Newton's Laws of Motion and the force of friction

The class began with an example of a lab report with formatting issues. Then the class moved outside for coverage of Newton's laws of motion. A presentation accompanied RipStik demonstrations.

Summer is a time for experimentation, sometimes prompted by serendipity. Heading to the midday lab session with only minutes to spare, the thought arose, "What if the friction lab was done without scales to mass the sled? This would simplify the weight calculations. The only downside would be  y-intercept."

The lab was launched without digital scales. All four groups would work on weight, no surface roughness group. 

As expected, the weight calculations were much more directly obvious.


Emars records data gathered by Clayton


Trishia records data gathered by Eray
Eric and Jonald work together to obtain data.


Ruthy "Shannon"makes measurements, Mary-ellen records the days.


As expected, the data came in with y-intercepts. Four groups made reflecting the data to the Smartphone easily possible. 

At this point a pivot was made to consider possible mathematical relationships. Shapes mean equations and equations mean shapes. A review of the shapes seen to date included linear direct, quadratic parabola, and a square root relationship. The fourth graph seen above was initially omitted. 

The presence of a y-intercept was a new feature this summer - a result of not considering the mass of the sled. This stumped the students. While labs one and two had been direct linear relationships, no lab had a linear relationship with a y-intercept. 



One student attempted the formula f₁~w₁f₁ but they hadn't used w₁ in their table header so Desmos set w₁ to 1. f₁~f₁ is a truism. At first, none of the other students had an alternative theory. 

The students were told to use Desmos, to experiment. Eventually Clayton deployed the linear regression tool to obtain a working equation, translated from xy space to wf space above. In the tradition of science the equation was dubbed Clayton's law. Yes, that is a linear equation with a slope and intercept, but to help the students understand how and why names get attached to pieces of mathematics, the solution above was Clayton's law. 

That no other student could stumble their way to the equation says something about mathematics education. Students can solve problems one to thirty even numbers only. Students are not thinking mathematically. 



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