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Abstract:

This exercise is NOT a complete unit, rather it supports teaching and learning about special relativity in a regular physics course. We provide experimental data in many forms for student use. Students can download an ASCII file which contains the data or view plots that we have generated. Whether they plot their own graphs or study those provided on the site, careful analysis of the data yields an understanding of special relativity constructed from data analysis. Students can derive a form of the relativistic correction factor often referred to as "gamma."
Introduction to Research:
The content is framed within a student scenario that contains an authentic student task, a challenging problem and requires multidisciplinary inquiry and investigation. The task will require collaboration with peers and possibly mentors.

Fermilab Experiment E687

In this experiment, a high-energy photon is created by a proton from the accelerator. The photon strikes a stationary slab of beryllium. This collision occasionally results in the creation of a charmed meson (D0). Charmed mesons do not live very long before they decay into two other particles, a pion (p-) and a kaon (K+).

How far do D0 charmed mesons travel before they decay? Their half-life is 4.0x10-13 s which means they cannot travel very far unless they are traveling very fast!

Learner Outcomes: Students will know and be able to:
• Experience the discrepancy between frame-dependent measurements.
• Predict how far an energetic particle will travel during its lifetime.
• Compare these predictions to data.
• Derive the velocity dependent correction factor that is used in relativity.
• Either draw their own plots or study those provided to determine the nature of a plot and a best fit to those plots.
• Perform a wee bit of algebra on the best fit curve to derive a correction factor for time measurements.
Research Question:
Our investigation is based on graphing particle physics data. Students will:
• Calculate how far charmed mesons will travel before they decay.

• Add 18 data points from E687 to their graph.

• Check how well their calculations match data across a much wider (and more interesting) range of velocities using computer-simulated (Monte Carlo) data with much lower speeds.

Assessment:
We envision this exercise as part of a larger unit in an introductory physics class. Among the multiple opportunities students should have throughout the unit, the assessment of this exercise might include . . .