Gas station without pumps

2011 October 29

Physics update

Filed under: home school — gasstationwithoutpumps @ 11:02
Tags: , , , , ,

We’re falling a bit behind on the physics course.  I was hoping we’d finish Chapter 3 this week, but one student has only done the problems and programs for Chapter 1 and read Chapter 2, and the other has done the problems and programs for Chapter 2 and only started the problems and programs for Chapter 3.  We will need to do at least 2 chapters every 5 weeks to finish on time, and I think that the later chapters will be a bit slower going than the early ones, so I really do want to try to do a chapter every 2 weeks for a while.

The lab write-ups have also not been happening.

Lab 3

The students have not yet analyzed the ball-drop clips we recorded 2 weeks ago. The assignment in Physics Lab 3 was

1. Analyze the ball-drop 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.

I still want to see the results of that, but I suggest some modifications: using the higher-quality clip in 00179.MTS and using Tracker to do the modeling, rather than writing a separate Vpython program (though a Vpython program would still be ok, and would make it easier to later model the bounces as well).

Lab 4

I also want to see a write-up of the spring lab (Physics Lab 4), for which the students got the following measurements:

```Spring Constant Data

Spring Letter
A       B       C       D       E       F       G       H       I       J       K

Dimensions
Relaxed Length (cm)    1.025   1.44    0.97    1.27    1.53    2.92    3.58    7.005   3.51    2.44    2.89
Coil Diameter (cm)     0.46    0.525   0.59    0.78    0.78    0.83    0.705   0.36    0.44    0.67    0.80
Wire Diameter (cm)     0.03    0.045   0.02    0.045   0.03    0.07    0.045   0.045   0.03    0.045   0.045

Forces
Stretch (cm)
0.5                    0.28    0.23    0.13    0.04    0.04    0.33    0.16    1.09    0.15    0.13    0.05
1.0                    0.47    0.34    0.23    0.06    0.06    0.48    0.26    1.57    0.24    0.18    0.10
1.5                    0.68    0.40    0.32    0.10    0.08    0.56    0.36    1.89    0.32    0.25    0.14
2.0                    0.87    0.57    0.39    0.12    0.11    0.68    0.47    2.37    0.38    0.31    0.19```

Note 1: the forces from the force gauge are inconveniently reported in kg, not N, so need to be converted by multiplying by the scaling factor that the gauge presumably used (9.8 N/kg).  We could be more precise and use 9.80665 N/kg, but the measurements are not accurate or precise enough to need the extra precision on the strength of the gravitational field.

Note 2: the students did not record the number of turns on each spring, which would provide a good check on the wire diameter, which was measured with a micrometer calibrated in inches.  The reported number is probably the result of a conversion, but the raw reading from the micrometer should have been recorded.

Correction: I have been informed that the students did not use the micrometer to measure the wire gauge, but the plastic calipers, which measure in metric units, but may not be very accurate for such small measurements.

I counted the turns myself:

```                         A       B       C       D       E       F       G      H      I       J       K
turns                   20      27      18.8    26      31.5    37.9      51     98.5   65      39.8    31.2```

Further corrections

I also remeasured the lengths, using new stainless steel calipers that just arrived this week (so the students couldn’t have used them).  It looks like spring K had been mis-measured (or, more likely, a “1” -> “2” typo).

```                         A       B       C       D       E       F       G      H      I       J       K
length(cm)              1.025    1.415   0.985  1.305   1.585    2.965  3.60    7.03  3.45    2.40    1.935```

Estimating wire gauge from these measurements, I get 4 different wire sizes:

```                         A       B       C       D       E       F       G      H      I       J       K
wire diam(cm)            0.05    0.05    0.05    0.05    0.05    0.08    0.07   0.07   0.05    0.06    0.06```

End Corrections

wire diam (cm)

End Corrections

For each spring, determine the following:

• Is the force to extend the spring linear with the increased length for each spring?
• If so, what is the spring constant (in N/m)?

Assuming that all 11 springs are made from the same material (which seems to be the case), come up with a model (a formula) that estimates spring constant given just the dimensions of the spring.

After looking at the data, I’m not sure that these measurements are accurate enough to be able to derive a good model from them. We may be able to do something by applying physical reasoning, the way we did for determining the effect of putting 2 identical spring in parallel or in series, but I don’t think that just doing arbitrary fits to the data will help us much.

Priorities

1. The highest priority should be on finishing the exercises and programs for Chapter 2, so that we can catch up.
2. Second priority should be on analyzing the data for the springs for Lab 4, so that we can discuss the data next week.  If it does not match our expectations (that is, if some of the springs seem non-linear, or if a couple of springs seem to be very different stiffness from what we predict), then we may want to redo some of the measurements, either to confirm that we measured and recorded the data correctly or to fix errors in our record-keeping. The formal writeup can wait until we have discussed the data (and redone measurements if necessary), but the analysis of the initial data should be done by Nov 4.
3. Third priority is reading Chapter 3 and finishing the problems and programs for Chapter 3. We will discuss the chapter at our next meeting, after clearing up any problems with Chapter 2 and discussing the spring data.
4. Fourth priority is playing with Tracker to try to extract data and model the ball drop.  Note that Tracker’s velocity and acceleration computations assume smooth changes in velocity, not the acceleration spikes you get from bouncing a stiff ball like a ping-pong ball.  I now have a copy of the source code for Tracker, and I am looking into providing better velocity and acceleration computations for collisions whose duration is less than the time between samples, but for now we’ll have to use the data that Tracker currently provides.
The data to play with is that in 00179.trk from the HD clip in 00179.MTS, which is of higher quality than the previous clips, though I’m sure we could do better with a brighter light and a dark ball in front of a light background.  The clip has at least 2 ball drops in it, but the trk file only tracks the first 7 bounces of the first drop.  Try creating a “dynamic particle model” that matches the fall until the first bounce.  (It is a bit messier to create a dynamic model in Tracker that matches multiple bounces, though a piecewise model could be built with the “if(cond, then-expr, else-expr)” construct.)
It might be worthwhile to try to create a new “Point Mass” object tracking the bounces of the second drop, setting up the coordinate frame so that the floor is at 0 and the ball starts on the positive y axis (rather than the negative x axis, as I did in tracking the first drop). You need to use Video-Filters-Deinterlace to get clean enough images for the Autotracker to work.
5. I never got writeups for how the ultrasonic range-finders work.  I still think that this is a valuable writing exercise, needing some on-line research.
6. Lowest priority is writing up what was done  in the Tracker lab with the ball drop.  We may let this one slide, since the main goal was familiarization with Tracker for later labs, rather than modeling physical phenomena.

Coming up

It might be valuable for us to try analyzing the low-speed collisions in Newton’s 3rd Law (or How to Make Effective Use of Video for Instruction)  More specifically to compute 2D momentum for each cart before and after collisions in the video clips for each collision.  Since we are not given the masses of the carts, we may have to estimate them from what should be happening (unless the long video at the beginning of the post gives us the masses—I didn’t watch it).

Since we do not have carts with hoop-spring bumpers like the ones in the video, it would be difficult for us to do this lab ourselves.