# Posts with «vpython» label

The Slinky Lab post got an interesting pingback from Engineering Failures » Secrets of the ‘Levitating’ Slinky, which describes the curious phenomenon that happens when you suspend a slinky vertically, then release the top end. The bottom end does not move for about 0.3 seconds, when the compression wave from the top reaches it. It might be worth videotaping that phenomenon in this week’s lab.

I think it might be interesting to try to calculate (either analytically, or as part of the VPython simulation) the movement of Slinky as you drop it. In particular, I’m curious at what point the compression wave becomes a shock wave (that is, when does the top of the slinky start moving faster than the speed of sound in the slinky). Note that the speed of sound in the slinky is best expressed as “coils per second” rather than m/s, in order to get a constant speed of sound in the non-uniformly stretched slinky.

The other lab/demo I was thinking of doing this week, measuring the speed of sound in a metal bar, is not going so well.  I was planning to use a setup similar to that in the Chapter 4 Lecture 3 video at http://courses.ncsu.edu/py581/common/podcasts/.  That is, a long metal bar, with a microphone at one end, tapped with metal striker at the other end.  A clock is started when the tap is made (a simple electrical connection), and the waveform is recorded at the other end.

The first problem was that I did not have a suitable microphone.  I found a quick workaround for that problem, as just last week my wife had given me a fine electromagnet that she had found in the street (we have a lot of “found objects” at our house).  The coil has a 68.3 Ω resistance and a laminated iron core, so waving a magnet around near the pole piece results in a fairly substantial electrical signal across the ends.  So I made my own “microphone” with the coil, a refrigerator magnet, and a folded piece of paper as a spring.  If I rest a piece of aluminum bar stock on it and tap the other end, I get a signal of about 0.3 v, which I can see clearly on my oscilloscope.  If it was a storage scope, I’d be almost done, since I could trigger on one channel and record on the other.  I might still have to do something like that with my analog scope.

What I had hoped to do was to use an Arduino to measure the time it took from the tap to the signal arriving at the other end. Using the micros() subroutine provides timing with a resolution of about 4 microseconds, and starting it on electrical connection from the tap is pretty easy.  I had initially thought to use the analogRead() function, but it is too slow: each analog-to-digital conversion takes about 100 microseconds, and the speed of sound in aluminum is about 6400 m/s, or about 150 μsec to go a meter.  I don’t think I can do speed measurements with that low a time resolution unless I had a bar of aluminum 100s of meters long.  That means that to use the Arduino for timing, I have to convert the analog signal to a digital one by some other means.  The most obvious method is to use a comparator chip, such as an LM339.  I looked through the spare chips I have from 30 years ago, and found one LM311-N14A chip, which has a comparator that takes only a +5v supply.  The data sheet even has a circuit for a “magnetic transducer”.  I tried the circuit, and found that  I needed to add capacitors across the input and the output to reduce noise that otherwise kept the comparator triggered.

Once I got the comparator circuit working, it was fairly trivial to hook everything up to the Arduino and write the following program:

```void setup()
{
//  put a 20k pullup resistor on pin 3
pinMode(3,INPUT);
digitalWrite(3, HIGH);
//  put a 20k pullup resistor on pin 2
pinMode(2,INPUT);
digitalWrite(2, HIGH);

Serial.begin(115200);
}

void loop()
{

// wait for pin 2 to go low
long start_1=micros();
long start_2=micros();
Serial.print(F(" start_1="));
Serial.print(start_1);
Serial.print(F(" start_2="));
Serial.print(start_2);
Serial.print(F(" diff="));
Serial.println(start_2-start_1);
delay(100);

}
```

I tried it out with a piece of aluminum about 1.026m long, and got numbers in the range 272μsec to 304μsec, which would be speed of sound of 3380 m/s to 3780 m/s. That is a little slower than I expected. One possibility is that the comparator is not responding to the movement of the magnet toward the coil, but the rebound as it moves away. If I flip the magnet over, I get even longer times (784μsec to 884μsec), so I suspect the first orientation was the correct one, and the speed of sound in this aluminum alloy is a little lower than I expected, or the comparator circuit is adding some delays.

