Rolling balls and linear relationships

This spring laboratory 022 was the first of the even "no write up" laboratories. Until this term, student's wrote up every laboratory as a full laboratory report. The reports were then marked for content, grammar, vocabulary, organization, and cohesion. The work load for the instructor, roughly 14 laboratory reports per term, was heavy. With 32 students, the instructor faced hours of grading every weekend, not including work load associated with their other courses. Making the course acceptable to other faculty in the system required reducing the enormous work load.
The eight o'clock class on a wet morning rolls the ball, students lined up to locate the ball at one, two, three, four, five, and six seconds.

This term only the odd numbered laboratories are written up, which cuts the number of laboratories to be marked in half. The unanswered assessment question is whether the writing benefit will be retained. The complication is that only grammar has ever shown a statistically significant improvement.

Alwihter holds the end of the tape at the 800 cm mark. The tape is only 800 cm long, so beyond 800 cm the tape is moved to determine distances.

In laboratory 022 the location of the ball at each second is marked by a different student. Then the distance to the timing mark is determined. This makes the time the independent variable and the distance the dependent variable. As often done in physics, the distance is preset and becomes the independent variable, with a timing determining the time to that fixed distance - such as a photogate.

Angie releases the ball from a quarter way up the ramp, ShirleyAnn is calling out the times.

The ramp permits rolling the ball at a specific velocity that can be repeated. This allows the timing markers to stand near to the correct location for their particular number of seconds. Only a single timer is actually needed, one student calls out the seconds while watching a stopwatch or other digital second timer. This also means that one does not need hundredths of a second.

The wet ground and slight north wind saw slowing the ball on all runs

The ball distinctly slowed down both in the morning and afternoon sections. In the past 022 has provided an example of linear, unaccelerated motion. This term the laboratory failed in this respect. The failure, however, was not as problematic for the curriculum as the failure might have been.

Using the RipStik, I had demonstrated constant velocity motion on Monday. As a result, 022 became an opportunity to focus on what happens on a time versus distance graph when the velocity is decreasing with respect to time.

On Friday quiz 024 was able to exploit this accidental enrichment. Next week's accelerated motion will also benefit: the student's should be able to predict the nature of the curve for my accelerated RipStik demonstration on Monday. That will lead to a homework assignment to confirm that acceleration occurred. The homework will also be able to include, building on questions seven and eight on quiz 024, the pillar-to-pillar velocity.
An overview of the layout of the laboratory

The laboratory was wrapped up by graphing the data in the field and discussing the resulting curves on the paper. Ideas such as tangents to the line, speed between timing marks were introduced.

Without the computer laboratory second half, the laboratory could use some further enrichment and development to really bring forward the idea of the mathematics as making predictions. Maybe the class could be asked to predict the distance based on the particular release height? The complication is that one would have to work graphically - the data was simply not linear this term.
1100 laboratory results

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