# Gas station without pumps

## 2014 July 6

### Battery connectors

Filed under: Uncategorized — gasstationwithoutpumps @ 02:32
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I spent a little time today working on my book, but I got side tracked into a different project for the day: designing a super-cheap coin-cell battery connector. I’ve used coin-cell battery holders before, like on the blinky EKG board, where I used a BH800S for 2 20mm CR2032 lithium cells. That battery holder is fairly large and costs over \$1—even in 1000s it costs 70¢ a piece. So I was trying to come up with a way to make a dirt cheap coin-cell holder.

The inspiration came from the little LED lights that “glovers” use inside their gloves. They are powered by two CR1620 batteries (that means a 16mm diameter and 2.0mm thickness for the battery). Because the lights have to be made very cheaply, they don’t use an expensive holder, but put the negative side of the batteries directly against a large copper pad on the PC board. The batteries are held in place by the positive contact, which is a piece of springy metal pressing the battery against the board—and each manufacturer seems to have a slightly different variant on how the clip is made.

Unfortunately, I was unable to find any suppliers who sold the little clips—though I found several companies that make battery contacts, it seems that most are custom orders.

My first thought was to bend a little clip out of some stainless steel wire I have sitting around (not the 1/8″ welding rod, but 18-gauge 1.02362mm wire). That’s about the same thickness as a paperclip (which is made out of either 18-gauge or 19-gauge wire), but the stainless steel is stiffer and less fatigue-prone than paperclips. I was a little worried about whether stainless steel was solderable, so I looked it up on Wikipedia, which has an article of solderability. Sure enough, stainless steel is very hard to solder (the chromium oxides have to be removed, and that takes some really nasty fluxes that you don’t want near your electronics). So scratch that idea.

I spent some time looking around the web at what materials do get used for battery contacts—it seems there are three main ones: music wire, phosphor bronze, and beryllium copper, roughly in order of price. Music wire is steel wire, which gets nickel plated for making electrical connections. It is cheap, stiff, and easily formed, but its conductivity is not so great, though the nickel plating helps with that. The nickel oxides that form require a sliding contact to scrape off to make good electrical connection. Phosphor bronze is a better conductor, but may need plating to avoid galvanic corrosion with the nickel-plated battery surfaces. Most of the contacts I saw on the glover lights seemed to have been stamped out of phosphor bronze. Beryllium copper is a premium material (used in military and medical devices), as it has a really good ratio of yield strength to Young’s modulus, so it can be cycled many times without failing, but also has good conductivity.

Since I don’t have metal stamping machinery in my house, but I do have pliers and vise-grips, I decided to see if I could design a clip out of wire. It is possible to order small quantities of nickel-plated music wire on the web. For example, pianoparts.com sells several different sizes, from 0.1524mm diameter to 0.6604mm diameter. I may even be able to get some locally at a music store.

My first design was entirely seat-of-the-pants guessing:

First clip design, using 19-gauge wire, with two 1mm holes in PC board to accept the wire. This design is intended for two CR1620 batteries.

The idea was to have a large sliding contact that made it fairly easy to slide the batteries in, but then held them snugly. Having a rounded contact on the clip avoids scratching the batteries but can (I hope) provide a fair amount of normal force to hold the batteries in place. But how much force is needed?

I had a very hard time finding specifications on how hard batteries should be held by their contacts. Eventually I found a data sheet for a coin battery holder that specified “Spring pressure: 50g min. initial contact force at positive and negative terminals”. Aside from referring to force as pressure and then using units of mass, this data sheet gave me a clear indication that I wanted at least 0.5N of force on my contacts.

I found another battery holder manufacturer that gave a tiny graph in one of their advertising blurbs that showed a range of 100g–250g (again using units of mass). This suggests 1N-2.5N of contact force.

Another way of getting at the force needed is to look at how much friction is needed to hold the batteries in place and what the coefficient of friction is for nickel-on-nickel sliding. The most violently I would shake something is how fast I can shake my fingertips with a loose wrist—about 4Hz with an peak-to-peak amplitude of 22cm, which would be a peak acceleration of about 70 m/s^2. Two CR1620 cells weigh about 2.5±0.1g (based on different estimates from the web), so the force they need to resist is only about 0.2N. Nickel-on-nickel friction can have a coefficient as low as 0.53 (from the Engineering Toolbox), so I’d want a normal force of at least 0.4N. That’s in the same ballpark as the information I got from the battery holder specs.

