Saturday, January 31, 2009

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.

Thursday, January 29, 2009

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

Kobe Bryant jumping over a car

Remember the video about the decay rate on a head of beer?

Turns out the author is one of our own alumni, and he has a fantastic blog with all sorts of interesting 'real world' physics problem, including a lot of video analysis and simulation.

For instance, here is an analysis of a video showing Kobe Bryant jumping over a car. Real, or not? Physics can help decide ... the same physics we just finished going through.

Check out the rest of the blog if you like seeing some more fun examples of what we've been doing.

Odd-numbered problems

By the way: the odd-numbered ones have answers in the back of the book, in case you didn't notice, so you can check your answers.

Why are there so many bastard problems?

So, I don't think this will make me seem like *less* of an ogre, but I thought I'd put down some of my reasoning behind your homework sets.

The homework is really, really difficult. I won't pretend otherwise. In fact, it is comparable to what physics majors at places like MIT would see - meaning if you are getting through it, or at least understanding the solutions after the fact, you are learning physics as well as anyone anywhere.

(Your exam problems will not be as hard. Not even close. I'll post some sample problems tomorrow to give you an idea.)

Out of every (say) three problems I give you, I usually expect one of them to be pretty easy or very similar to an example problem in the book or online. A second one usually has a painful but straightforward brute-force solution, and a more mathematically sophisticated but shorter solution. Then, there is usually the bastard problem, which is just going to suck.

So why the bastard problem? One, I can't really see how much you have learned, and whether you can apply it in unfamiliar situations, if you ace all the problems. In that regard, it is OK, and expected, if you don't complete the whole thing. On the toughest problems, you will be well-rewarded for just trying something sensible, I tend to grade the 'bastard problems' pretty leniently. If you don't get those problems, you are still going to end up just fine - you will not need to solve all of them to get an "A." With the partial credit scheme based on the homework template, even just setting up the bastard problem, without solving it completely, can get you 75% partial credit.

Two, it is still very valuable if you try the problem and get stumped. There is heavy partial credit for trying, but that is not entirely the point either. If I just solve the really tough problems in class for you, without you having tried them, they will either be hard to follow or seem deceptively easy. So the theory goes, at least.

Three, for most of you it is going to 'click' at some point, particularly once we learn some new techniques in the coming weeks. Most of this week's homework can be solved in a few lines with the benefit of hindsight we'll have at that point. It is just hard in the beginning, period.

Four, you are free to (and encouraged to) collaborate. This is not a justification for making the homework difficult, but a reminder that you should help each other get through it when you can ...

Finally, part of the point is that our students often get to 300 level physics classes and get creamed. I'd rather it be reversed, at least for honors students - by the time you get to PH301, you should manhandle it.

So how do I calibrate the homework? I solved all of this week's problems on Friday night and just made a second pass to double check. If I can't do the whole homework set in about an hour, using only the same things we covered in class, it is too much.

As an aside: part of this is about time management as well. Is it OK to spend time x and get 90% credit, or should you spend time 2x to get 95%? Multiply that by 4 or 5 courses and life outside classes ... don't spend three extra hours on physics for 5% more if you can spend it on calculus for 25% more.

Thursday's lab procedure

Tomorrow, we'll do a lab to verify Newton's second law. Please print one copy per group when you arrive. If you get time before class, have a look through the procedure.

Solutions to Tuesday's problems

Here you go, solutions to PS3, problems 1-3. They are a bit rough yet since it is late ... hopefully they will see some editing tomorrow.

In particular, number 3 can be made quite a bit more elegant, but I am a bit too sleep-deprived to properly write it down right now.

Tomorrow, I'll put up solutions to problems 4-6, as well as some details about the impending exam.

Wednesday, January 28, 2009

Hints on PS3, cont.

The hint file now contains a free-body diagram for number 6.

Remember, the centripetal force must be the result of forces in the radial direction for circular motion. It is not a separate force acting on a body, but a constraint that must be obeyed to satisfy circular motion.

