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2012 April 27

Pressure and volume lab

Filed under: home school — gasstationwithoutpumps @ 19:25
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I decided to do a lab out of order of the textbook today.  There were two reasons for this:

  1. I had just gotten a bunch of physics toys that I had ordered from Arbor Scientific.
  2. I wanted the students to start working on designing a water-bottle rocket simulation and experiment.

Elasticity of gases demo machine from Arbor Scientific. Picture copied from Arbor Scientific website.

One of the toys I had bought was an “Elasticity of Gases” demo. This simple device has a large syringe with a plug that you can screw into the tip, and a pair of sturdy fiberboard disks to act as a stand and a load platform.

I had the students pour water into a bucket, weigh bucket, then balance it on the platform, reading the volume in the syringe.

Here is the data as they recorded it:

# Pressure-volume relation for air in a cylindrical plunger
# The cylinder has a cross-sectional area 6.64 square cm
# Mass of applied weight (kg), Volume of gas (cubic cm)
0.0   50
1.56    42
2.49    38
3.39    35
5.385   29

I then challenged their data, since pressure times volume is supposed to be a constant. It took a bit more nudging than I had expected for them to realize that there was atmospheric pressure at the beginning. Then one of the students did a quick fit with gnuplot and got that everything fit fairly well.

We tried measuring the cross-sectional area of the syringe two ways: measuring the inside diameter of the syringe with calipers and measuring the scale on the side of the syringe. The calipers produced a substantially smaller estimate of the cross-sectional area, probably because the calipers couldn’t reach past the bump on the end of the syringe that makes it difficult to pull the plunger all the way out.  We ended up using the estimate from measuring the scale on the side of the syringe.

I redid the gnuplot script to use proper metric units:

set title "volume vs. pressure"

set xlabel "applied pressure (N/m^2)"
set ylabel "volume (ml)"
set key top right

area=6.64E-4    # cross-sectional area of cylinder in m^2,
# estimated from measuring the length of the scale on
# the syringe:  7.53 cm for 50 ml

g = 9.7995    # local gravitational field in N/kg
# according to the Wolfram Alpha's gravitational widget

press(mass) = mass*g / area    # pressure in N/m^2 (Pascals)

fit a/(x+b) 'press-vol.gnudat' using (press($1)):2 via a,b

# The fit got
# a               = 5.66175e+06      +/- 1.398e+05    (2.47%)
# b               = 112736           +/- 3338         (2.961%)

platform = 0.150    # platform weight 150g

d=102800    # barometric pressure of 102.8kPa measured at
fit c/(x+press(platform)+d) 'press-vol.gnudat' using (press($1)):2 via c

fit e/(x+press(platform)+f) 'press-vol.gnudat' using (press($1)):2 via e,f

plot 'press-vol.gnudat' using (press($1)):2 title "data", \
a/(x+b) title "fit PV and barometric pressure",  \
c/(x+press(platform)+d) title "fit PV, barometer=102.8kPa, 150g platform"

Volume versus pressure graph, showing an excellent fit between theory and measurement. The estimated barometric pressure is about 10% too high. Using measured barometric pressure and correcting the force by the weight of the platform is almost as good a fit, but not quite.

Gnuplot’s fit was
a = 5.66175e+06 +/- 1.398e+05 (2.47%)
b = 112736 +/- 3338 (2.961%)
so the initial pressure in the cylinder is estimated as 112.7kPa  (the ± 3.3kPa is bogus, as that just reflects the error in the fit, not the error in the measurements—the volume measurements were probably about ±1ml, which would be a 2–3% variation). According to a local weather station the barometric pressure at the time was 102.8 kPa, so our correction of 112.7kPa was about 10% too high—perhaps some of the problem was due to the weight of the platform, which could have increased the pressure so that the 50ml corresponded to a pressure a little higher than atmospheric. Adding the force for the 150g platform reduced the estimate of barometric pressure to 110.5kPa, which is still 7.5% too high.  It might have helped to have more measurements, averaging out some of the noise, to get better estimates of atmospheric pressure. (Masses around 500g, 1kg, 4kg, and 6kg would have been useful to add, but we ran out of time.)

