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Newton's Law And Accelerometer Integration Applied To Impact Analysis

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1996 Annual Conference


Washington, District of Columbia

Publication Date

June 23, 1996

Start Date

June 23, 1996

End Date

June 26, 1996



Page Count


Page Numbers

1.339.1 - 1.339.6

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Paper Authors

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Zhi Shi

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Clarence Calder

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NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract


Session 2668

Newton’s Law and Accelerometer Integration Applied to Impact Analysis

Clarence Calder, Zhi Shi Oregon State University


This paper presents an experimental technique which illustrates to the student an application of Newton’s law, the use of an accelerometer, and numerical double integration of the acceleration to obtain displacement. The simple impact experiment consists of a falling rigid projectile striking a sample. Data analysis utilizes Newton’s law and double integration of the accelerometer output to obtain the dynamic load-deflection curve for the sample. An oscilloscope, digital data transfer to a PC, and manipulation of the data using spreadsheet software are incorporated in the experiment.


The rate of loading is well known to strongly influence the mechanical behavior of many materials. However, there is a tendency in the design of dynamic applications to utilize readily available material property data determined from quasi-static type tests. For example, synthetic and natural gut strings used in tennis rackets are commonly compared using slow test results from a tensile testing machine where the load- deflection behavior is typically very nonlinear and with high hysteresis. In application, the string is pre- tensioned and subjected to a loading cycie (ball impact) of just a few milliseconds. Dynamic tests under similar conditions to the actual application have shown that the behavior is very linear with negligible hysteresis. (1) The conclusion is that the designer should always use material properties which have been determined under rates of loading and other conditions which are similar to the application.

In this study a weight-drop impact apparatus with an accelerometer attached to the falling weight is used to obtain a dynamic force-deflection curve for the sample. The concept is similar to that used in an earlier study on shock absorption of athletic shoes.(2) An oscilloscope is used to capture the acceleration- time data and a PC is used to process the data. When used as a classroom or laboratory demonstration, or laboratory/project assignment, this experiment illustrates the following to the student: 1. Determination of the impact force-time record using Newton’s law. 2. Evacuation of the displacement-time record by double integration of the acceleration and enforcing proper initial conditions. 3. Technique and advantages of smoothing the experimental data. 4. Convenience of spreadsheet software to process and analyze the raw data, and to plot the results. 5. The energy absorbing and loading-rate effects of using a material such as foam.

Test Apparatus and Procedure.

The test arrangement consists of a cylindrical steel projectile instrumented with an accelerometer which is guided under free fall by an acrylic tube. The projectile strikes a sample and the accelerometer output is recorded on a digital oscilloscope. The digital data is transferred to a PC equipped with ;~:! % }; 1996 ASEE Annual Conference Proceedings ... %cn,tiy,...,

Shi, Z., & Calder, C. (1996, June), Newton's Law And Accelerometer Integration Applied To Impact Analysis Paper presented at 1996 Annual Conference, Washington, District of Columbia.

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