I’ll have to make a bit more robust way of holding the magnet and stuff, before Friday’s lab/demo, since everything is currently rather wobbly (the magnet is held to the coil with a PostIt note to act as the spring).

Tagged: AP physics, Arduino, comparator, high school, physics, Slinky, speed of sound, VPython

The Physics Lab 2 post and Physics class progress described some experiments we were going to do this week with the ultrasonic range finder(s).

What we actually did, after spending a fair amount of time discussing the schedule for the year and expectations (one of the students has not started yet, because of the amount of time he was putting into his Stanford essays—I hope he gets in after all the effort he has expended, was to drop balls and try measuring the drop with both the Maxbotix sensor and a video camera.

We tried both a ping-pong ball and a slightly larger plastic ball.  With both of them the Maxbotix sensor only detected them intermittently, and we go no useful data from the rangefinder.

The HD video from the camera was more usable, but I was not aware that Tracker could use MTS (AVCHD format) files, since it greyed them out. I wasted a lot of time converting the movies to .mov format using iMovie, a piece of software that I have come to hate for its slowness, inefficient use of disk, rigid insistence on a specific directory structure, and generally unfriendly and unintuitive user interface. I’ve gone so far as to buy Premiere Elements, with the hope that it is not so awful (but I’ve not tried to use it yet, so it might be just as bad).

It turned out that my son had not installed the Tracker software on the desktop machine, so we had to get out my laptop and try analyzing the frames there.  I remembered how to calibrate and get the autotracking set up, but I forgot how to specify the beginning and ending frame (I eventually figured it out, but only after some false starts).  The data was pretty clean, though autotracking did lose the ball at one point because of some really stupid projections about where it ought to be.  Redoing the autotracking fixed that problem.  The errors in the tracking due to motion blur were not noticeable in the position plot, made small wiggles in the velocity plot, and made huge wiggles in the acceleration plot.  We did get a chance to talk about how a ±1mm error in position results in a ±3 cm/sec error in velocity and a ±90 cm/sec2 error in acceleration, when using 30 frames per second.

I tried redoing the autotracking using the AVCHD format directly from the camera, but it turns out that AVCHD uses interlaced images, so one gets two pictures of the ball in each frame. When the ball is motionless, this makes a nice circle, but when the ball is moving fast, you get two striped circles that may overlap. Tracker has trouble handling the interlacing, though a really clever algorithm could take advantage of it to get effectively double the frame rate when tracking large objects moving with reasonably constant acceleration.

Bottom line was that neither the ultrasonic rangefinder nor Tracker resulted in fast, painless measurement. We’ll have to try again next week, perhaps with bigger targets for the rangefinder. I initially thought that brighter light for the video would reduce motion blur by reducing shutter time, but it seems that the motion blur is due to interlacing, not to a slow shutter, so changing the lighting won’t help. Algorithmic changes to Tracker would be needed.

## What to do in next week’s lab

1. Analyze the balldrop clips (in .mov format). For calibration, the distance we measured between the top and bottom stile of the file cabinet was 112cm. Since the ball was a few cm in front of the file cabinet, there may be some perspective error in using that measurement to calibrate the drop. Get Tracker to give you position, velocity, and acceleration plots. Use the fluctuation in the acceleration estimates to estimate the errors in the velocity and position measurements.
2. Write a Vpython program that simulates the motion of the falling ball including the initial pause before dropping, but not including the bounces.

## Other homework

• Work problems 3.P.36, 3.P.40, 3.P.43, 3.P.46, 3.P.52, 3.P.65, 3.P.72.
• Do computational problem 3.P.76. Note that the computational problems for Chapter 3 are not independent of each other, and you should read all the preceding problems to get hints for this problem.

Tagged: AP physics, Arduino, high school, physics, rangefinder, Tracker, ultrasonic sensor, VPython