Incorporating Materials Science into an Undergraduate Applied Physics Curriculum
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Incorporating Materials Science into an Undergraduate Applied Physics Curriculum Claudio Guerra-Vela1 and Fredy R. Zypman2 Department of Physics and Electronics, University of Puerto Rico at Humacao, 100 Tejas Avenue, Humacao, PR 00791-4300, U.S.A. 2 Department of Physics, Yeshiva University, 500 185th Street, New York, NY 100333201, U.S.A. 1
ABSTRACT The Intermediate Physics laboratory is a pivotal course of the undergraduate physics curriculum. Besides its intrinsic importance for introducing modern physics experiments, this laboratory also plays an important role in addressing the needs of the future applied scientist and engineer using contemporary equipment for data acquisition and control. This laboratory course has a mix of standard (usually not directly addressing materials science questions) and newer experiments. Among the newer experiments, we have developed a kit for measuring the transverse and longitudinal Young and Shear modulus of a homemade concrete block by analyzing their standing modes of vibrations. The technique is similar to that of the C-215 American Society for Testing Materials (ASTM) Standard, but more appropriate for university educational setting, using ordinary student laboratory equipment and piezoelectric transducers. From these measurements, we also deduce Poisson’s ratio. Students start measuring during the curing process of the concrete sample, something that it is not possible with the standard technique. However, our results have a precision comparable to that of the standard. Through the experiment, students learn about the properties of concrete. They make the samples following the C192 ASTM standardized process, and review several concepts about waves such as wave equations, resonant modes of vibrations, dispersion relations, and standing modes.
INTRODUCTION A simple way to produce standing waves in a thin cylindrical unconstrained metal bar was found while working in the design of an educational large-scale version of a scanning force microscope’s cantilever-tip system [1, 2]. The resonant frequencies of vibration of the bar depend on the bar’s geometry and the dynamic elastic constants of the metal. This technique was used to study elastic properties of concrete in an intermediate physics laboratory course because it works with equipment available in any general physics laboratory, and deals with fundamental physics ideas. Concrete was chosen for it is easy to obtain, inexpensive, and socially and economically relevant. A long, thin, cylindrical rod free at both ends is able to vibrate in three different forms: transversely, longitudinally, and under torsion. For each type of vibration, we can write [3] the values of the three elastic constants that can be obtained from our experiment. For transverse motion
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Et =
212 l 3T Mn 2 , ξ = 3.011, 5, 7,... 3 4 4 π ξ d
(1)
In this equation, Et is the dynamic Young’s modulus determined from the transverse mode, l, d, and M, the length, diameter and mass of the sample, and T, a geometric correction factor [4]. F
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