The pressure vs. volume theory is not until Chapter 13 (Gases and Engines) and we’re still on Chapter 11 (Angular Momentum).  But I really want the students to design and execute a soda-bottle-rocket lab. I even bought a medium-priced launcher from Arbor Scientific, instead of having them use the much cheaper friction-fit launcher I’ve had for the past 5–10 years, so they could get more repeatable launch pressures. I considered making my own trigger-release launcher, but at $26 the launcher was cheap enough not to entice me to build my own. (I probably could have done it for under $10, but I don’t have much time over the next 2 weeks.)

We haven’t done the full ideal gas law—we’ve left temperature out of the equation for now.  We’ll get to that when we do Chapter 13. But the adiabatic simplification (constant temperature) is good enough for now.

I don’t believe that they can come up with reasonable equations for the force expelling water from the bottle and for the mass of the water still in the bottle, unless they can model the volume of the air and the pressure in the bottle as they change with time.  I think that this will most likely have to be a computational model, rather than an analytic one, as too many things are functions of time.  Maybe everything simplifies so that analytic solutions are reasonable, but I suspect not.

2012 April 26

San Leandro fund-raising for AP Physics

Filed under: home school — gasstationwithoutpumps @ 22:46
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According to a Patch article, Advanced Physics Class $8,500 Away – San Leandro, CA Patch, an anonymous donor contributed $10,000 if the community could match it, in order to fund $20,000 worth of instructional materials and lab equipment to start an AP Physics class at San Leandro High.

While I applaud the donor(s) for trying to start a physics class in San Leandro, I wonder a bit at the price tag.  It is certainly possible to spend that much on high school lab equipment—I get the Pasco catalog and they do have some high-priced toys!  But it is also possible to teach AP Physics with much less equipment and with much cheaper equipment (even just changing to a lower-price vendor like Arbor Scientific can save a lot).  I’ve been home-schooling AP Physics this year and most of the equipment was stuff we had around the house. Even buying it all new would probably come to only $300, plus $90 for the textbook.

Granted, equipment designed to last several years in the hands of teenagers might need to be a bit more robust than what I could cobble together at home to last for one lab session, but I suspect that a class of 30 (about all they’re likely to get the first year) could be reasonably well equipped and provided with new textbooks for under $10,000.  I’m curious what the $20,000 will buy.

I’m also curious to hear from people who have been teaching AP Physics for a while.  How much does a decent (not luxurious) lab setup for AP Physics cost these days?  I suppose there are several components:  consumables (1/student every year), textbooks (1/student, good for 5–7 years), student lab equipment (1/group of 2–3 students), classroom equipment (1/classroom), and school-wide equipment (1/school).  What I’m interested in hearing how the budget is divided among the different components.  Put another way—if you had $20,000 to start an AP Physics class (for equipment and materials, not staff), how would you spend the money?

My expenses have been small in part because I don’t need much “demo” equipment—nothing needs to be seen from the far side of a classroom, so I can use little things rather than big ones.  I also had the luxury of having students who were good at math—they already knew how to visualize and add vectors, so I did not need to do all the force table demos and labs.  I was also limited in the time I had with the students (2 hours a week to cover all the material, do the labs, and check the homework), so I may have shortchanged the students a bit on labs. I hope they got enough good lab experiences, and we’re going to do almost all lab stuff after the AP exams, but I do wonder if they would have gotten more useful lab work in a traditional class.

Of course, a big part of savings comes from the simple fact that I’m cheap.  For a one-time lab, I’d rather duct-tape together something that works well enough than pay hundreds of dollars for the shiny Pasco toys, as fun as they are to look at in the catalog.  (Since I’m an engineering professor, they send me the “Engineering” catalog, which I think has even fancier and more expensive building toys than the “Physics” catalog.)  It may well be that the time it takes to make and debug jury-rigged equipment would make it more expensive than the commercial stuff, if a teacher or other staff person were actually being paid to do it, and if the labs had to be run year after year.

2012 April 25

Photoeletric effect

Filed under: home school — gasstationwithoutpumps @ 16:30
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Brain Frank has just posted an exploratory exercise on his blog Teach. Brian. Teach.: Photoeletric Effect.  This exercise relies on a simulation from the University of Colorado at Boulder.

The simulation is of a standard phototube experiment.  A phototube is a vacuum tube diode, in which the cathode is illuminated by a light source.  The photons excite electrons in the cathode, raising some of them to high enough energy levels to become unbound from the atoms and leave the cathode.  The electric field accelerates them toward the anode (or repels them, if the diode is biased backward).  The energy of the electrons is basically the energy of the photons minus the energy needed to raise the electrons from the ground state to the unbound state.  (At very high illumination levels, you can have one photon exciting the electron out of the ground state and another raising it to the unbound state, but I don’t think that effect is being simulated.)

