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TE Activity: Applying Hooke's Law to Cancer Detection

Contributed by: VU Bioengineering RET Program, School of Engineering, Vanderbilt University

A spring depicting the fundamentals of Hooke's law.

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Summary

In this activity, students will explore Hooke's Law in small groups at their lab bench. They will collect displacement data for a spring with an unknown spring constant, k, by adding various masses of known weight. After exploring Hooke's law and answering a series of application questions, students are asked to apply their understanding to explore a tissue of known surface area. Students will then use the necessary relationships to depict a cancerous tumor amidst normal tissue by creating a graph in Microsoft Excel.

Engineering Connection

Hooke's law defines the direct proportionality between a spring's deformation and the restoring force which results. Most commonly, this law is not used in engineering applications directly, but rather, a derivative of the law is used. The relationship more commonly used directly relates stress and strain. For example, the stress- strain curve is commonly used by material scientists and engineers of all types in selecting materials for particular structures. Within the linear region, the slope is defined by the Young's Modulus of Elasticity. Civil engineers often study the stress-strain curve when using strain hardening and other methods to increase the yield strength of a material. In this activity, particularly in the investigating questions 6 and 7, students explore the relationship between Hooke's law and the stress-strain equation. In addition, students must apply their understanding of Hooke's law to create a strain plot.


Contents

  1. Pre-Req Knowledge
  2. Learning Objectives
  3. Materials
  4. Introduction/Motivation
  5. Vocabulary
  6. Procedure
  7. Attachments
  8. Investigating Questions
  9. Assessment
  10. Extensions
  11. Activity Scaling
  12. References

Grade Level: 11 (10-12) Group Size: 3
Time Required: 90 minutes
Expendable Cost Per Group : US$ 0
Keywords: Breast Cancer, Ultrasound, Hooke's Law, Force, Stress, Strain, Spring
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Related Curriculum :

subject areas Physical Science
Physics
curricular units Using Stress and Strain to Detect Cancer!
lessons Stress, Strain and Hooke's Law

Educational Standards :    

  •   Maryland Science
    • The student will use models and computer simulations to extend his/her understanding of scientific concepts.(NTB) (Grades 9 - 12) [2002]
    • The student will use computers and/or graphing calculators to perform calculations for tables, graphs, or spreadsheets.(NTB) (Grades 9 - 12) [2002]
    • The student will pose meaningful, answerable scientific questions.(NTB) (Grades 9 - 12) [2002]
    • The student will develop and demonstrate skills in using lab and field equipment to perform investigative techniques.(NTB) (Grades 9 - 12) [2002]
    • The student will learn the use of new instruments and equipment by following instructions in a manual or from oral direction.(NTB) (Grades 9 - 12) [2002]
    • The student will test a working hypothesis.(NTB) (Grades 9 - 12) [2002]
    • The student will demonstrate safe handling of the chemicals and materials of science.(NTB) (Grades 9 - 12) [2002]
    • The student will investigate career possibilities in the various areas of science.(NTB) (Grades 9 - 12) [2002]
    • The student will select appropriate instruments and materials to conduct an investigation. (Grades 9 - 12) [2002]
    • The student will describe similarities and differences when explaining concepts and/or principles. (Grades 9 - 12) [2002]
    • The student will recognize mathematics as an integral part of the scientific process.(NTB) (Grades 9 - 12) [2002]
    • The student will identify meaningful, answerable scientific questions. (Grades 9 - 12) [2002]
    • The student will formulate a working hypothesis. (Grades 9 - 12) [2002]
    • The student will identify appropriate methods for conducting an investigation (independent and dependent variables, proper controls, repeat trials, appropriate sample size, etc.). (Grades 9 - 12) [2002]
    • The student will organize data appropriately using techniques such as tables, graphs, and webs (for graphs: axes labeled with appropriate quantities, appropriate units on axes, axes labeled with appropriate intervals, independent and dependent variables on correct axes, appropriate title). (Grades 9 - 12) [2002]
    • The student will manipulate quantities and/or numerical values in algebraic equations. (Grades 9 - 12) [2002]
    • The student will recognize safe laboratory procedures. (Grades 9 - 12) [2002]
    • The student will use experimental data from various investigators to validate results. (Grades 9 - 12) [2002]
    • The student will determine the relationships between quantities and develop the mathematical model that describes these relationships. (Grades 9 - 12) [2002]
    • The student will express and/or compare small and large quantities using scientific notation and relative order of magnitude. (Grades 9 - 12) [2002]
    • The student will apply the skills, processes, and concepts of biology, chemistry, physics, or earth science to societal issues. (Grades 9 - 12) [2002]
    • The student will use relationships discovered in the lab to explain phenomena observed outside the laboratory. (Grades 9 - 12) [2002]
    • The student will defend the need for verifiable data. (Grades 9 - 12) [2002]
    • The student will analyze data to make predictions, decisions, or draw conclusions. (Grades 9 - 12) [2002]
    • The student will check graphs to determine that they do not misrepresent results. (Grades 9 - 12) [2002]
    • The student will describe trends revealed by data. (Grades 9 - 12) [2002]
    • The student will use ratio and proportion in appropriate situations to solve problems. (Grades 9 - 12) [2002]
    • The student will identify and evaluate the impact of scientific ideas and/or advancements in technology on society. (Grades 9 - 12) [2002]
    • The student will explain how development of scientific knowledge leads to the creation of new technology and how technological advances allow for additional scientific accomplishments. (Grades 9 - 12) [2002]
    • The student will analyze the behavior of forces. (Grades 9 - 12) [2002]
Does this curriculum meet my state's standards?       

Pre-Req Knowledge (Return to Contents)

A basic understanding of the concepts of Hooke's Law, stress, and strain as presented in Lesson 2.

