### Week five is friction

Week four did not see an emphasis on the impact of friction. Wednesday I had worked ½mv² = mgh and ran the homework as a regression against velocity = constant × √height where the constant was predicted to be √1960 or about 44.27. The quiz on Friday had a high coefficient of variation, so I covered the quiz Monday and then ran the full linear kinetic energy plus rotational kinetic energy equals the gravitational potential energy: ½mv²+ ½Iω² = mgh derivation. For the marble I = 0.4mr² and ω = v/r. The result is that v = √1400h or v = 37.42√h. Ahead of class on Monday I graphed the data, 44.27√h, and 37.42√h using Desmos and printed out the results.

The graph then allowed me to categorize the remaining loss of energy as being due in part to friction with the track. A thin bridge, but enough to walk across into laboratory five. The core argument I made was that the speed of the marble on the prior Wednesday in the banana leaf marble ramp demonstrations was not as high as predicted due to friction. The idea is that this opens the door to exploring friction as an external force.

Note that the ability of Desmos to regress against the square root model really puts this exercise together. Desmos can handle any function. In a separate analysis for statistics class, I ran a four variable logistic function against swizzle frequency versus speed data for a RipStik. Desmos happily optimized all four variables in the logistic function.

Wednesday I left my gear outside the south faculty building, walked down to class, and announced that as an experiment in best practices I would be presenting a PowerPoint. I walked the class back to the sidewalk to do the PowerPoint.

The first three slides. When I did this before I carried the slides. Posting the slides using masking tape worked much better. Students had a longer opportunity to copy down the three laws. I delivered my presentation while riding my RipStik The RipStik, and a ball held in my hand, allowed me to demonstrate the three laws. That the RipStik can coast or be propelled makes the RipStik an ideal vehicle for demonstrations of Newton's laws of motion.

I demonstrated pushing off of a post, frames of reference with the four square ball I was carrying while riding (momentum of the ball is zero for me and stays zero, momentum of the ball for the class is not zero and remains that non-zero value)

I noted too that friction was what allowed the RipStik to accelerate forwards. I wrapped up the class with a yurt circle. I do the yurt outside on the lawn ensuring we are far from all buildings and trees, on level ground. The circle was odd with 23 students, so I joyed the circle. I first had them count off and made sure they knew whether they were even or odd. I suggested a wrist-lock hold, but most chose to hold hands. I cautioned taller students to lean more slowly. Then I had the even students lean in, the odd students lean out. Done right, the whole circle stands like a yurt. This exercise is done standing and does not involve duct tape. The activity dates back to the new games movement of the 1970s.

The Thursday laboratory then seeks to measure the force of friction and to explore the factors that contribute to friction. The equipment used is laid out above. The sleds are pieces of glass louvers. Glass makes an unusual substance that behaves rather differently from the wood blocks often used in this sort of experiment. The experiment focuses on sliding (kinetic) friction, not static friction.

Mandylae and Mayleen test roughness via five grades of sandpaper

Due to the confusion having the students test all variables, I repeated the procedure of last fall. Some pairs explored the effect of weight on sliding frictional force. Other pairs explored varying only the grit of the sandpaper. A couple pairs explored surface area using a modification of a sled developed by a student in a previous term.

Regina and Maygen test the effect of weight while using the same sled and grit

Anjannet and Tristan tackle the most complex slide: Three double sided sided glass sleds with strings in the middle

Detail view of the three sleds. Each sled is glued together by hot melt glue with a string in the middle. The whole rig is 984 grams. By changing which sled is face down on the bottom, and towing from the bottom sled, the effect of surface area can be measured while weight and grit are held constant. '

Six pane sled at run's end

Jayvin and Saleen were testing the effect of grit on the force of friction

Just for fun, during class I tried regressing data from surface area versus force against a logistic function on my Motorola Moto G4 Play Android phone running the Desmos app. Throughout the class I worked with students who had Desmos on a smart phone plotting data and running linear regressions.

I would save the Desmos graphs from the app on my phone and then I could pull them up on the television at the back.

The television was connected via HDMI to the ChromeBook I am using. With thanks to just-in-time IT support, I had sufficient WiFi for the laptop to pick up a signal.

The real key is that Desmos is visual and intuitive. My students who had smart phones with the app did not have difficulty entering data. Once they knew the entry format for a linear function, y1~mx1+b, they had no difficulty entering that and obtaining the slope m and the intercept b. The use of Desmos during the laboratory fundamentally changed the analysis capabilities on the ground in the laboratory.

Dorothy enters data points into Desmos on her cell phone

Setting up the domain and range for the graph

Screen shot of Desmos on Dorothy's phone

The desktop view of the same data, graph, and analysis. As one types the equation, the line first appears through (0, 0) as one types y1~mx1. Then the line moves to the y-intercept when +b is added. The process is very interactive and intuitive. Linear equations literally come to life.

The next day, Friday, the students presented their results during lecture. They were to share whether there was a relationship and the nature of the relationship. Questions on board for guidance were:

• Did you identify a mathematical model that fits the data?
• How good a fit is the data to that model?
• If you did find a model that fits the data, what are the specifics for that model? If linear, what is the slope, intercept?

Pelida noted a positive linear relationship for surface area.

Vanessa noted a positive linear slope of 0.51 for surface area versus frictional force. An analysis run just before class, however, failed to reject a null hypothesis of a slope of zero at a 95% level of confidence. The residuals were near normal in their distribution suggesting random processes were responsible for them.

Mandylae soloed a presentation on the effect of grit, concluding that there was no relationship.

Aimina anchored the presentations with data that was claimed to be both non-linear and no relationship.