Acceleration

Last academic year I tried to mimic the arc of a ball in the air using the RipStik, gliding up slope until my initial speed was spent, then turning around and letting the same slope accelerate the RipStik and I back down slope. The resulting time versus distance graph was usually a rather smooth parabola. This shape was used to argue for the quadratic nature of the constant acceleration relationship.

Starting at rest. Distance 0 cm. Speed 0 cm/s.

The complication was that the graph confused the students, especially the underlying fact that the acceleration was actually a constant negative value throughout the whole run. Despite the change in direction of the board, the velocity declined at a constant negative rate, dropping through 0 cm/s as I turned around at the top of the slope. This also confused the students, and the constant negative acceleration was truly baffling.

Accelerating through the 300 cm mark

The arc also did not well connect to the lab on Thursday which does not produce a complete parabola but rather a half parabola. Thus last summer I returned to an acceleration from distance 0 cm and speed 0 cm/s, which mimics the situation with the falling ball in laboratory three.

Out near the 800 cm mark

An 800 cm run appeared to work well last summer and in trial run this term, so I used the distance in class on Monday.


This worked better than expected. Not only did I get a fairly smooth parabolic acceleration for time versus distance, and one which closely resembles that obtained for a falling super ball between 0 and 500 cm, but the time versus velocity trend line had an equation of v = 39.1t + 4.5 while the time versus acceleration trend line had an equation of a = 0.3t + 39.1. That the "a" in v = at + v0 was equal to the "a" in a = jt+ a0 where j is the jerk (and was intended to be zero) was a pleasant surprise. Neglecting the small time rate of change in the acceleration, the constant acceleration of 39.1 cm/s² showed up as identical values in the acceleration and the velocity equation. I should note that the acceleration implied by the best fit parabola is lower at 35.6 cm/s², only nine percent lower. Given the inherent error in the timing, these values are in generally good agreement. Self-timing is not optimal, especially while trying to hard accelerate a RipStik while not falling off. The time available and the reaction time errors students might introduce inveighed against having them measure split times.

Regina Moya, Marsha Karel, and Ioakim Walter work on measuring the acceleration of gravity

Laboratory three used the 0, 100, 200, 300, 400, 500 cm drops of the most recent editions of the text, forgoing the drops at every 20 cm. Timings were far better than in the past. The only difference from prior terms was a change back in laboratory two: the students used the chronographs in laboratory two for the first time this term. This yielded much better results in this laboratory. Almost every group obtained results within five to ten percent of the published value for the acceleration of gravity. This was a first - values have been up to 20% low in past terms. In the past, however, laboratory two used a single chronograph and measured the distance to timing marks post hoc. An experimental change last summer to measuring the time at fixed distances gave the students the chance to time the ball rolls. Both laboratory two and three have much improved data.

Macy Johannes records data, Callany David times and drops the ball, Mary-Ann Lekka handles the meter sticks, Dalynda Park also records data.

Haworth Padock and Renster Hackson review their data

Petery Peter records data, Veralyn Celestine drops and times, Marcyliza Semens on the far left holds a meter stick

Mary-Ann attempts a 300 cm drop 

Marvin Louis drops and times while Monaliza Mauricio steadies a meter stick

Erika Billen drops and times while Casan-Jenae Joab holds the meter stick. 

Sahn Samuel drops and times assisted by Michael Panuelo and Jamie Barnabas

Adelma John, Justacia Celin Kanichy, and Patty Mario work out the logistics of the laboratory

Justacia drops and times, Adelma record data.

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