Learning Objectives (Return to Contents)

After this activity, students should be able to:

  1. Understand Hooke's Law.
  2. Apply Hooke's Law relationships to analyzing tissue of known surface area.
  3. Depict a cancerous tumor using graphing methods in Microsoft Excel.

Materials List (Return to Contents)

Part 1:

Each lab group will need:

  • Physics lab stand
  • Meter stick
  • Spring (with hooks)
  • Pendulum Clamp
  • Slotted mass set
  • Computer with Microsoft Excel (or other spreadsheet program)

Part 2:

Each group will need a computer with Microsoft Excel. The handouts have instructions specifically for Excel, but if you change the instructions, another spreadsheet program could be used.

Introduction/Motivation (Return to Contents)

Have you ever wondered how the value of the gas constant was measured/discovered, or the charge on an electron, or the Young's Modulus of Elasticity values we used in the problem set yesterday? Ever wondered where all these values come from? Well today we are going to solve for one ourselves. In groups of three, we are going to experimentally find the spring constant, k, for a few springs. After collecting data, we will use the relationship given by Hooke's Law to solve for an approximation of the constant. After exploring Hooke's law and answering a few application questions, we will apply what we've learned to study a body tissue with known surface area. Because Hooke's law applies to springs, we must make a few adaptations to the expression F= -k Δx, to account for area. By the end of the activity, you will be able to apply what you know about Hooke's law, stress and strain to depict a tumor amidst normal tissue using a graph in Microsoft Excel.


Vocabulary/Definitions (Return to Contents)

Ultrasound Imaging: The application of ultrasonic waves to therapy or diagnostics, as in deep-heat treatment of a joint or imaging of internal structures.
Cancer: A malignant and invasive growth or tumor tending to recur after removal and to metastasize to other sites.
Stress: The physical pressure, pull, or other force exerted on a system by another, producing a strain. Measured by the ratio of force to area.
Strain: Deformation of a body or structure as a result of an applied force beyond limit.
Force: An influence on a body or system, producing a change in movement or in shape or other effects.
Spring: An elastic body such as a wire of steel coiled spirally that recovers its shape after being compressed, bent, or stretched.
Young's Modulus of Elasticity: A mathematical constant that represents how difficult a material is to stretch

Background

This activity constitutes the Research and Revise phase of the legacy cycle. Students will explore Hooke's law in a hands-on, laboratory situation. They will experimentally solve for the spring constant, k, of a given spring by measuring the spring's displacement when a mass of known weight is added. After answering some application questions on Hooke's Law, students will relate Hooke's Law to a body tissue of known surface area. Continuing their research and revising their initial thoughts for solving the engineering challenge, students will follow step by step instructions in order to depict a cancerous tissue in a graph generated in Microsoft Excel. Though students will be working in groups, it is expected that students will complete their own Hooke's Law (doc) activity handouts. Students may discuss the questions but should answer the questions individually.

Before the Activity

Provide each lab station with the necessary materials. Assign groups of three for the activity. Photocopy the attached handouts (Hooke's Law(doc), Generating a 1-D Strain Plot(doc)), one for each student.

This is a depiction of the lab set up.
Sample Lab Setup.
click for copyright

With the Students

  1. Pass out the Hooke's Law and 1-D Strain Plot handouts.
  2. Have the students split up into the assigned groups and go to their lab bench.
  3. Explain to students that instructions may be found on their handouts. Remind students that they may work together, but each student is responsible for completing and turning in their solutions.
  4. When students are ready to move on to the strain plot, they should remain in their groups and only one graph needs to be turned in per group. Remind students to return to their initial thoughts notes and add any new notes which may help them solve the challenge.

Investigating Questions (Return to Contents)

  1. How do Hooke's law and the stress-strain relationship relate. Which variables correspond?
  2. What do we know about cancerous tissue that will allow us to use these concepts to depict it?
  3. What types of software would be appropriate for our imaging?
  4. Using these methods, will our imaging method be painless? Will it be effective and reliable? How about cost effective?

Activity Embedded Assessment

The Hooke's Law application questions and the 1-D Strain plot both function as a means of assessment. Students must first develop an understanding of Hooke's law. Then they must relate this concept to a tissue with known cross-sectional area. This concept may be used to detect a cancerous tumor where the tumor's elastic properties differ from that of normal tissue.

Activity Extensions (Return to Contents)

To extend the hands-on aspect of exploring the tissue, you may consider obtaining ballistic gel (e.g. http://en.wikipedia.org/wiki/Ballistic_gelatin or http://www.myscienceproject.org/gelatin.html) of differing stiffness. This may be used to mimic the differing tissue structure of cancerous and normal tissue as represented by varying Young's modulus of elasticity.

Activity Scaling (Return to Contents)

  • For upper level students, remove the step by step instructions for generating the 1-D strain plot.
  • For lower level students, take the time to relate Hooke's Law to the stress-strain relationship as a class. Make this connection with the students, using a visual representation on the board.

Dictionary.com. Lexico Publishing Group,LLC. Accessed December 28, 2008. (Source of vocabulary definitions, with some adaptation) http://www.dictionary.com

Contributors

Luke Diamond, Primary Author, Meghan Murphy

Copyright

© 2007 by Vanderbilt University
Including copyrighted works from other educational institutions and/or U.S. government agencies; all rights reserved. The contents of this digital library curriculum were developed under a grant from the National Science Foundation RET grants no. 0338092 and 0742871. However, these contents do not necessarily represent the policies of the National Science Foundation, and you should not assume endorsement by the federal government.

Supporting Program (Return to Contents)

VU Bioengineering RET Program, School of Engineering, Vanderbilt University

Last Modified: August 23, 2010
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