Linear and accelerated motion

The summer session of SC 130 Physical Science has seen a number of modifications and improvisations. I combined the linear and accelerated run of the RipStik along the walk way in front of the science laboratory. The columns were used as timing posts and are 4.6 meters apart. My skill on the RipStik is vastly improved over last January. For the second run, the run in which acceleration is a non-zero constant, my ability to ride more slowly than last January allowed me to accelerate more slowly and thus maintain the acceleration over a longer distance.

I was surprised again at how nicely the data laid out. My first run at zero acceleration yielded a nice straight line on a time versus distance chart. My ability to hold a constant speed surprised me. The speed was a reasonable two meters per second, 1.99 m/s based on a linear regression.

The accelerated run provided the curved time versus distance data for which I was hoping. Plotting the time versus velocity, on the same graph, yielded an acceleration of 0.12 m/s²

In the compressed summer schedule, laboratory 032 followed directly on the heels of the above exercise. I ran the morning session using the same procedure as the spring term. The timing data was, however, problematic. I had to take the median of the five groups to generate marginally usable data.

In the afternoon I tossed the usual plan and improvised. I assigned one group to do five drops at 100 cm, another group to do five at 200 cm, a third tackled five drops of a ball at 300 cm. I went outside with the remaining four students and supervised five drops each at 400 cm and 500 cm. The data was averaged and then I graphed the resulting average times on the board, rather than have the students graph the data.

Then I squared the times, graphed the time squared versus the distance on a new chart on the white board, and then used a calculator to obtain the slope. This process was accompanied by questions and discussion. This went better, but ultimately the mathematics was too much too quickly for a summer class. The data, however, was excellent. The improvised afternoon procedure produced a result within 4% of the textbook value.

The slope of the line is one half of the value of the acceleration of gravity g. 1018 m/s² is only 4% over the commonly accepted value of 980 m/s² /

LaToya, Leslie, and McHelita work on drops of over 200 centimeters.

Randy sights a drop height in the morning class.

Outside the morning class works on 400 cm and 500 cm ball drop heights.

The afternoon data and left board work associated with the laboratory. Click on the image for a larger view. Plotting was done with the assistance of a meter stick.

The right board data.

LaToya and McHelita.

This particular laboratory remains mathematically complex, the complexity almost certainly interferes with student comprehension, yet I value showing that the quadratic drop time versus distance relationship can be transformed into a linear relationship which can then be resolved using traditional linear slope calculations.

The approach of the afternoon session worked particularly well and may be useful in future terms. Each lab group tackles only one height and produces an average drop time for that height. Data is then gathered on the board. This may be worth replicating in future terms.