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.
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- Common Core State Standards for Mathematics: Math
- 6. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.<sup>★</sup> (Grades 9 - 12)  ...show
- 5. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. (Grades 9 - 12)  ...show
- International Technology and Engineering Educators Association: Technology
- N. Identify criteria and constraints and determine how these will affect the design process. (Grades 9 - 12)  ...show
- P. Use computers and calculators to access, retrieve, organize, process, maintain, interpret, and evaluate data and information in order to communicate. (Grades 9 - 12)  ...show
- L. Telemedicine reflects the convergence of technological advances in a number of fields, including medicine, telecommunications, virtual presence, computer engineering, informatics, artificial intelligence, robotics, materials science, and perceptual psychology. (Grades 9 - 12)  ...show
- Maryland: Science
- The student will determine the relationships between quantities and develop the mathematical model that describes these relationships. (Grades 9 - 12)  ...show
- The student will use analyzed data to confirm, modify, or reject a hypothesis. (Grades 9 - 12)  ...show
- The student will explain scientific concepts and processes through drawing, writing, and/or oral communication. (Grades 9 - 12)  ...show
- The student will use ratio and proportion in appropriate situations to solve problems. (Grades 9 - 12)  ...show
- The student will use computers and/or graphing calculators to perform calculations for tables, graphs, or spreadsheets.(NTB) (Grades 9 - 12)  ...show
- The student will express and/or compare small and large quantities using scientific notation and relative order of magnitude. (Grades 9 - 12)  ...show
- The student will manipulate quantities and/or numerical values in algebraic equations. (Grades 9 - 12)  ...show
- The student will apply the skills, processes, and concepts of biology, chemistry, physics, or earth science to societal issues. (Grades 9 - 12)  ...show
- The student will identify and evaluate the impact of scientific ideas and/or advancements in technology on society. (Grades 9 - 12)  ...show
- The student will recognize mathematics as an integral part of the scientific process.(NTB) (Grades 9 - 12)  ...show
- The student will analyze the behavior of forces. (Grades 9 - 12)  ...show
- 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.
Lesson Background and Concepts for Teachers
Legacy Cycle Information
- Young's module: 200x109 E(Pa)
- cast iron
- Young's module: 100x109 E(Pa)
- Young's module: 20.0x109 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.
|stress:||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.|
|strain:||Deformation of a body or structure as a result of an applied force. Stretch beyond the proper point or limit.|
|radiologist:||A medical specialist who examines photographs of tissues, organs, bones for use in the treatment of disease.|
- 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.
Dictionary.com. Lexico Publishing Group,LLC. Accessed December 28, 2008. (Source of vocabulary definitions, with some adaptation) http://www.dictionary.com
Luke Diamond, Meghan Murphy
© 2013 by Regents of the University of Colorado; original © 2007 Vanderbilt Univerity
VU Bioengineering RET Program, School of Engineering, Vanderbilt University
Last modified: April 20, 2015