Random info on PS3

I had an email exchange with one of you regarding tomorrow's problems, so I thought I'd reproduce it here in case it helped someone else.
In my notes i have the position function for the inclined plane problems as x(t)=.5(a_x)(t^2)-(h/sin(theta)). My question is why is the last term there? It is the same as the hypotenuse of the plane, so it could be the x initial if I rotate the x-axis to be parallel to the plane, but wouldn't it make more sense to make the top of the plane the origin giving an x initial of 0? Or is the origin placed at the end of the ramp in order to more easily compute the trajectory after the block leaves the ramp/table? Sorry, I'm just a little confused about it
all.

If you call the length of the ramp along the tilted part L, then you would say sin(theta) = h/L, or L=h/sin(theta). So, the h/sin(theta) part is just the hypotenuse. We put it in this form because for the problem we did in class, we were given the height above ground level, not the ramp length.

You are also right that if you choose the origin to be the starting point, it is just x(t) = 0.5(a_x)(t^2) for the position along the ramp. I chose the end point of the ramp to make the trajectory easier, as you suggest, but it really doesn't make that much of a difference. You can put the origin at the starting position, and for the trajectory it isn't that much harder either way.

What you do need to keep in mind is that once the thing hits the bottom of the ramp, you should define a new x-y coordinate system to do the trajectory - it will be easier for that step with x & y vertical and horizontal as usual, the rotated coordinate system will just make things harder. At that point, you could actually just redefine the origin of the new system as well to be at the end of the ramp.

So basically, you are right. It is really easier to treat it as two separate problems, and give each their own coordinate system and origin - first do the ramp, then start over with the velocity you found and do the projectile.

Tuesday, January 27, 2009

Gallalee has its own episode of FAIL

Due to the renovations on the restrooms. The water in Gallalee Hall will be shut off today, January 27th. The faculty, staff and students will need to find alternatives today and maybe the rest of the week.
I'm not kidding, I only just found out this morning myself. Take your restroom breaks before you head over ...

And on the lighter side of physics ...

Modeling the head on a glass of beer.

By the end of the semester, we should be able to do better. Of course, we will not have an associated laboratory experiment.

Monday, January 26, 2009

Another hint on PS3, #1

See this link.

Further hints on #2 and #3 will follow later this evening.

UPDATE: the equation for the parabola had an "R squared," but that should have been just "R." The error has been corrected in the linked file.

DOUBLE SECRET UPDATE: Problem 3 was assigned in MIT's course 8.01*, F03 semester. Check out their OpenCourseWare.

* MIT's courses are all numbered. Course 8 is physics, class 1 is mechanics. Course 18 is mathematics. Everything is numbered at MIT. Some of the buildings don't even have names. I worked in building 8 for a time, and later building NW-14.

Sunday, January 25, 2009

Saturday, January 24, 2009

PS3 #1, 2

Number 1: set it up just like last time ... you have a circle and a parabola. You do not want them to intersect. Should you find a condition that gives an imaginary result ... there you go.

Number 2: terminal velocity means constant velocity, which means zero net acceleration.

There will be an episode of FAIL on Sunday.

In case you haven't heard, there will be serious network outages tomorrow involving all campus services ...
All campus networking, Internet access, and central computer services will be unavailable Sunday, Jan. 25 beginning at 8 a.m. This is necessary to replace the central UPS, which is inoperable, and prevent unplanned power outages from damaging equipment and losing University data. Office of Information Technology staff members will begin shutting down machines at 8 a.m. Critical systems, including the network, medical systems, e-mail, Web sites, Banner, myBama, eLearning, and Bama, are expected to be operational by 1 p.m. Other central systems should be up no later than 3 p.m.

Friday, January 23, 2009

Problems 8 & 9 for today

If you found these two really, really difficult ... that is OK. Don't fret, they were extremely difficult problems, and I'm very pleased at what I've seen so far. There will not be anything of comparable difficulty on an exam.

Sometimes we just throw you a curveball, just to see what you can do with it. Grading on these two problems will be very lenient - if you made a good solid attempt, you will get substantial credit.

