Gas station without pumps

2011 November 13

Physics homework with dominoes

Filed under: home school — gasstationwithoutpumps @ 00:04
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Almost a month ago, in post Physics Lab 3, I assigned the following 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.

but neither of the two students has completed it yet.  The one who got a late start is just finishing the previous homework from Chapter 2, and the other has been having trouble getting himself to work on the Chapter 3 problems—not because they are difficult but because they are a bit tedious.

To re-ignite interest in the student who found the textbook problems tedious, I got him interested in the problem of modeling domino chains (see, for example, the video on the dy/dan blog  [3ACTS] Domino Skyscraper).  This problem is harder than the ones in the book, as it requires careful thinking about how simple the models can be and still represent reality well enough. One obvious simplification was to assume that there is infinite friction on the surface, so that dominoes don’t slide around.  Another is that the dominoes don’t bounce off the surface—these two assumptions mean that they are effectively hinged around the edge on the side that they are falling towards.

The students only have point-mass models at this point, which makes the conversion from a horizontal push to a rotating domino more complicated to conceptualize. But decomposing the force due to gravity into  components along and perpendicular to the line between the center of mass and the hinge is easy, so converting the fall into a rotation is not too hard. (Well, I did have to review dot products with him for a minute.)

I’ve set him a series of subproblems in Vpython to get to where he wants to be (simulating arbitrary domino chains with different size dominoes and splitting of domino chains):

• Simulate a single domino falling in response to a sideways nudge (and rocking but not falling if the nudge is too small).
• Simulate one domino hitting another the same size with parallel faces.
• Simulate one domino hitting a larger one with parallel faces.
• Simulate one domino hitting another with non-parallel faces.
• Simulate one domino hitting multiple others.

I think that the hardest part conceptually will be modeling what happens when one domino hits another.  We could try for 100% transfer of horizontal momentum, with the first domino stopping on contact (and then continuing to fall from there as the supporting domino moves away).  I suspect that this model is not very realistic, but may be good enough to start with.

Later on, when we’ve had more sophisticated modeling concepts, we might try modeling stick-slip friction at the “hinge” edge or elastic bounces on contact.  We might even model dominoes bouncing on the surface.  For now, even the simplified model of a hinged domino knocking over another hinged domino seems tricky enough.

One of the advantages of home schooling is that I can adapt the problems to maintain student interest, though I’ve been a slow about doing that for Chapter 3.  I think I’ll still want the students to do some of the inverse-square computations for gravitational or electrostatic forces, but I can cut back on them.