignment for Thursday which I'll discuss tomorrow. Most likely, it will be to determine a reasonably-accurate form of the drag force on our rockets, but this also depends on whether said rockets are delivered or not ...

Even-numbered problems for this week

Numerical answers for the even-numbered problems ... just so you can see if you're on the right track.

10.32

• a: 2.3e-9 rad/s^2
• b: 2600 yrs
• c: 0.024 s

10.42

• a: 8.35e-3 kg m^2
• b: 0.22%

10.66

• 1.42 m/s

HW 8

I was going to finish it tomorrow, but somehow I was inspired. So ... Here is homework 8.

You still only have one problem due for Tuesday, viz., one of the exam problems.

Next HW

The next homework set in full will be out tomorrow. My struggle with FAIL continued through a good portion of Saturday, and I am a bit behind ...

For now, you have only one problem to do for Tuesday: solve one of the exam problems you did not choose to solve on the exam itself.

You can find the exam here.

Recent episodes of FAIL

So, here's how it is. Thanks to weather-related FAIL today, I'm stuck in Miami for another day. I had hoped to get back late tonight, go grab the exams tomorrow morning, and have them graded and back by Tuesday.

At the earliest, I'll now be back in town Saturday afternoon. If all goes well, I can still get the exams graded by Tuesday ... I will try. At the very least, I will get you solutions to the exam by Tuesday, one way or another. I really did choose all the problems there for a reason, and I want you to see how they are worked out while the ideas are still fresh in your mind.

For Tuesday ...

All you need to do for Tuesday is to have formed your groups for the ballistics project, we will start work on this in earnest next week.

I'll post some details about the project and the tasks you'll have to perform this weekend. The first thing we will do is work on measuring the drag force on our rockets, and how to accurately model its trajectory ... the actual rocket launchers should be here on Tuesday.

Stupid tricks for your TI-89

A lot of you seem to have TI-89's or related instruments ... here's a nice how-to guide.

Formula sheet

Well, if you aren't going to get some rest, you can peruse the formula sheet for the exam.

Subject to small changes / additions as I find typos & omissions.

Get some rest.

Seriously, cramming isn't going to help, there is nothing to memorize. You need really only need two things for the exam:

• conservation and defnitions of energy
• conservation and definitions of momentum

The rest is all smoke & mirrors, it is just these two things for every problem (assuming you remember how to define position, velocity, and acceleration).

Get a decent night's sleep so you're at maximum cleverness tomorrow. Most of the problems have subtleties in them that require careful thinking, and the math will get ugly very fast if you miss little things here and there. You will be tested on problem solving, keep that in mind.

If you were able to follow all of the problems we did on Tuesday, you will be in good shape for the exam.

Tuesday's class

Today, we have really only two tasks:

(1) review for the exam on Thursday
(2) get started on our projectile guidance system

The first part will basically be problem solving - working out some of the current homework problems, and a few extras.

The second part will largely be learning how to numerically calculate ballistic trajectories in the presence of resistive forces, i.e., drag. We have to get this out of the way before we start building and measuring things. Part of this will also include organization - forming teams and dividing tasks, defining the scope and details of our little ballistics project.

Finally: in light of the exam on Thursday, there will be no recitation this Friday. (Also, I am out of town on Friday.)

Homework 6 solutions

Here they are, a bit more than half complete right now.

I'll try to get the rest of the solutions finished by some time Tues afternoon.

Exam II

Just FYI ... the rules for Thursday's exam are basically like those for the previous exam.

You will have a choice of problems, though a bit less choice this time. You can bring in one formula sheet with whatever you like on it, I will provide the basic formulas and numbers needed.

The exam will nominally cover chapters 7-9, though I think it is clear that the material thus far is somewhat cumulative. Details on precisely what sections are covered (and which ones aren't) will follow later today.

I should have HW6 solutions up before tomorrow's class to aid in studying. Your latest homework set is also meant to get you solving the sort of problems I'll ask on the exam. Yes, it will be harder than the last one, but nothing you can't handle, and nothing we haven't gone over in class. Really, the only way to study for this one is to work problems.

HW 5 solutions

The solutions to Homework 5 are out.