We'll run through those two problems on Tuesday in detail (solutions will be out tomorrow morning) so you can see any steps you missed.

PS 3 is out

Your next homework is out. First problems are due Tuesday, 27 Jan 2009.

By the end of Tuesday, you will know how to do all of Thursday's problems, and most of Friday's. I will be giving copious hints in class on Tuesday and Thursday.

PS 2 solutions so far

Here are the solutions to problem set 2, up through yesterday's problems.

Tomorrow, the full solution set, including today's problems, will be out.

Thursday, January 22, 2009

PS 2 #8,9

For question number 9 on the current homework, you do not need to provide a sketch or a numeric solution. Since you are only asked to prove a mathematical relationship, neither is really applicable.

Similarly, you do not need a numerical solution for number 8.

Scroll down a few posts to see a hint I posted about number 9. Also, check out the notes for a very large hint (toward the end of the document).

Wednesday, January 21, 2009

Physics Help Desk Hours

The hours for the physics help desk are now posted.

The idea behind the help desk is that you can get assistance from any graduate assistant (GTA) from any 100-level course. They are all qualified to help you, so go to whichever GTA's office hours suit your schedule the best.

This is particularly important since we have no TA of our own ...

Lecture video / office hours today

Based on the poll response so far, I'll begin taking video (and audio) of the lecture portion of class starting tomorrow. I would have started yesterday already, but forgot the mic ...

If you are having trouble with the homework problems for tomorrow, I'll be in my Bevill office and mostly available after 2pm today. Failing that, I should be in my Gallalee office for the hour before class tomorrow.

Finally ... the notes I posted contain a huge hint for problem 9 on the homework. For problem 8, first find the acceleration vector, and then note that

a_t = \vec{a}\cdot\hat{T} = \vec{a}\cdot\frac{\vec{v}}{|\vec{v}|} = \frac{\vec{a}\cdot\vec{v}}{|\vec{v}|}
and

a_n^2 = |\vec{a}|^2 - a_t^2

Lab for Thursday 22 Jan

Here is a draft of tomorrow's lab procedure. Have a look through it before class if you can.

There is no need to print a copy before coming to class ... it will probably undergo some tweaks and reformatting before tomorrow's class. The basic procedure will not be affected, however, so it is still worth a read.

Notes for Tuesday's class

Update: I just heard you went over the same stuff in Cal III about ten minutes later. Excellent! Those of you not in Cal III would probably benefit from talking with you colleagues who are ... sometimes hearing the formal mathematical version is clearer than the physicist's handwaving version.

----

I have made some notes for the material we covered in class today. It is not in the book. Only tiny parts of it will be on the test, for that matter. It is very cool though.

The notes are *marginally* more rigorous than what I did in class, and probably follow a more logical path. With the benefit of hindsight, and in the absence of time restrictions, it is much easier to explain these things. Or so it seems to me, YMMV.

I realize I have gone a bit above and beyond what many of you have been exposed to in your previous math classes, but that is in a way the point. Tuesday's lecture was to familiarize you with a few mathematical concepts (in a handwaving way) that will be very useful soon, which you will undoubtedly cover in your math classes in a more rigorous way. We just want to have the machinery in hand, so we can put it to use. The math department will make sure you cover the finer points I missed.

On Thursday, we will go over the main 'take-home' points of what we need to continue on. The details of the derivations are not as important as the main results, and that is what we will focus on from now on. Basically: don't be discouraged if Tuesday's lecture seemed very abstract and difficult, there are only a few key points you need to remember, which I will summarize on Thursday.

Anyway: keep in mind I typed up these notes up in excessive haste this 'evening' over the course of a few hours. There may be many instances of typos/errors/handwaving, and I welcome any corrections, comments, or requests for clarification. Some of you have covered these topics in math classes already; I welcome any suggestions you have for making the material more accessible.

