Online coding

If you're not so happy with Python, and would rather use another language for calculating your rocket's motion, I've found a site with a much larger set of available languages for coding within the browser. If you already know, say, fortran or C++, this might be much easier - you can use what language you want and not have to worry about bringing a laptop.

Rocket launchers, first deliverables

From now on, our 'labs' will be characterizing the rocket launchers and figuring out how to predict their motion. Each lab session, you'll get your launcher and tell us what sensors or equipment you might need for that session. We will not have written procedures or detailed lists of tasks, just a final goal and a set of deliverables each week.

For example, next week (by Friday), your primary deliverable is to have figured out the muzzle velocity of the launcher as well as some estimate of its uncertainty. A secondary deliverable is to sketch out how you will proceed during the following week. How you choose to proceed is up to you, I will only give advice as to whether your plans are reasonable or not, and how you might alter them if they are not reasonable.

Your deliverables will take the form of a short memo (2 pages maximum), one per group, due by the end of the day Friday March 7. Any reasonable format is accepted (hard or soft copy). This memo should contain, at least, the following key points:

• What is the launch velocity, with an estimate of its uncertainty. Does it depend on which rocket and which turret you use?
• How did you determine the velocity, in brief? (E.g., what sensor did you use.) Define your measure of uncertainty, or how you quantified uncertainty.
• What are the appropriate equations of motion for your projectile, including drag? That is, what does the force depend on? (You do not need to solve the equations yet, just figure out what they are.) 
• At launch time, you will have the ability to measure the target coordinates. Besides that and the muzzle velocity, what else do you need to know to set up your launch to hit a target?
• What quantities can be determined experimentally ahead of time, and which will only be known once you know the target coordinates?
• What are your potential sources of uncertainty, and how could you characterize them? A detailed plan is not necessary, just an idea.

As the week progresses, we'll discuss the finer points of your memos. All you really need is a measure of the velocity, and a rough idea of what things you're going to need to figure out over the next weeks.

HW4

Homework 4 is out. We may go through a few of these on Friday already.

Society of Physics Students Meeting

We have an SPS meeting Wednesday, March 12th, at 6: 30 PM in Gallalee Room 200. Dr. Araujo will give a presentation (see attached flyer from the SPS).  In case you are teaching undergraduate students, please spread the word.
Thank you very much and greetings,
Claudia Mewes
(SPS faculty adviser)

Exam 2 solutions

Exam 2 solutions are available. You'll get the exams back at the start of Wednesday's class.

Tomorrow's lab

Tomorrow, we'll do one more 'regular' lab before starting with the rocket launchers. The main point is to learn how to use photogates for timing, which will be useful for characterizing your launchers. A secondary point is to verify conservation of momentum in 1D collisions.

Also: the rocket launchers just arrived yesterday, so tomorrow I'll show you what they look like and how they work. We'll need a couple of days to install the right software on the lab computers, but either this Friday or next Monday we'll get started with them.

HW 3 solutions / Exam

HW 3 solutions are out. Reading them carefully would be a good way to study ...

As a reminder for tomorrow's exam, you are allowed 1 sheet of standard paper (front and back) with notes. You'll also be given a formula sheet that should have everything you need, a draft of which is here.

Class for Wed 19 Feb / upcoming exam

We'll continue our discussion of momentum a little bit, time permitting, at least as far as figuring out how to handle collisions. A larger portion of the class will be related to homework problems, which are directly relevant for the exam, and another lab on programming.

For the homework, you should be a little bothered by #6, I'll outline 2 methods to solve this one. Number 7 should be quite mysterious, and that is OK - the technique you need to solve it is related to the experimental propagation of uncertainty - if you change one variable a little bit, how do the others change? This is related to how you move along surfaces in 3D, something you are learning or have learned in Cal III.

Number 8 requires some thought - the equilibrium spacing is where U(r) is minimum, or where dU/dr = -F = 0 and the net force is zero. Find this first. The breaking point of molecule is when you exceed the maximum restoring force implied by U(r). If you find F(r) = -dU/dr and look for its maximum, this will occur for a particular r, beyond which the force binding the atoms together is exceeded and the atoms will come apart. Mathematically, that means setting dF/dr = 0 to find the maximum, that's the radius beyond which you break the molecule. Using the result for the equilibrium spacing, you can write it in terms of only n, m, and the equilibrium radius. I might have asked this question before if you are willing to dig a little.

For the exam, the format is exactly like the last time. It will likely consist of 6 problems, of which you have to solve 4. The questions will only be on work, kinetic energy, potential energy, and conservation of energy - 2 chapters in the book. You'll have a formula sheet given like last time, and can bring 1 sheet of paper of your own. I will post HW3 solutions by Thursday morning, hopefully, to help you study.