Just for 'fun,' I included code snippets in various languages to solve the last problem, in which you needed to sum the harmonic series over 75 terms. Actually, I wrote quick versions in several languages, such was the depth of my procrastination. Represented are

• C (iterative and recursive solutions)
• Pascal
  
• Perl
• LISP
  
• Python
• Java
• shell (bash) script
• Postscript
• Fortran

If you are similarly bored, how about some submissions in other languages? Or perhaps some particularly obfuscated solutions in some of the languages above?

(In particular, my postscript solution could be fancied up quite a bit for prettier output. The bash script is also a bit cheap and approximate, since one can only use integers.)

HW 7 is out

Here you go.

Differences this week:

• all problems are due Thursday, just before the exam
• you do not need to use the template this time
• consider this an exam review ...

[EDIT: the last problem should be 9.69, not 9.70. This is only an issue if you downloaded the homework between 19:14 and 19:27.]

Midterm grades

Except for the very last lab (momentum) and homework set (#6), all grades should now be up on Moodle.

I have included a separate field for your midterm grade, which was calculated by dropping 1 lab, 1 homework, and 1 quiz. The relative percentages are in the syllabus for the curious.

Midterm grades are due Monday evening, so let me know ASAP if you see any irregularities or have any questions.

Thursday's lab

We will take two carts, and run them into each other.

Also: we will spend time setting up a few of the homework problems. You aren't putting them off, right?

Typo 9.45

There is a typo in the numerical answer in the back of the book. It should be +45, not -45.

Draw the initial velocity vectors, and it will be clear why (I think) even if your math doesn't jive.

Random homework hints

9.8 Of course, you know the liquid density owing to the fact that you know the mass and volume when the can is filled. This is enough to calculate the liquid mass when the can is filled to a depth x. It is advisable to plot the resulting center of mass versus x.

9.15 You can easily find the velocity of the projectile at the top of the trajectory. At that point, apply conservation of momentum. If the falling particle has no initial velocity ...

9.45 Don't overthink this one. Conservation of momentum before and after along x and y axes. Symmetry is useful.

9.48 Both energy and momentum must be conserved, right?

Quiz 7 and its solution

Here you go.

Homework 5 solutions should follow this evening.

Grading

I'm still a bit behind on grading, but nearly caught up.

Moodle how has quizzes 1-7 and homework sets 1-4.

Outstanding things are homework set 5, and your last two labs. I'll have these posted Wednesday or Thursday, which will put everything up to date.

The overall grades you see in Moodle are artificially low, in that I have not (yet) dropped any quizzes, labs, or homework sets. Consider the displayed total a worst-case scenario!

Midterm grades are due this coming Monday. By this Friday, I will have accurate mid-term grades available on Moodle for you to review ... so you can let me know if anything looks incorrect before Monday's deadline.

Homework #6

This week, we'll have a bit of a change in the homework procedure.

Rather than have problems due every day, I will let you turn in all problems at the end of the day on Friday. Do not take this freedom lightly: it is unlikely you will be able to complete all of these problems in a single night (e.g., Friday night). You will need to work on this throughout the remainder of the week to have hopes of finishing all the problems.

Anyway: this week's homework consists of the following problems from your textbook: 9.5, 9.8, 9.15, 9.33, 9.45, 9.48, 9.53, 9.59, and 9.68.

A more formal-looking version of the homework is here.

Homework 5, #7

By the way, here are a few code-based solutions that you submitted to homework 5 problem #7. Quite a variety - Fortran, C/C++, and Python are all represented.

My own (hastily-composed) version is here, in standard C. It should compile with vanilla gcc. It takes a command-line argument N, where N is how many terms of the harmonic series to evaluate. For "fun" I also included code (commented out) to calculate the same sum recursively.

For reference, here is the source of the problem (Car Talk), here is their answer, which employs the Euler–Mascheroni constant.

Next HW

I am a bit behind on getting this week's homework set out ...

There will be a new homework set posted later today. Since I am late in getting it out, there will be no problems due until this Wednesday evening.

Basically: no homework due tomorrow ... but don't get too comfortable :-)

Friday's class

Tomorrow: yet more on potential energy ... we'll try to tie up the loose ends and put things together so we can start in with momentum next week. Finally, things will start colliding.

For example.

I have gotten a bit behind on the grading at the moment, and am working to rectify that right now. Tomorrow, you should get back a great deal of homework and a couple of lab reports. I'm trying to keep the turnaround at 2-3 days, but it has slipped a bit this week.

HW Clarification

A question from one of you:

Is a symbolic solution necessary for the simple parts of 8.41
such as part a? Also, our b part should serve as a sketch shouldn't it?