Based on the eye-rolling in class today, I realize I have a few math majors in class (or at least a few people who paid serious attention in calculus classes). I promise not to do such unspeakable things with differentials in the future, and have tried to be marginally more rigorous in the notes. Not enough, mind you, this is where your comments can come in handy :-)

Tuesday, January 20, 2009

Solution to today's quiz (Q3)

Here you go, today's quiz and its solution.

Later tonight: notes for 'motion on curved paths.'
Later later tonight: lab procedure for Thursday.

Solutions to PS 2 part 1

Here are solutions to today's problems. Thursday, I'll go over some other possibilities for double checking your answers (you may want to remind me of this).

Later tonight, I'll have notes from today's lecture as well as a solution to today's quiz.

Sunday, January 18, 2009

Solutions to PS 1, part 3

The solutions to the last three problems are now out. I've merged all the partial solutions into a single file [pdf] to make things easier.

Friday, January 16, 2009

Homework 2 is out

You can find it here [PDF].

The first problems are due on Tuesday, 20 Jan 2009, and cover material from today's class. The remaining problems are due on Thurs and Fri next week, and by the end of Tuesday's lecture, we will have covered enough material for you to solve them.

Submitting homework electronically

I do prefer PDF, but will accept essentially any format. I can read all common image, office suite (e.g., powerpoint/word/openoffice/etc), or markup (e.g., html/tex) formats. It is unlikely that you will send me a format I cannot read.*

* That is not a challenge. Problem sets submitted in Visicalc or Appleworks will try my patience, but I will read them.

Thursday, January 15, 2009

Solutions to PS 1, part 2

Solutions to today's problems are now available. Again, if you notice any typos/errors/irregularities, please let me know.

Note that your problems for tomorrow are not due at the beginning of class, but merely by the end of the day. Not that I'm saying you should put it off ...

Today's quiz and its solution

You can find both here.

Solutions to today's homework problems will follow later this afternoon.

Today's lab

I apologize for this being a bit late, but the lab I originally had planned was fraught with difficulties, so I made a new version.

Here is the lab procedure for today. If you don't have time to read this before class, that is OK ... I will give some extra time in class for that.

Wednesday, January 14, 2009

HW 1 due 15 Jan CLARIFICATION

student asks:
In problem four of the homework due Jan 15, when you say "find the
magnitude of and angle of a + b," do you mean the angle of a + b
relative to b, like in bullet number two?
Ok, that is not quite clear enough ...

For the last two cases in that problem, I mean the angle with respect to the x axis.

For example, if
\vec{c}=\vec{a}+\vec{b}
then the angle is
\tan^{-1}{\left(c_y/c_x\right)}

Finding the magnitude of a vector

I had a question earlier about finding the magnitude of a vector. The easiest general way to find the magnitude of a vector is to take the scalar product of the vector and itself, since the angle between a vector and itself is zero:
\vec{A}\cdot\vec{A} = |\vec{A}||\vec{A}|\cos{\theta} = |\vec{A}|^2

If you know the vector in x-y component form,
\vec{A}\cdot\vec{A} = \left(A_x\,\hat{\imath}+A_y\,\hat{\jmath}\right)\cdot\left(A_x\,\hat{\imath}+A_y\,\hat{\jmath}\right) = A_x^2 + A_y^2 = |\vec{A}|^2

It works out this way because the unit vectors are orthogonal (perpendicular) in our cartesian system:
\hat{\imath}\cdot\hat{\imath}=1, \quad \hat{\imath}\cdot\hat{\jmath}=0 

If you do it this way, it will work in all coordinate systems. Treating the vector as a little right triangle only works if you know the vector in x-y component form.

Tuesday, January 13, 2009

Problem-solving template clarification

I just graded the first problems, and it was good. I realized that I should explain the problem-solving template a bit more explicitly. There are six sections to the template:

Find/Given: state what you are supposed to find, and what is given in the problem. Usually trivial.

Sketch: this should be something that helps solve the problem, not just a picture. If you are given a function, sketch its graph. If you have a physical situation, draw a picture with rough dimensions noted to help clarify the geometry a bit better. Once we start with problems on motion, this will be more obvious.

