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Periodic Motion of a Pair of Physics Carts: Experiment and Theory

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Submitted by Rich on Thu, 05/10/2018 - 01:54

A Physics Challenge

In this lesson, AP and college students are challenged to derive equations for the periods of two fundamental modes of oscillation of a pair of coupled physics carts.  Derivation will involve Hooke's law, Newton's Second Law of Motion, and principles of simple harmonic motion.  Theory is then compared to experimental results obtained from PocketLab Voyager rangefinder data using Phyphox software.

For additional experiments involving two carts with Phyphox and PocketLab, click this link as well as this link.

The Experiment Setup

Physics Challenge Experiment Setup
Figure 1

Figure 1 shows the experiment setup, in which three springs are used.  One spring connects the two carts.  Two other springs connect each cart to to solid ring stands on the far right and left.  PocketLab Voyagers are attached to each cart with their rangefinders facing white card boards that are leaning on the ring stands.  The rangefinders will keep track of cart location while the carts are oscillating.  An Android tablet in the foreground shows typical experimental data displayed with Phyphox. A good source for the springs (5 N/m) can be found by clicking this link.

Phyphox Software

Phyphox (physical phone experiments) is a free app developed at the 2nd Institute of Physics of the RWTH Aachen University in Germany.  The author of this lesson has been working with a pre-release Android version of this app that supports BLE (Bluetooth Low Energy) technology to transfer data from multiple Voyagers to the Phyphox app.  Since then, a public Android version of Phyphox has been made available.

The experiment of this lesson is in a file named TwoCarStudy3.phyphox and accompanies this lesson. This file can then be opened in Phyphox and will appear in the PocketLab Voyager category of the main screen, similar to that in Figure 2.

Phyphox "PocketLab" Menu
Phyphox "PocketLab" Menu
Oscillating Physics Carts Experiment Setup
Grade Level
Additional Content