Finally, the lab: we'll continue with coding. You have two basic tasks.

1) I assert that the sum of the first n cubes of integers (sum of i^3 from i=1 to i=n) is the square of the sum of the first n integers (square of the sum of i from i=1 to i=n). Write a program that can check this for specific values of n. Print out your code and results for n=10 and n=17. Basically: sum the integers, square the sum, and compare to the sum of the cubes of integers.

2) Write and evaluate a program to calculate the range of a projectile under only the influence of gravity (no drag forces). Verify that it gives the correct result (within a few percent numerical error) for a launch speed of 25 m/s and a launch angle of 45 degrees. (You already know how to calculate the range without a drag force ...) Note that links I gave previously, and specific folders here are highly useful. Print out your code and note your results for the conditions noted.

Homework 3, number 7

This is a very tough one, and I planned on going over it in class on Wednesday. I'll sketch out the approach below.

If power is constant (which we're basically told it is for the default car), then the work done is W=P*T where T is the time over which the power is being supplied. This work done must be equal to the car's change in kinetic energy. If the car starts from rest, the work just equals the final kinetic energy, 

W =PT = (1/2)mv^2

This relates P, T, and velocity, but we don't know velocity. We do know the track length though. What we want to do is solve that for v, and integrate it to get x. Since the length of the track (x) is fixed, that will let us relate power and time by themselves.

v = sqrt(2PT/m) 

x = (integral) v dt = sqrt(4PT^3 / 3m)

The question now is what happens if we vary P by some little amount dP, what happens with T? By how much does it decrease dT? The distance x is a function of the variables P and T. It is fixed, so any change in P will have to be accompanied by a change in T to keep it constant. 

The question we're really asking then is for the function x(P,T) to remain constant, what must the rates of change in P and T be? We'd need to know the slope along the "P axis" (so dx/dP) and multiply by the tiny change in P (let's call that change DP instead of dp to keep the change straight from the derivative). We'd also need to know the same along the "T axis". Basically, the change in any function is slope times displacement for each axis, all added together. This is the same way we propagate experimental uncertainties, by the way, something I hope we will cover soon.

If the function were f(x,y), we'd approximate a small change in f due to small changes DX and DY in x and y as

Df = f(x+dx) - f(x) = (df/dx)*DX + (df/dy)*DY

In the simpler case, if you just have y(x), all this says is DY = (dy/dx)*DX. Back to the problem at hand, if we have x(P,T), 

Dx = (dx/dP)*DP + (dx/dT)*DT

Since the track length is fixed, we know Dx = 0. Thus,

(dx/dP)*DP = - (dx/dT)*DT

or   DT = -DP*(dx/dP)/(dx/dT)

Given the function above, take the derivatives with respect to P and T, divide them, and that times the change in power gives you the corresponding change in time.

I'll plan on going over this on Wednesday too.

Homework typo

I just realized that there is a typo in the due dates. Problems 3 & 4 are due today, but problems 5-10 are not due until Wednesday, 19 Feb (not today). 

Starting with Python

For tomorrow's "lab", we'll start messing around with python. Nothing fancy, just a few simple examples so you can learn to do basic calculations (like multiply stuff) and display the answer. We'll work our way up to more complicated things. If you are interested enough to mess around on your own, try the excellent tutorial here. Don't feel bad if you haven't programmed before. It will be weird at first, but you'll pick up enough to do what you need to in no time.

Starting our project

As I mentioned on Friday, from now on we're going to stop with the usual labs and work on a project for the rest of the semester. The basic project is to characterize and simulate USB-controlled foam rocket launchers.

The ultimate goal will for you to be able to calculate numerically the flight of a realistic projectile and use this result to actually hit a target with the launcher. You will have to include drag forces and everything - using measured values of launch velocities, drag coefficients, etc. The experimental end of this will be measuring launch velocities, their variability, and trying to measure drag coefficients using the sensors we have. How to get a good measure of the drag coefficient will require some time and care. By the end, we should be able to specify a target, and you will perform the calculations and then actually hit the target.

The theoretical end of this is figuring out how to calculate things numerically. Projectile motion with drag can't be done analytically, so we'll need to learn how to simulate things. To start with, we can do this in pseudocode, as I did on Friday, just learning the appropriate algorithm for calculating trajectories numerically. Once you've got your head around how the process works, we can start with actual code. For those of you that can program, you're free to use any language you want and any methods you want. What you do has to make sense, and it has to work. For those of you that can't program, I'm going to teach you just enough Python to get the job done. We'll start learning basic python coding tomorrow; see the next post.