So how stiff does the wire have to be? I specified a 0.2mm deflection, so I’d need at least 2N/mm as the spring constant for the contact, and I might want as high as 10N/mm for a really firm hold on the batteries.

So how should I compute the stiffness of the contact? I’ve never done mechanical engineering, and never had a statics class, but I can Google formulas like any one else—I found a formula for the bending of a cantilever loaded at the end:
$\frac{F}{d} = \frac{3 E I}{L^{3}}$, where F is force, d is deflection, E is Young’s modulus, I is “area moment of inertia”, and L is the length of the beam. More Googling got me the area moment of inertia of a circular beam of radius r as $\frac{\pi}{4} r^{4}$. So if I use the 0.912mm wire with an 8mm beam I have
F/d = 200E-6 mm E.

More Googling got me some typical values of Young’s modulus:

material E [MPa = N/(mm)^2]
phosphor bronze 120E3
beryllium copper 135E3
music wire 207E3

If I used 19-gauge phosphor bronze, I’d have about 24N/mm, which is way more than my highest desired value of 10N/mm. Working backwards from 2–10N/mm what wire gauge would I need? I get a diameter of 0.403mm to 0.603mm, which would be #6 (0.4064mm), #7 (0.4572mm), #8 (0.5080mm), #9 (0.5588mm), or #10 (0.6096mm), on the pianoparts.com site. I noticed that battery contact maker in Georgia claims to stock 0.5mm and 0.6mm music wire for making battery contacts, though they first give the sizes as 0.020″ and 0.024″, so I think that these are actually 0.5080mm and 0.6096mm (#8 and #10) music wire.

It seems that using #8 (0.020″, 0.5080mm) nickel-plated music wire would be an appropriate material for making the contacts. Note that the loop design actually results in two cantilevers, each with a stiffness of about 4N/mm, resulting in a retention force of about 1.6N. The design could be tweaked to get different contact forces, by changing how much deflection is needed to accommodate the batteries.

How much tweaking might be needed?  I found the official specs for battery sizes (with tolerances) in IEC standard 60086 part 2: The thickness for a 1620 is 1.8mm–2mm, the diameter is 15.7mm–16mm, and the negative contact must be at least 5mm in diameter.  The standard also calls for them to take an average of 675 hours to discharge down to 2v through a 30kΩ resistor (that’s about 56mAH, if the voltage drops linearly, 67mAH if the voltage drops suddenly at the end of the discharge time).  If the batteries can legally be as thin as 1.8mm, then to get a displacement of 0.2mm, I’d need the zero-point for the contacts to be only 3.4mm from the PC board, not 3.8mm, and full thickness batteries would provide a displacement of 0.6mm, and a retention force of about 4.8N.

If I were to do a clip for a single CR2032 battery, I’d need to have a zero-point 2.8mm from the board, to provide 0.2mm of displacement for the minimum 3.0mm battery thickness.

So now all I need to do is get some music wire and see if I can bend it by hand precisely enough to make prototype clips.  I’d probably change the spacing between the holes to be 0.3″ (7.62mm), so that I could test the clip on one of my existing PC boards.

Update 2014 July 6: I need to put an insulator on the verticals (heat shrink tubing?), or the top battery will be shorted out, since the side of the lower battery is exposed.

## 2014 May 21

### Establishing the habit of writing

Filed under: Circuits course — gasstationwithoutpumps @ 09:19
Tags: , , ,

In Preparing for AP Physics 1: establishing the habit of writing Greg Jacobs writes

I’m in the infant stages of planning my AP Physics 1 course. The big trick is going to be establishing my students’ ability and willingness to write their reasoning, to get them to focus on communication rather than on getting a correct numerical answer. Once it’s clear that they are not taking a math course—once they see that the solution to a problem looks much more like what they’ve done in biology or economics than in calculus—I think the students will be able to move along quickly and enthusiastically through the material.

Students must get comfortable with calculation. However—as was correctly pointed out to me at the AP consultant meeting in April—if we start the course with lots of pure calculation, students will think that getting the answer is the holy grail of physics problems. If instead we begin the course demanding description, explanation, and all sorts of prose, students may become accepting of the idea that a numerical answer is merely the result of careful reasoning.

