Internal Energy of the "Partial Derivative Machine"

Keywords: Small Group Activity, PDM, Derivative, Partial Derivative, Change of Variables

Highlights of the activity

This small group activity is designed to provide students with the means to the potential energy of an elastic system in one dimension.
Students use the “Partial Derivative Machine” to experimentally measure quantities in order to compute the potential energy of their system.
The whole class discussion focuses on how to experimentally measure integrals and how to represent integrals in multiple ways.

Reasons to spend class time on the activity

This activity occurs early in the junior year during “Symmetries and Idealizations” when students have been previously introduced to integrals in introductory physics and calculus courses. When students learn to calculate the electrostatic potential of a continuous charge distribution, they may be encouraged to think about integration as “choppping and adding” together contributions from small pieces of the charge distribution. Students may not be immediately ready to work with this idea of integration because many times integration is thought of as an operation to perform on a particular set of mathematical symbols. This activity emphasizes that integration can be done as “chopping and adding” which can be estimated experimentally. We would like our students to have an understanding of how to measure integrals and their relation to real physical quantities. This activity uses the “Partial Derivative Machine” in order for students to measure small changes in physical quantities to determine the potential energy of the system.