Acceleration Energy Friction

Week two began with measuring the acceleration of gravity. This laboratory is no longer led off by two days of acceleration, thus the front end of the laboratory was spent introducing the concept of acceleration. This has lengthened the duration of the laboratories, with some laboratories extending out beyond three hours.

Blossom and Allison measuring from two meters

Nicole and Angelica entering data

Joyleen working at two meters

Shrue

Blossom preparing 

Angelica and Joyleen working at two meters

Four and five meters can be done safely from the porch. 

Data came in low for all the groups this term, no particular reason could be identified.

The board reflects the path from laboratory two linear motion to accelerated motion - a hand waving argument built off of the three slopes. 

Laboratory four followed the same setup as spring 2021 with the double chairs being used to secure the leaves.  The laboratory was preceded by the demonstration of the conservation of momentum for marbles on a ruler. This again lengthened the laboratory, but is the path by which conservation of energy is introduced with kinetic energy as the integration of the momentum with respect to velocity. I do not attempt to teach the students calculus, but I do not think that showing students something they do not yet know how to do is inappropriate from a curriculum sequencing perspective. Sometimes you stand on a mountaintop and see places you have not been and may not comprehend. 

Angelica, Nicole, and Melissa

With the leaves from across the road, heights were limited to 70 cm. That would prove perhaps problematic. 

The theory apparently puts the focus of the square root parabola for the experimental data above out around a height of 300 cm.

The data is over too small a range for the parabolic nature to become obvious. With experimental error, some students obtained data that better supported a linear relationship.

Joyleen and Ilani

Higher drop heights are possible, but only for a leaf hung from the central rolling hook rack over the center table. I guess the students could share one larger leaf, but these leaves had a closed petiole groove out beyond the 70 cm height point. Larger leaves would be needed. 

Shrue, Allison, and Blossom

I opted to forgo having the students do five runs to obtain a median time, perhaps an error on my part. I chose instead to have the students record more data points: every 5 cm instead of 10 cm or 20 cm. That may have been a mistake. The students tend to decide the data must be linear and start keeping runs that show a steadily rising progression of evenly spaced values. They may discard runs that do not fit to their intuition that the speed increases must be by equal increments.

Shrue, Allison, and Blossom

I think fewer runs done using a median time might help, plus more height. Note that all runouts were to 150 cm to control for the issues that arise when one increases the length of the speed trap. The marble can slow significantly in the speed trap, so increasing the speed trap length can lead to the next highest height being slower than the previous height. Keeping the trap the same length is the only way I know to control the issue of the marble slowing. But this contributes to errors at lower speeds when the marble spends more time wandering slowly across the table over the trap length.

Class layout with hook rack just visible upper left.

Linear data as seen on a student's computer. Note how the data is neatly bisected by the square root function. The square root function is also rather "flat" over the small relative arc length involved. Data out towards the focus would help.

The boards indicate that lead in background that was done.

Laboratory four was rather a fail from the perspective of proving to the students that a theory can produce a model that matches their data curve. Perhaps having the students share a single large leaf hung higher would work, fewer data points, and the median of five measurements.

Laboratory five is somewhat awkward in the blended class. In the full residential class there would have been a series of demonstrations which fall slightly short due to friction. So by lab five friction is an oft mentioned concept. In the blended course friction unintentionally gets a shorter shrift. 

Melissa gathered roughness data which Allison recorded

This laboratory behave nominally as NASA ground control would usually say. Which is good. It generated the data it usually generates.

Angelica works on the effect of weight on friction

Nicole and Ilani also worked on the impact of weight

Nicole pulling, Ilani recording

Joyleen pulling while Angelica records

The two weight investigations produced roughly linear relationships. I tried to figure out why Nicole and Ilani obtained such a convincing negative y-intercept. I was unable to determine the source of the problem. They did appear to have taken into account the mass of their glass louver sled. The roughness experiment came out with a negative slope - a result consistent with other terms. While the slope often fails a null test against a possible slope of zero, term after term the result is often a negative slope, so that feels real at this point. Larger grit sizes yield less friction with glass. The sounds counter-intuitive, but glass is both rather hard and has a very small scale surface structure. As the sandpaper gets increasingly fine, the grit gets closer to the microscopic feature size of the surface of glass. So friction increases and particle size decreases. Or at least that is what I think might be happening.