If this change in AP Physics actually works (something I’m always skeptical about in any curriculum reform, particularly at the high school level), it may help engineering students in college. Engineers do far more writing than most professions, with far less training at doing it.

I don’t think that a prompt that just says “In a clear, coherent, paragraph-length explanation, describe how you would figure out …” is going to do the trick, though. If they could already write clear, coherent paragraphs about how they would figure something out, then they would not need the curriculum change—they might not even need a physics class at the level of Physics 1.

I’m struggling with this problem in my applied circuits course, in which I require weekly design reports for the circuits they design and build. The students are staying in lab until they finish the designs and demo them, so they are clearly capable of doing the work (though not always as quickly as they should). But only a few students can explain their computations for the design parameters (like gain, corner frequency, and component values) clearly—others put down any nonsense that has a few of the right buzzwords in it.

The top students have gotten better at their explanations as a result of feedback, but the bottom students are still often producing word salad. Although there is some indication of a general writing problem (lack of topic sentences, poor grammar, and misused vocabulary), the problem is most pronounced when they are trying to explain how they selected component values. The more steps that there are in the underlying math, the more jumbled their explanations, even if the problem is just a chain of multiplications.

From time to time, I’ve suspected that the students don’t produce coherent sentences about how they computed something may not have actually done the computation, but “borrowed” the result.  This is not an explanation I believe in strongly, though, as the students have been (mostly) coming up with different solutions to the design tasks, so there isn’t simple copying going on. I’ve also seen the design process the students use, as they have been doing their pre-lab work in lab (instead of at home), so I hear them discussing the problems.  They do ask each other not just what answer they got, but how to get the answers, so they are trying to learn the method.

In looking at the pre-lab homeworks that were turned in on Monday I realized what part of the problem is—the students keep absolutely awful design notes. What the students turned in on Monday (even the top students) was mostly incomprehensible scribbling of numbers, with no indication where the numbers come from or what they were attempting to compute.  Half an hour after writing down the notes, I’m pretty sure that they could not reconstruct their reasoning—hence the often magical methods in their design reports, where they copy numbers out of their notes (some of which are correct), but can’t put together a coherent chain of reasoning that leads to those numbers. On the long multi-step computations needed to figure out what gain an amplifier needs, they can usually do each step (though often needing coaching on one or two of the steps, either by me or by one of the better students in the course), but they don’t record the meaning of each step or even what the sequence of steps is, and the “answer-getting” mentality causes them to flush the process from their minds as soon as they have a number.

I’ve seen a lot of lab exercises for other courses that try to scaffold the process by providing worksheets that give the step-by-step process and have the students fill it out as they go along. I don’t think that this is helpful though, as it encourages students to solve one step at a time and then forget about it—the scaffold prevents the students from exercising the very skill that I most need them to learn. Showing them worked examples, as I have done in class, doesn’t seem to help much either—they can follow along as I break the problem down with them, and think they understand, but then not be able to do the same thing themselves.  Again, the scaffolding prevents them from exercising the skill I most need them to learn—identifying problems and them into subproblems.

For next year, I’m probably going to have to come up with some exercises which get students to organize their thoughts external to their heads. So far, the only thing I’ve thought of is to have them create a fill-in-the-blank worksheet for each lab (like an income tax form), and turn in the blank worksheet and try filling out each other’s worksheets.  If they get in the habit of writing down the steps as steps, it may help them be able to reconstruct their work when they convert it into full sentences for the final reports. It may be too late for me to do anything formal this year (only 2.5 weeks left), but I’ll suggest it to the students anyway.

The advice I’d give to Greg Jacobs is to leave the “clear, coherent paragraph” until later in the quarter—get them to create worksheets first.

I’d welcome any suggestions from my blog readers on ways that I can get students to learn to organize their thoughts in a way that they can present them coherently to others. Block diagrams alone don’t seem to be enough, and vague things like “mind maps” are likely to do more harm than good.