Correct on both accounts - if the problem just asks for a number in one part, no symbolic solution is necessary. Since the problem asks for U(x), that is sufficient for a sketch.

Thursday's class

FYI: schedule change.

There are scheduling difficulties with the lab we had planned for today (nothing interesting, merely difficult), so we will instead focus on problem solving for a good chunk of the class. Part of that will be setting up this week's homework problems.

I will first go into some more detail on potential energy and conservation of energy, but will try to confine that to 45min or so ... such that most of the time will be spent figuring out how to use the new ideas.

Thursday's homework

Change of plans (for the better):

Let's have tomorrow's homework due at the end of the day rather than at the beginning of class, so you have a chance to ask questions if need be.

Lab for Tues 10 Feb 2009

Tomorrow, we'll measure the coefficient of restitution.

Basically, this is a measure of how velocity is lost by an object due to impact with another object. The Wikipedia has some (limited) background information on why this is a useful metric.

(Baseball-related paper ... Rockies fans take note.)

Exam 1 solutions

UPDATE: the solutions are now complete, but probably require some proofreading yet. The link below is still correct.

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I am busy making up the solutions, here is the progress so far.

I'll be updating the solutions throughout the day, and will post here when they are complete. The filename will not change, so the above link will remain useful.

Problem set 5

Problem set 5 is now out.

Since it is coming out a bit late, tomorrow's problems are not due until the end of the day (as opposed to at the beginning of class). I'll set those two problems up in class to help you get started.

Solutions to HW4 are now out, and exam solutions will follow later today.

Quiz 5 and 6 solutions

Quizzes 5 and 6 are out now, along with their solutions.

A new problem set will be following shortly, which will have some problems due on Tuesday. You can also expect some problem set solutions over the weekend.

Physics of the Death Star

We won't cover gravitation until just before spring break ... but file this away for later.

Another great blog full of neat physics posts, highly recommended.

This Friday's homework

By the way: typo on the homework.

Friday's problems are due at the end of the day, i.e., 1 minute before midnight, not at the beginning of class as the problem set claims.

In other news, we will begin studying work & energy tomorrow (Ch. 7). Reading Ch. 7 before class tomorrow, or at least skimming it is a Good Idea.

By the way: I tried to choose a textbook this semester that would make the reading less ... painful. I don't point out each day what you should be reading, mainly because I think it is sort of obvious from the schedule - if we start Ch. 7 tomorrow, you should read Ch. 7 for tomorrow. I am naively assuming that you do the reading each time (!), and that the more studious of you are working through the example problems on your own.

Here's a good little post on physics textbooks, FWIW. I have nearly written my own book for ph102 out of sheer frustration; the fact that I have not even thought of this for ph125 speaks to my high regard for the classic H&R text. YMMV.

Have free time?

Our IT guy over here in MINT is looking for a gopher to install software, swap out computer hardware, etc. Anyone looking for a few hours a week of work and need a little cash?

Exams are graded

Your exams are graded, and the results are on moodle (instructions). I have only made one pass at grading, so I will have to double check things yet. Caveat lector.

The average was an astounding 89.7 (std. dev. 5.8). I did go a little easy on the grading, but not that easy - you did very well, and I was pleasantly surprised.

Below are some nerdy plots for you (click for larger version): a histogram of sorts; the percentage of you choosing each problem; and of those that chose each problem, the average score. We'll discuss briefly on Thursday what I think they're telling us, if anything.


Hard to draw too many conclusions when the average is high and the standard deviation is low ...

HW4 / Exam

Here is your fourth homework, with problems due this Thursday and Friday.

Part of the homework is to solve exam problems you did not choose. For that, you will need a copy of the exam.

It would be very, very nice if you used the 2-page problem template. I can print them for you if necessary.

Draft of the exam formula sheet

Find it here.

It still needs proofreading, but not much should change. This is basically what you'll get tomorrow.

More practice problems

I'm not saying you should do all of these tonight, but here are some problems from each chapter I think are worth glancing at. If you know how to do one already, skip it and move in. If you're not sure ... give it a try. These are all odd-numbered problems, so you have the answers in the back of your book.

Ch. 1
not on the exam.