Scholarship/Grant opportunities

Alabama Space Grant Consortium Undergraduate Scholarship

Online Application:  https://spacegrant.net/apps/?pk=als1

Amount:  $1,000

Duration:  12 months (may renew for 1 additional year)

 

Requirements:

Must complete a short report at the end of the school year or participate in a volunteer outreach activity

Eligibility:

US Citizen

Full-time undergraduate student (Junior or Senior during Fall 2014 semester)

GPA of 3.0 or greater

Majoring in Science, Technology, Engineering, or Math

 

Alabama Space Grant Consortium Teacher Scholarship:  Undergraduate Pre-Service Teachers in Science & Mathematics

Online Application:  https://spacegrant.net/apps/?pk=als1

Amount:  $1,000 (non-renewable)

Duration:  12 months

Requirements:

Must complete a short report at the end of the school year or participate in a volunteer outreach activity

Eligibility:

US Citizen

Full-time undergraduate student

GPA of 3.0 or greater

Enrolled in a track that leads to teacher certification as a K-12 math or science teacher

Some notes from last class (curved paths)

These notes cover what we did in class on Monday (since it isn't in the book). We won't dwell on these results for now, but will re-use them when we revisit circular motion and when we talk about general gravitation. 

New HW is out.

Here you go. First daily problems due this coming Friday, a couple more next Monday, and the whole thing due next Wednesday.

Lab for tomorrow

Work and energy.

Writing center hours

Not really relevant for this class, but FYI.

The UA Writing Center (Lloyd 322) announces its Spring semester hours:  Monday-Thursday, 10 am-6 pm; and Friday, 10 am-3 pm.  Walk-in hours are available at Java City/Gorgas Library, Monday-Thursday, 7 pm-9 pm.

The UA Writing Center offers free, friendly writing consultations to all UA students.  Writing Center consultants are prepared to work in numerous subject areas, and at any stage of the writing process.  For complete details, including appointment scheduling, please visit writingcenter.ua.edu.  

Exam 1 solutions

Here you go.

I've also posted the solutions to your quizzes so far.

Women in Physics & Society of Physics Students meeting

A opportunity for stargazing with cookies and tea tomorrow night. Open to all interested.

We invite all women interested in physics & astronomy
(undergraduate and graduate students, postdocs and research assistants
associated with science & engineering) to our
Joint Meeting with SPS: Spring Meeting with Stargazing
Wednesday February 5th, 7:00-9:00 PM
223 Gallalee Building and dome on top of Gallalee Hall

Please join us for some interesting discussions with cookies and tea under the stars.
We are looking forward to seeing you
Prof. Claudia Mewes, Prof. Preethi Nair, Prof. Dawn Williams

Lab for 5 Feb

Tomorrow, we'll do a relatively simple lab on friction.

Additionally, we'll start to talk about work & energy, and figure out some better problem-solving methods that are less tedious than what you've dealt with so far. If there is time, I'll sketch out the solutions to the exam problems, but that may have to wait until Friday.

Given that I was out sick yesterday, and am not feeling great today, I am not sure when the exams will be graded. I'm hoping for Friday, but Monday at the latest.

Formula sheet for exam 1

The formula sheet I'll give you tomorrow will look a lot like the one I used last time I taught PH125. A few things to note:

• The exam was later last time, so there are a few things on the formula sheet we haven't covered (drag force, curved paths)
• I will add at least the trajectory y(x) for a projectile launched from the origin (in addition to the parametric x(t) and y(t) equations already there. 
• You can still bring in 1 sheet of your own in addition to what I provide. 
• Don't forget to bring a calculator tomorrow. Check the batteries.

Homework 2 solutions

Here you go. I didn't get a solution finished for #8 yet, but since that required a trick that we'll not really cover in class until next week, it isn't something that would show up on the exam anyway.

Exam 1 details

As you may be aware, exam 1 is Monday during our usual class time in our usual classroom. While this is a 2 hour class period, I am designing it to be a 1 hour exam. You will have 2 hours if you need it, but if you finish in an hour (like I hope) you can just leave early.

Here are the sections from the textbook covered

• 1D motion (2.3-2.9)
• 2D motion (4.2-7)
• Force & motion (5.2-9, 6.2-3, 6.5)

There will be 6 problems in total, of which you must complete 4. If you do more than 4, I will grade them all and use the best 4 (but try to get 4 done well first). There will be a formula sheet provided with all the basic formulas and any numerical constants you will need, and you can bring in one sheet of 8.5x11in paper of your own with notes, etc. What you put on the one sheet you bring in is entirely up to you, and you can use the front & back of the sheet.

There will be heavy partial credit on the exam, so show all your work and be as clear as possible about what you are trying to do.

Good things to study? Old homework and exams, and the homework problems I've given you so far. The exam questions will be easier than the homework I've given you, so don't worry too much. Doing the example problems in the book, or the odd numbered end of chapter problems is also good (so you can see the answer when you're done).

I'll be posting HW2 solutions shortly.