## 2013 December 23

### Different levels of the “same” course

Filed under: Uncategorized — gasstationwithoutpumps @ 12:46
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In thinking about the redesign of the bioengineering curriculum, I’ve had to pay a lot of attention to what level of courses the engineers would be required to take.  Our campus offers physics at three different levels (one algebra-based, the other two calculus-based) and calculus at 4 levels (honors for math majors, for physicists and engineers, for life scientists, and for economists). Do I allow the students to take either of the calculus-based physics courses? Do I allow any of the three calculus classes (excluding the one for economics majors)?  I’ve wrestled with this problem for a while (see for example, my post Physics for life-sciences majors from last June).

### In favor of allowing the lower level courses:

Usually there is the most scheduling flexibility for the second-lowest level—the level aimed at biology majors—because that is where the largest numbers of students are, so the courses get offered repeatedly during the year, while the more advanced courses get offered only once.  So from a scheduling standpoint, it would be best if students were able to take those courses.

In bioengineering, we also get a lot of students who start out in biology, but who later realize that other majors are more interesting (freshman year everyone thinks they want to go to med school—most have given no thought at all to engineering).  Because the biology majors are advised to take the calculus and physics courses intended for biologists, the students have taken only those and not the higher level calculus and physics courses intended for engineers.  So a change of major is easier if students are allowed to take the biology-level calculus and physics.

One thing I’m trying hard to avoid in the bioengineering curriculum redesign is “creeping prerequitism”—the tendency for most courses to gradually increase the prerequisites in order to have better prepared students in the course.  In many cases the prerequisites are irrelevant to the material of the course (like multi-variable calculus for a data structures course or genetics for a cell biology course), but are just filter prereqs, to make sure the students have more “maturity” by having passed a gantlet of other course.  Because of these prerequisites (both real ones and filter ones) being added independently by each of the 8 or 9 departments that teach courses required for bioengineers, we end up with a program grossly overloaded with lower-division “preparation” courses, and not enough upper-division “application” courses.

### Against allowing the lower-level courses:

In exit interviews with seniors last spring and this fall, we asked them about their experiences in calculus and physics.  Those who had taken the lower level of calculus-based physics course felt that it had been a waster of their time—neither their classmates nor their professors seemed to care much about whether the material was learned, and everything was covered rather superficially.  (We didn’t get the same info about calculus, because most had been forced to retake the higher-level calculus class if they had only taken the biology-level one.)  So from a pedagogic standpoint the students get a better course if they take the higher level with students who expect to use the material and with professors who expect their own majors to be taking the course.

Some upper-division courses do rely on math and physics skills of the more advanced courses.  For example, the upper-division probability and statistical inference classes do rely on students being adept at integration, the statics and dynamics course relies on students knowing Newtonian mechanics well and being able to handle differential equations, and the electronics courses require some skill with calculus and differential equations.

### Concluding thoughts

I read an blog post today by a high-school physics teacher addressing a similar question at the high-school level: Jacobs Physics: How do you tell the difference between AP and “regular” physics?.  He doesn’t have to face what courses students are required to take, but only which ones they should be advised to take, but the underlying questions are the same. In the post, Greg Jacobs writes

If an AP and a Regular course cover the same “standards,” how are the two classes different?

Don’t use standards to define courses; use tests and exams, preferably as written by someone external to the course, to define courses.  Once you’re clear on the level, topics, and depth of question that your students will be expected to answer, then you can make up a concordance with any state standards you need to.

The AP Physics 1 exam covers much of the same material as regular/Regents. The major difference is the depth of that coverage, as evidenced in the test questions.

A regular question can generally be categorized in a single topic area, and can be answered in one step, or two brief steps, or a one-two sentence explanation with reference to a single fact of physics.

An AP question generally requires cross-categorization across two or three topic areas. Most require multi-step reasoning, or a two-three sentence explanation with reference to more than just one fact of physics. AP questions, for the most part, require students to make connections across skills and topics.

As an additional comparison, you might consider a conceptual class. Conceptual Physics can cover many of the same topics as “regular” physics, but without using a calculator.  …  A conceptual approach provides a greater contrast between AP and non-AP physics.

The key idea here is that the difference between levels is not in what subjects are covered, but in the expected skills of the students after taking the course. That holds true at the college level as well—I can’t decide based just on catalog copy what level of course students need, because the catalog copy only lists topics, not the complexity of the problems that students who pass will be able to solve.

