Laboratory four momentum pre-thoughts
Laboratory four has been reworked many times. The problems have been many.
Fundamentally, linear momentum is not conserved for marbles.
Secondly, timing measurements are problematic and plagued by
reaction time errors coupling up with very short time intervals.
Originally laboratory four attempted to show conservation of momentum for marbles using one into a line of five on a ruler. When this did not go as well as planned, track friction was blamed.
WD-40 was used to reduce track friction, but this caused the scotch tape that held the ruler tracks down to release. The WD-40 wound up on everything including laboratory sheets. Results run with lubricated tracks still showed a strong loss of momentum. At this point I realize that rotational momentum was also in play and was definitely not a conservable quantity. The inbound marble stops spinning, while the outbound marble has to spin up.
Long tracks were also tried, with no useful improvement in the results. The long tracks were intended to remove timing errors which plagued the sub-second times on the short 30 cm ruler tracks. The following term saw the use of pairs of three different sizes of marbles. The three marble set worked better, but the nature of linear regressions is that the point farthest from the origin carries the most "leverage" on the slope. A bad measurement of the largest taw marbles leads to spurious results. The taws were also faulty and prone to fracturing, breaking.
The lab morphed into an open ended discovery exploration with presenting on what they had measured and found. The first term I did this, the lab went sparkingly well. And there were some interesting problems. The outbound marble is significantly slower than the inbound marble. If the inbound marble is accelerating down a ruler ramp slope, however, the distance/time is the average speed. About half of the terminal speed of the marble. The result is a nice confirmation of the conservation of momentum, but the inbound speed calculation is incorrect. The students never realize this, although I did point it out one term.
Long tracks came back with a vengeance summer 2012, but results were still a mixed bag. Fall 2012 I returned to the discovery learning/presentations approach and a few strong students carried the lab. That seems to be a key. A few students with prior lab experience and a natural tendency to lead and speak up are crucial to the lab working well. The lab continued in this vein spring 2013.
Separately I was noting that students were still having difficulty "seeing" the science through the lens of the underlying mathematical models. I wanted to move linear regressions into more laboratories, and laboratory four was hit and miss in this respect. Some groups would not stumble upon a graph of any sort. There is an argument to be made that the unguided discovery learning is valuable, but I was also seeing many students reach the end of the term without synthesizing the math at the core. Lab seven would be moved to a linear relationship summer 2013.
Summer 2013 I simplified laboratory four to mass in versus mass out in search of a linear relationship core for the laboratory. This decision was driven in part by the very weak math and graphing skills I was seeing in the summer students. The new approach went rather well and still stimulated discussion.
Fall 2013 Pohnpei Liberation Day canceled the 041 banana leaf marble ramp in class demonstration. I opted to run 041 as laboratory four. The laboratory was confusing for the students, in part because the relationship is not linear. Timing issues and speed loss issues, issues I adjust for in the demonstration version, plagued their results.
Spring 2014 I tried using banana leaf ramps for conservation of momentum, and came close with flat leaves, and the one-into-five layout. There was too much friction with the leaf and timing errors were again a problem. The banana leaf had so much drag that at low speeds the students had to be told to measure shorter distances, and marble slowing was still problematic. At high speeds accurate timing, especially of the inbound marble was nigh on impossible.
My thought this term is to have the students do part I on the ruler with one into five on their own, generating a number in versus number out graph, maybe mass in, mass out graph if that does not seem too ambitious. All marbles will be duck marbles in this section.
Then I am thinking putting paper on the tables, putting one marble at center, two timers as used in the flat banana leaf variant of spring 2014, and shooting the edge of a circle on the sheet, target at center. Speed would vary and distance/time would get inbound and outbound speed. A circle will allow outbound marble to go on its own path and take out the vector issue. The problem is how much momentum might remain in the inbound marble - hits should be as dead on as in order to bring the inbound duck to a stop.
The idea will be to wrap up with presentation of results in class, comparison of data and hand plotted charts.
Originally laboratory four attempted to show conservation of momentum for marbles using one into a line of five on a ruler. When this did not go as well as planned, track friction was blamed.
WD-40 was used to reduce track friction, but this caused the scotch tape that held the ruler tracks down to release. The WD-40 wound up on everything including laboratory sheets. Results run with lubricated tracks still showed a strong loss of momentum. At this point I realize that rotational momentum was also in play and was definitely not a conservable quantity. The inbound marble stops spinning, while the outbound marble has to spin up.
Long tracks were also tried, with no useful improvement in the results. The long tracks were intended to remove timing errors which plagued the sub-second times on the short 30 cm ruler tracks. The following term saw the use of pairs of three different sizes of marbles. The three marble set worked better, but the nature of linear regressions is that the point farthest from the origin carries the most "leverage" on the slope. A bad measurement of the largest taw marbles leads to spurious results. The taws were also faulty and prone to fracturing, breaking.
The lab morphed into an open ended discovery exploration with presenting on what they had measured and found. The first term I did this, the lab went sparkingly well. And there were some interesting problems. The outbound marble is significantly slower than the inbound marble. If the inbound marble is accelerating down a ruler ramp slope, however, the distance/time is the average speed. About half of the terminal speed of the marble. The result is a nice confirmation of the conservation of momentum, but the inbound speed calculation is incorrect. The students never realize this, although I did point it out one term.
Long tracks came back with a vengeance summer 2012, but results were still a mixed bag. Fall 2012 I returned to the discovery learning/presentations approach and a few strong students carried the lab. That seems to be a key. A few students with prior lab experience and a natural tendency to lead and speak up are crucial to the lab working well. The lab continued in this vein spring 2013.
Separately I was noting that students were still having difficulty "seeing" the science through the lens of the underlying mathematical models. I wanted to move linear regressions into more laboratories, and laboratory four was hit and miss in this respect. Some groups would not stumble upon a graph of any sort. There is an argument to be made that the unguided discovery learning is valuable, but I was also seeing many students reach the end of the term without synthesizing the math at the core. Lab seven would be moved to a linear relationship summer 2013.
Summer 2013 I simplified laboratory four to mass in versus mass out in search of a linear relationship core for the laboratory. This decision was driven in part by the very weak math and graphing skills I was seeing in the summer students. The new approach went rather well and still stimulated discussion.
Fall 2013 Pohnpei Liberation Day canceled the 041 banana leaf marble ramp in class demonstration. I opted to run 041 as laboratory four. The laboratory was confusing for the students, in part because the relationship is not linear. Timing issues and speed loss issues, issues I adjust for in the demonstration version, plagued their results.
Spring 2014 I tried using banana leaf ramps for conservation of momentum, and came close with flat leaves, and the one-into-five layout. There was too much friction with the leaf and timing errors were again a problem. The banana leaf had so much drag that at low speeds the students had to be told to measure shorter distances, and marble slowing was still problematic. At high speeds accurate timing, especially of the inbound marble was nigh on impossible.
My thought this term is to have the students do part I on the ruler with one into five on their own, generating a number in versus number out graph, maybe mass in, mass out graph if that does not seem too ambitious. All marbles will be duck marbles in this section.
Then I am thinking putting paper on the tables, putting one marble at center, two timers as used in the flat banana leaf variant of spring 2014, and shooting the edge of a circle on the sheet, target at center. Speed would vary and distance/time would get inbound and outbound speed. A circle will allow outbound marble to go on its own path and take out the vector issue. The problem is how much momentum might remain in the inbound marble - hits should be as dead on as in order to bring the inbound duck to a stop.
The idea will be to wrap up with presentation of results in class, comparison of data and hand plotted charts.
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