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Airplane on a String

by Matt Vonk, University of Wisconsin River Falls
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Summary

This video is a fun example of the classic conical pendulum problem. Students will analyze a video featuring an airplane on a string. The tension in the string can be read from an on-screen scale, timing measurements can be made from the frame-counter, and the angle of the string can be determined from an overlaid protractor. While this doesn't seem like enough information, it's actually enough to allow students to calculate the angular and linear velocity of the plane, the mass of the plane, the radius of its circular path, and the length of the string.

It's an engaging problem that forces students to think clearly about some concepts that they frequently find confusing, like tension, circular motion, and centripetal acceleration.

The video at right is a preview of the video students use for the activity. A downloadable QuickTime video that allows students to step through frame-by-frame is below.

Learning Goals

The primary goal of this activity is to give students a chance to apply concepts of circular motion and centripetal acceleration.

Context for Use

This activity should be used with students who are familiar with drawing free-body-diagrams, applying Newton's 2nd Law, and calculating centripetal acceleration. It is designed for small-group use in an algebra-based introductory physics course. It can be used as in-class work, homework, or pre-lab work. The activity requires approximately a half hour of time, but requires no special equipment other than a computer with QuickTime. It would not be difficult to adapt this activity to other settings such as a conceptual physics class.

Description and Teaching Materials

Here is an airplane on a string worksheet (Microsoft Word 2007 (.docx) 959kB Nov13 13) that can guide students through this activity.

Airplane on a string worksheet Solutions (Acrobat (PDF) 74kB Aug25 14).

This worksheet has fairly explicit directions for which measurements the students should make, but does not give much support for how students are to use those quantities to complete the required calculations. I would recommend that the instructor be on-hand to give tips if students get stuck.

The Airplane on a string video page contains all the available file types for this video.

Teaching Notes and Tips

Assessment

This activity requires students to make calculations based on measurements they have made. If students are able to successfully calculate the mass and velocity of the plane, and the length of the string then the students will have demonstrated a proficiency at solving a problem with centripetal acceleration.

References and Resources

The Hyperphysics treatment of circular motion.

See a solution to a similar conical pendulum problem.