In the interest of minimizing filter prereqs, but making sure that all genuine prereqs are met, I’m suggesting requiring the higher level for the bioelectronics and assistive technology: motor tracks, but allowing the lower calculus-based physics for the biomolecular and assistive technology: cognitive/perceptual tracks.  I am suggesting requiring the physicist/engineer track for calculus in all tracks, since it is needed for a higher-level course in all of them. It’s not the same course in each track, but electronics, statics and dynamics, and statistical inference all require greater facility with calculus than the calculus-for-biologists track provides.

## 2013 August 4

### Units in physics again

Filed under: Uncategorized — gasstationwithoutpumps @ 17:22
Tags: , , ,

Joe Redish has a series of posts on The Unabashed Academic on the use of units in math and physics courses: Units and stoichiometry, Cutting mathematicians some slackTeaching units, and A higher power—units again.  I just re-read that series of articles today (having read one or more of them when they first came out).

The Teaching units post had one paragraph that particularly caught my attention:

In addition to suppressing units when we do pure math, we might also note that when writing computer code we often suppress units. (This led to a multi-million dollar failure at NASA.) But any object-oriented programming language can correctly retain (and even check) units. I doubt that classes in computation, either in computer science, engineering, or physics departments, teach objects with units—despite the fact that it would be incredibly useful for scientists.

I used Vpython with my son in learning calculus-based physics, and was irritated by its inability to play nicely with units (see Units in physics and Physics simulations). It would be a fairly simple modification to Vpython to allow a “units” option for each plotting or drawing routine  There could be a global option to change the defaults from None (for legacy Vpython code) to “m” for lengths, “s” for time, and “Hz” for frequencies (like the “rate” function), and to require units using the Unum package for all plotting and drawing.

For teaching physics, having unit checks on all computations would help students debug both their programs and their physics understanding.  I really don’t understand why this was not included from the beginning in Vpython, since the language was intended for use as a language for teaching physics. Carrying the units around like this does slow the code down (perhaps by a factor of two), but the pedagogical value of being able to debug incorrect-unit bugs far exceeds the pedagogical value of faster simulations.

Next year, in the circuits course, I’m going to be a stickler about students always including units in their computations, as a consistency check on their thinking, since many of the bioengineers do not have good number sense or algebraic intuition.  Forcing them to carry units throughout may make them a little less likely to do random algebraic manipulations.

## 2013 July 4

### Caballero on teaching physics with computation

Yesterday, Danny Caballero left a comment on my blog with pointers to three preprints of papers he’s been a co-author on:

I couldn’t agree more with the overall sentiment in this post. Computing is important for all students of science and for science teachers. However, as you say, I do think my dissertation work has been misconstrued a bit in this post. So, let me clarify.

The inventory you mention measures a small slice of mechanics taught in introductory physics. It’s been an important slice, but maybe now it’s time to think beyond it. What are students learning above and beyond this assessment? In M&I, they are learning about modeling, computing, and connecting the two. My work shows that the present implementation of M&I doesn’t produce great gains on this assessment, that students make mistakes in their code, and that they are less inclined towards computing after instruction.

So what? We are getting to teach students how science is done and they are using computing to investigate models. Now, this implementation is not the most polished one, which means we have a good way to go. But, that’s OK, because we are not going to fix all these issues overnight. We have been working on them for the last two years in various contexts. But, we need to figure out how to teach science and computing together. And we need to figure out how to do it well.

So, I’ll point you to a few other publications on computing in physics that I’ve written. Two concern high school, and another deals with physics majors. The high school work shows we can implement ideas from my dissertation work at the high school level (as others are doing). Moreover, we find that students who know physics and computing ideas can make good models of systems and are not memorizing lines of code. In my dissertation work, we didn’t do any qualitative work like student interviews, but it’s clear that doing so is necessary. The work with physics majors is one of the first forays into integrating computing in upper-division physics. We show that a new model for implementation can positively affect student attitudes.

Upper-division:
http://arxiv.org/abs/1303.4355

This morning I read his three papers.  They all describe prototype courses that use computational modeling to teach physics, with some analysis of the outcomes.  They are not controlled experiments, but prototyping proof-of-principle projects (as are most educational research “experiments”).  This is not a criticism of the papers—one generally has to do a lot of prototyping before arriving at a method that is robust and repeatable enough to be worth the difficulty and expense of controlled experiments.  Engineers see the need for prototyping, but too many people in other fields think that things have to work perfectly the first time or be discarded forever.

