This year, we tried a new lab practicum for the constant-acceleration particle model unit. I don’t think we came up with on our own, but I don’t remember where I saw it. Students are presented with a constant-velocity buggy, a ramp, and a marble. They have to mathematically and graphically model the motion of the buggy and marble as it rolls down the ramp. After they have created their models, I provide them with a displacement for the buggy perpendicular to the end of the ramp. They then calculate from where to release the marble such that it rolls into the seat of the buggy.

Based on my observations of my class today as they worked on the lab, I was very surprised when most groups missed the buggy entirely. Only after checking over their calculations after school did I realize that most groups made the same mistake. They incorrectly interpreted the slope of their linearized position vs. time squared graph as the acceleration of the marble when, in fact, the slope is one-half the acceleration of the marble. They then used this incorrect value of the acceleration to calculate the initial displacement of the marble.

We now have something to discuss tomorrow.

##capm ##practicumlab ##setbacks

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How did your students gather position data for the marble?

Since the ramp was very shallow, they were able to measure the time sufficient accurately with stopwatches. They choose at least five positions along the ramp and measured the time for the marble to roll from that position to the end of the ramp. They performed at least five trails at each position.

I’m a new modeler and have had a similar problem with my students and the one half factor. Perhaps this shows a gap in my own understanding, but I have no idea how to explain where the .5 comes from without invoking calculus. How do you intend to rectify the situation for your students? I’d love any help.

In this particular case, it was pretty easy because the students were already familiar with the traditional kinematic equation. Once I wrote the linearized equation they experimentally determined next to their use of the slope in the traditional kinematic equation, they realized their error.

They are at least somewhat comfortable with the kinematic equation because we derived it graphically from the area under the curve in a general velocity vs. time graph.

I am a first time modeler and am having a similar problem with my students. Perhaps this shows a gap in my own understanding, but I cannot figure out how to explain where the 1/2 comes from without invoking calculus. I have yet to see an explanation of how students determine the slope of their linear position vs. time^2 graph is 1/2 acceleration. Any help is greatly appreciated.