Ch. 2
15, 29, 45, 51, 109

Ch. 3
there are no questions on the exam specifically from Ch. 3, but here are some vector practice problems that are useful: 35, 39, 43

Ch. 4
13, 25, 27, 35, 41, 61, 65

Ch. 5
19, 43, 51, 53, 59, 101

Ch. 6
17, 23, 27, 31, 41, 81, 109

I'll do some of these at the review session tonight - if you have time, glance through these and have some suggestions for which ones I should do on the board.

Reminder: review session tonight 7:15pm

Tonight, 7:15pm, 203 Gallalee hall. Come armed with questions. I'll come with some additional practice problems to work out, similar to what will be on the exam.

Remember my phone number in case for some reason the building gets locked up early ... I will be checking outside around 7:15 as well.

Checking grades online

I how have a system set up so you can log in and see your grades.

1) go here: http://faculty.mint.ua.edu/~pleclair/moodle/

2) Click on "Physics 125 / Dr. LeClair"

3) Then, to log in to the system:

• your username is same as your bama email address
  

• Thus, if your bama email is "jdingus@bama.ua.edu" your username is "jdingus"
  

• your password is the last four digits of your CWID. You can change the password if you like after logging in.

Once you have logged in successfully, you should be at the main ph125 course page. There are a great number of things on this page, most of them are not useful. This is a new (and free) online course system I'm test-driving, so most things are just placeholders.

From this page, you can access your grades. You should see a link for "Grades" on the left-hand side of the page, about halfway down, under "Administration." For that matter, you can change your profile, create a little blog or discussion board, or all sorts of other things.

Any feedback you have on this system is helpful. Let me know if it works ... and I should have more grades entered early next week. Right now, all four quizzes and the first two lab and homework grades are there.

Practice Exam solutions

UPDATE: full solutions are now up. (The filename has not changed, I just updated the contents.)

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Here are the solutions to about the first half of the practice problems. They are a bit terse, which reflects my haste this evening/morning, but I think they should be understandable.* With luck, complete solutions will follow tomorrow in the early afternoon.

These problems are not as diverse a set as I would have liked,** but I think if you can get through all of these fairly quickly without much trouble, you will be fine on the exam. Another good thing to do is study the example problems in your text.

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* Most likely, I am just too long-winded in my normal solutions, and these are fine ... feel free to weigh in on this point, since I am writing these things for you.

** On the other hand, at least one of these practice problems will show up verbatim on the exam. Really.

Practice exam questions

Here you go.

Answers provided in a couple of hours ... solutions we'll go over at the review session on Monday (7:15pm, 203 Gallalee).

On average, they are easier than I would really ask on the exam, but the idea is to get you practicing on some of the main concepts.

*cough*

Huh, I guess I did this problem before.

Quiz 4 and its solution ...

... can be found here.

PS3, Number 7

Miscellaneous correspondence with one of you:

On the top block, you have the normal force up, and its weight down, so the normal force is just the mass of the block times g.

That means the friction force is (mu)(mg). For motion to occur, you need (mu static)(mg) < (pulling force). This is true in this case, so the block is moving to the left, but also sliding against the bottom slab. Even though there is no friction between the slab and the ground, the block can pull away from the slab if the pulling force is big enough.

Since the block is moving, the *kinetic* friction force is (mu kinetic)(mg). The two horizontal forces are then this one and the pulling force, their difference gives mass times acceleration for the top block.

Now, if the top block has a friction force to the right due to the interaction with the bottom slab, the slab itself must feel the same force in the opposite direction by Newton's third law. Thus, if the top block is slipping off the bottom slab, the bottom slab has to feel the *same* friction force (but in the opposite direction) that the block feels. This is the only horizontal force on the slab, since it has no friction with the floor, nor is there a pulling force directly on it. So, (m slab)g = (friction force on top block) = (mu kinetic)(m block)g

I'll draw this out in class tomorrow and hopefully it will be clearer.

Conical pendulum

Problem 6.60 involves a conical pendulum, a classic problem you can easily turn up online with even the most cursory search ...

Problem 6.34 has numerical answers of about 6 and 1 m/s^2 respectively.

More details to follow.

Exam details, part one

You have an exam this comingTuesday. Here are some details:

• There will be 8 problems, you can do any 4 - your choice
• Heavy partial credit, no multiple choice
  
• Covers chapters 1-6
• You can bring in 1 sheet of 8.5x11 inch paper with whatever you want on it
• I'll provide a basic formula sheet with all end-of-chapter formulas and constants