These papers bracket the previous work Danny did that studied computational modeling for first-year calculus-based physics.  The two high-school papers are about a 9th grade physics class that uses the Modeling Instruction approach to teaching physics, to which was added computational modeling using VPython.  The “upper-division” paper discusses adding computational modeling to a 2nd-year classical mechanics course for physics majors, following a traditional 1st-year calculus-based physics course.

I was a little unclear on the level of the 9th-grade course.  In one place he refers to it as “conceptual physics”, but in other parts of the description it sounds more like an algebra-based high school physics course (covering the mechanics half of AP Physics B), a step-up from conceptual physics.

From his description, it seemed fairly straightforward to add a computational component to the Modeling Instruction approach, and it helped students see that all the different “models” taught in that approach are really special cases of the same underlying general model.  They used Vpython with a couple of additional packages (PhysKit and PhysUtil) to make creating graphs and motion diagrams easier for beginning programmers.  The additional packages allow lines like

    motionMap.update(t)
timerDisplay.update(t)
graph.plot(t, cart.pos.x)


in the inner loop, simplifying the usual VPython interface a bit.

It sounds like the students were finishing the course with a mix of students who knew what they were doing and those who still hadn’t quite grasped the physics or hadn’t quite got the programming.  He did try analyzing some of the student work to see whether students were having difficulty with the physics or VPython for making the simulations, but I found the results hard to interpret—raw numbers don’t mean much to me, because I don’t have a good prior expectation of what 9th graders at a private high school should be able to do.  I’m curious whether difficulties with programming correlated with difficulties in understanding the physics, and whether grading the computational homework gave insight into the misconceptions the students had about the physics.

One of the strong points of the computational approach is that it allowed the students to model phenomena usually beyond the scope of 9th-grade physics (like a soccer ball with linear drag forces).  I found this to be the case for calculus-based physics also, where we modeled pendulums without the small-angle approximation (problem 4.P.89 in Matter and Interactions) and the magnetic field lines of a helical solenoid.

Some of his observations are unsurprising: “Students find debugging their programs difficult; that is, they have trouble determining whether they have made a coding error or a physics error and how to deal with that issue. ”  He also noticed that some students found installing the software difficult—I believe that the VPython developers have been working on that problem, though it is not yet at the level where all 9th graders will find it easy.

Personally, I’d like to see the physics simulations for high school students use computations with units throughout—this would help them catch a lot of their physics errors earlier.  I see this lack of units as one of the biggest flaws in VPython as an instructional tool for physics.  I’ve blogged about this before in Physics with Units, and I’ve done some VPython programming using Unum.  Unfortunately, the Vpython plotting and animation code does not play nicely with Unum, and having to strip out the units before plotting or drawing negates most of the advantages of keeping units around. I realize that for professional physics simulations, units are always implicit (in comments and variable names) rather than explicit, because that makes more efficient use of the computer, but for instructional purposes explicit units would be worth the inefficiency.

The 2nd-year classical mechanics course used Mathematica to solve ordinary differential equations (ODEs), and provided only minimal instruction in Mathematica.  The main improvement to the course from my perspective was the addition of a final project that allowed students to study an open-ended physics question of their own choice using computational modeling.  This improvement was discarded in subsequent offerings, because it required too much instructor time. Caballero wrote, “For junior and research-focused faculty, the computational project is a significant investment of their time and energy given the large enrollment in CM 1. Developing authentic, scientific experiences for students that can be sustained with little faculty input is challenging.”

This is a theme that I see repeatedly in course design in all disciplines and at most universities: the really good parts of prototype courses take a lot of instructor time and get discarded.  I think that the goal “sustained with little faculty input” is a wrong goal, but it is one shared by many faculty and administrators, who think that teaching is a burden that should be given as little effort as they can get away with. I’ve decided, rather deliberately, not to design my courses that way, but to design them around high faculty involvement.  I believe that the value of a University education depends on high-contact courses, and I’m willing to resist the MOOCification of the university at least in my own courses.  This does take a lot of my time, and I’ve given up on writing grant proposals to make the time—not a choice that most junior faculty could afford to make, given that promotion these days is based more on how much money is brought in than on the quality of teaching or research.

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