Relevant equations: list all equations you will need to solve the problem, such as dm/dt=0.

Symbolic solution: (there was the most confusion on this section) without plugging in any numbers, algebraically solve for the variable of interest. This is supposed to be a general solution, in the next step you plug in the numbers you have. Your answer should (in most cases) be an equation, solved for the quantity of interest.

Numeric solution: now use the previous result, plug in the numbers and units/conversions, and state the numerical value of the quantity of interest. Include the proper units and significant figures or error margin.

Double-check: Just what it sounds like, find a second method of solving or estimating the answer of the previous step to confirm that your methods are correct. Two usual ways to do this are to make sure the units of the answer are correct, and to make a "ballpark" estimate (order-of-magnitude).

As an example of how to go about this, see the solutions to the first homework problems. I have been a bit more ... pedantic ... than you need to be, but hopefully you get the idea. The point of the template is to help you learn good problem-solving techniques that can serve you generally. It seems painful when the problems are easy, as they are now, but it pays off considerably when things get more involved (soon).

Finally, grading of homework & quizzes is directly based on this template. For a given problem, each of the six sections above is worth a total of 2 points: 2 points if that section is fully correct, 1 point if it is partially correct, and 0 points if it is absent or deeply flawed. Thus, each problem is worth a total of 12 points. I tried to grade today's problems very leniently, since it was the first time around.

Office Hours/contact info

Now that we have homework to do, you will probably have questions. There are number of ways to go about asking me things.

* Office hours will formally be Mon 11-1 in Bevill and Thursday 3-5 in Bevill 228. Other times are more than likely possible, if you send me a quick email/sms/etc (see below) to confirm.

* Most of my day is spent in the Bevill building where I do research, room 228 (office) or 180 (lab). I am really only in my Gallalee office just before and after class, typically. If you would rather meet me in Gallalee, either at the times above or otherwise, this is possible.

* I am on facebook, you can message me there.

* I read email somewhat obsessively.

* You can comment on this blog, I will reply.

* I have an IM account set up for this sort of thing. It is an AOL instant messenger account:
* Give me a call or send a text:

* I am usually up until about 2am. Calling that late is probably bad, though email/IM/etc are fine at all hours.

You can use what ever method of contact you find most convenient, they are all OK by me. Don't hesitate to ask questions outside class if you are having trouble with something ... if I didn't want you to ask questions, I wouldn't bother posting all of this ;-)

Today's quiz and its solution

You can find both here [PDF].

Let me know if you find any errors/typos, or need some further clarification. Same goes for the homework solutions.

Solutions to PS 1, part 1

The solutions to the first part of problem set 1 (PS 1) are now out [PDF]. Your submissions will be graded & returned at the start of Thursday's class (when you have three more problems due).

The solutions to today's quiz will be out later this evening, check back here.

Monday, January 12, 2009

This week

Today we'll review some math we'll need very soon, including basic calculus and vectors in some detail. For some of you, this may be a bit of review, but I suspect that much of the vector topics we cover will be substantially new for most of you. At the end of class, there will be a short quiz (15 min or so) based on what we have covered in the lecture.

For Thursday, three things need to happen.

First, there are three more problems due at the beginning of class. After tomorrow's lecture, you should have all the information you need to solve them. Chapter 3 in the text covers the necessary material.

Second, we will begin studying motion in one dimension. For this, you should read chapter 2 before class on Thursday. Really ... even if you only skim.

Third, there will be a lab. I will post the procedure here later by Wednesday, please have a look at it before Thursday's class as well (it will be short).

Office Hours Today

Well, I am back in the country as of last night ... I will be in my office in the Bevill building today, room 228, until about 6pm this evening. If you have any questions about the homework, class format, etc., today, feel free to drop by.

Thursday, January 8, 2009

Problem-solving template

In case it wasn't clear so far, you can simply use the template as a guide to format your own hand-written solutions. You don't need to actually solve the problems on the template itself (there may not be enough room), just follow the same steps as on the template.