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04 September 2012

Wolfram calculators, and a conceptual physics kinematics possibitily

I've been using Wolfram Alpha scripts regularly as I prepare conceptual physics questions.  I need to know, say, the critical angle for light traveling from Lucite to water.  I'm more than competent to use a scientific calculator to figure that out; however, getting up to fetch the calculator* is more trouble than it's worth.  I just go to, type in "critical angle calculator," and input values. Voila.  

* and not finding the calculator, and swearing mildly, and looking somewhere else, and... honestly, I've got no grounds to complain about students, Burrito Girl tells me.

In conceptual physics, I don't want students doing any plug-and-chug problems that truly require a calculator.  They can find the speed of a mass dropped from rest after 3 seconds:  add 10 m/s of speed each second.  But they can't find the maximum height for a ball shot upwards at 4.8 m/s.  

That said, by the time we get to kinematics, I *do* want my students to be able to fill in known and unknown variables in a chart, with appropriate signs.  With no calculation, students can recognize that  "maximum height" means final velocity equals zero; that initial velocity and acceleration must have opposite signs; and that the problem is solvable with three of the five kinematics variables.

The final skill I'd like to teach is recognizing the reasonability (or unreasonability) of the answer.  We can develop a feel for how fast 4.8 m/s is -- that's a bit more than 10 mph, so we can all throw a ball much faster than that.  If someone tells me that the ball will go 120 m, I know that's silly: no matter how hard I throw, I cannot get a ball to reach the top of a skyscraper.  But the (correct) answer of 1.2 m is reasonable, 'cause that's a bit higher than a meterstick, and I can certainly throw higher than that.

Now, Wolfram Alpha will, in fact, spit out kinematics answers given input values, just like it spit out critical angles.  But the script for kinematics is not neat and clean.  Look up speed under constant acceleration on wolfram to see what I'm talking about.  I can easily get to an answer, but it often takes three clicks to choose the right input format, and then much sorting through a wide variety of output formats (e.g. 480 ms and .48 s and such). That's too complicated for freshmen.

I've taught kinematics for years using a five-entry chart, always in the same order, for each problem:  initial velocity, final velocity, displacement, acceleration, and time.  I'd like to see a script somewhere that takes these exact inputs in this exact order, and that spits out the missing values.  

Now, the simplest solution is to use the TI-83 calculator.  My colleague Alex Tisch actually programmed something like this.  But I've tried to move away from that evil, expensive, and complicated calculator.  Among other things, I don't want to have to teach the class the five buttons to press just to enter the program.  Instead, I want a simple app on a smartphone or on a computer.  (I'm getting ipads for use in class this year, and here would be a great use for them.  Plus most of the students have smart phones that they can use on dorm.)

Such an app cannot be that difficult to program... in fact, if you give me an Apple 2c or a TRS 80, I could still, now, create such a program.*  Thing is, I don't know how this dagburn newfangled technology works. Can someone point me to such a script?  Or, could someone program such a script?  If you do, I will send you a can of skyline chili upon request.


10 print "Nachos!";
20 goto 10
30 tell teacher computer is broken
40 wait to hit "ctl-c" until she's called three different colleagues for help
50 I never actually did this, but I had several teachers who deeply deserved it.

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