Conservation of marble momentum

Laboratory four begins with a line of marbles on a ruler. Before I roll one marble into a line of five marbles, I ask the students to predict what will happen. Some guess that all of the marbles will move, others guess that one will move. Then I roll the marble. I follow-up with predictions and observations of two marbles rolling into four, three into three, and so forth. I also demonstrate that speed in equals speed out.

Jessica, Brian, and Elizabeth, solo inbound marble measurements
I usually focus the student's attention on the penultimate marble in the stationary line. I ask, "How does this marble know whether to stay or to go?"  This term one student suggested "energy force." Another noted that the marble can "feel" the number of marbles that hit the end of the line of marbles. This usually leads to a discussion of what marbles can feel, and whether they have those feelings hurt. "Can marbles fall in love?"

I note that the marbles not only have no feelings, but the marbles also do not know about force or energy. The marble do what they do. The attaching of words to why the marbles do what they do is a peculiarly human enterprise. All of the words and concepts are simply human constructs applied to the marbles, none of them - not at some deep level - actually explain why the marbles do what they do.

I tie this back to a Freeman Dyson quote - nature is fundamentally mathematical, and this is mysterious.

For a physicist mathematics is not just a tool by means of which phenomena can be calculated, it is the main source of concepts and principles by means of which new theories can be created... ...equations are quite miraculous in a certain way. I mean, the fact that nature talks mathematics, I find it miraculous. I mean, I spent my early  days calculating very, very precisely how electrons ought to behave. Well, then somebody went into the laboratory and the electron knew the answer. The electron somehow knew it had to resonate at that frequency which I calculated. So that, to me, is something at the basic level we don't understand. Why is nature mathematical? But there's no doubt it's true. And, of course, that was the basis of Einstein's faith. I mean, Einstein talked that mathematical language and found out that nature obeyed his equations, too.

As noted in class, "We can calculate how the marbles ought to behave and when we run the experiment, the marbles know the answer."

Iumileen masses a marble
In the second part of the laboratory the students collide three size of marbles, determining the momentum before and after the collision. This term the students noted that the tiny duck are called sinsai and the taws are called palas on Pohnpei.

The experiments collide one moving marble into a single stationary marble of nearly equal mass. This minimizes the complexity and calculations. The result for the three marbles is a linear regression which theoretically would have a slope of one if there was no friction nor loss of energy in the collision.
Joshua with the alternate marble track arrangement
Note the silver track layout above - this is a new approach that appears to reduce frictional error. As long as the outbound marbles remain within a small angular range of parallel with the track, the velocity is not significantly affected. In fact, the impact appears to be smaller than the frictional effects of the tracks, especially for the sinsai marbles.

A group that completed their data gathering early engaged in the field of statics and architectural engineering.
Adam and Yvonne Sue

Popular posts from this blog

Box and whisker plots in Google Sheets

Traditional food dishes of Micronesia

Creating histograms with Google Sheets