At forward voltages, the current is determined by the illumination, independent of the bias—essentially all the released electrons go to the anode. At reverse biases, only the higher energy electrons have enough speed to make it to the anode. The energy of the highest-energy electrons can be estimated from the reverse-bias voltage at which the current drops to zero.

The simulation seems pretty good, but I don’t know exactly what effects they are modeling.  For the zinc target with high forward bias, there is a current peak around 135 nm, but from the spectral lines at NIST, I would have expected a peak around  127 nm.  I don’t know if the problem is a limitation of the simulation or a limitation of my understanding.

I know that my understanding of quantum effects is very limited, and the simplistic view of the photoelectric effect given in Wikipedia does not cover some of the phenomena being simulated here.  But since I don’t know exactly what phenomena are being simulated, I have no way of predicting the behavior.

I find it frustrating to do the sort of discovery experiment that Brian is proposing using a simulation.  If I knew precisely what was being simulated, there would not be much discovery, but trying to reverse engineer a simulation from its behavior seems to me a rather irritating and frustrating exercise. I not only have to guess at what physics is important, I also have to guess at what physics the writer of the simulator thought was worth including, and what simplifying assumptions he made.  (For example, is the simulation including the absorption of the glass or quartz tube holding the vacuum?)

I suppose I could read the source code (PhET provides that) or read the 17 “Teaching ideas” on the web page for the simulation. The teaching ideas look like a wide range of different lesson plans for labs, demos, and homework questions.  I looked at one of the “advanced” ones, but it seemed to only use the Wikipedia-level model, which does not explain a drop in current with shorter wavelengths.

I’d much rather have real experiments than simulated ones—even if the crudeness of my measurement tools limits the quality of the data I can collect.  The value of simulations is more in writing them and seeing that they predict the behavior you observe than in running someone else’s black-box model.

Circus physics

Filed under: Uncategorized — gasstationwithoutpumps @ 11:21
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The latest edition of the newsletter of the American Society for Engineering Education has an article about some great physics labs for schools that happen to be located near circus schools: An original dynamics course brings engineering under the Big Top Connections Newsletter—April 2012.

The idea is simple: a lot of circus acts are based on fairly simple physics.  Five acts that can be performed safely by novices with appropriate safety equipment were chosen, and students attempt them after modeling what should happen.  Standard physics-lab data logging equipment was used to gather and analyze data from the performances by students.

The five acts chosen were the German wheel, a bungee trapeze, the flying trapeze, the low-casting trapeze, and the Spanish web.  (Only the German wheel is shown in the article.)

This article has been a long time making it to print: the class was taught once in 2009.  I wonder how much it costs to put on a class like that—there are at least 2 suitable places in the San Francisco Bay Area (National Circus Center in San Francisco and Trapeze Arts in Oakland).  I suspect that they could attract a lot of Silicon Valley engineer families if they offered physics lessons along with the circus lessons.

2012 April 23

Locally disabling Python CGI scripts

Filed under: Uncategorized — gasstationwithoutpumps @ 21:08
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A couple days ago, I posted Fitting a sphere, describing some Python code I had written to fit a hollow sphere to a cloud of points.  I distributed the code on Saturday (which I have since added to) on a web page on my computer at work, but I was a bit frustrated, because the “.py” extension on the files was causing problems.
The .py extension is needed on the files for Python to be able to find the module and import routines from it, but the Apache webserver (as configured by our webmaster) insists on treating all .py files as executable scripts. Since the .py files are not marked as executable, it fails and reports an error message to the browser, rather than delivering the text.
After complaining about this to some random grad students this afternoon, I spent a few minutes today searching the web, and found some simple instructions: How-to locally Disable Python CGI scripts. | Kevin Deldycke.

The technique is really simple: you create a .htaccess file in the directory that contains the .py files, and add the line

RemoveHandler .py

to the .htaccess file. That tells Apache that it doesn’t know how to interpret .py files in this directory, and it should just deliver them to the browser.

Even better, the .htaccess file applies recursively to all subdirectories, so if you put the file in your top-level directory, then all your .py files in any subdirectory will be available as text, not executed (at least, until some .htaccess file does something like “AddHandler mod_python .py“.

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