Summary
Students are introduced to Hooke's law as well as stress-strain relationships. First they learn the governing equations, then they work through several example problems, first individually, then as a class. Through the lesson's two-part associated activity, students 1) explore Hooke's law by experimentally determining an unknown spring constant, and then 2) apply what they've learned to create a strain graph depicting a tumor using Microsoft Excel®. After the activities, the lesson concludes with a stress-strain quiz to assess each student's comprehension of the concepts.
Engineering Connection
Educational Standards
Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards.
All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standard Network (ASN), a project of JES & Co. (www.jesandco.org).
In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics; within type by subtype, then by grade, etc.
Click on the standard groupings to explore this hierarchy as it applies to this document.
Pre-Req Knowledge
Learning Objectives
- Explain the stress and strain concepts and the relationship between them.
- Explain Hooke's law and apply it to analyze springs.
- Use Microsoft Excel® to make a simple strain plot.
- Relate stress and strain to the unit's engineering challenge.
Introduction/Motivation
Lesson Background and Concepts for Teachers
Legacy Cycle Information
Lecture Information
- steel
- Young's module: 200x10^{9} E(Pa)
- cast iron
- Young's module: 100x10^{9} E(Pa)
- concrete
- Young's module: 20.0x10^{9} E(Pa)
- A 3340 N ball is supported vertically by a 1.90 cm diameter steel cable. Assuming the cable has a length of 10.3 m, determine the stress and the strain in the cable.
- Consider an iron rod with a cross-sectional area of 3.81 cm2 that has a force of 66,700 N applied to it. Find the stress in the rod.
- A concrete post with a 50.8 cm diameter is supporting a compressive load of 8910 Newtons. Determine the stress the post is bearing.
- The concrete post in the previous problem has an initial height of 0.55 m. How much shorter is the post once the load is applied (in mm)?
- A construction crane with a 1.90 cm diameter cable has a maximum functioning stress of 138 MPa. Find the maximum load that the crane can endure.
- Consider Hooke's law as a simple proportionality where F is directly proportional to Δx. Therefore, we know the force stretching a spring is directly proportional to the distance the spring stretches. If 223 N stretches a spring 12.7 cm, how much stretch can we expect to result from a of 534 N?
- Figure 1 shows a column of fatty tissue, determine the strain in each of the three regions.
Vocabulary/Definitions
A medical specialist who examines photographs of tissues, organs, bones for use in the treatment of disease. | |
Deformation of a body or structure as a result of an applied force. Stretch beyond the proper point or limit. | |
The physical pressure, pull or other force exerted on a system by another. A load, force, or system of forces producing a strain. The ratio of force to area. |
Associated Activities
- Applying Hooke's Law to Cancer Detection - Student groups explore Hooke's law by collecting displacement data for springs with unknown spring constants by adding various masses of known weight. After answering a series of application questions, they apply their new understanding to explore a tissue of known surface area. Then then apply the pertinent relationships to depict a cancerous tumor amidst normal tissue by creating a Microsoft Excel® graph.
Attachments
Assessment
Post-Introduction Assessment:
Post-Lesson Assessment:
References
Dictionary.com. Lexico Publishing Group,LLC. Accessed December 28, 2008. (Source of vocabulary definitions, with some adaptation) http://www.dictionary.com
Contributors
Luke Diamond, Meghan Murphy
Copyright
© 2013 by Regents of the University of Colorado; original © 2007 Vanderbilt Univerity
Supporting Program
VU Bioengineering RET Program, School of Engineering, Vanderbilt University
Acknowledgements
Last modified: December 1, 2015