Applying Hooke's Law to Cancer Detection

Hooke's law defines the direct proportionality between a spring's deformation and the restoring force that results. Most commonly, a derivative of Hooke's law is used in engineering applications—a relationship that directly relates stress and strain. For example, the stress-strain curve is commonly used by material scientists and engineers while selecting materials for 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.

After this activity, students should be able to:

• Describe what is meant by Hooke's law.
• Apply Hooke's law relationships to analyzing tissue of a known surface area.
• Depict a cancerous tumor using graphing methods in Microsoft Excel.

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

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.

Background

This activity constitutes the Research and Revise phase of the legacy cycle. Students explore Hooke's law in a hands-on, laboratory situation. They 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 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 follow step-by-step instructions to depict a cancerous tissue in a graph generated in Microsoft Excel. Though students work in groups, it is expected that they complete their own activity worksheets. 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.
• Make copies of the Hooke's Law Worksheet (PDF) and Generating a 1-D Strain Plot Handout (PDF).Example lab setup.CopyrightCopyright 2007 Luke Diamond, Vanderbilt University

With the Students

1. Pass out the two handouts. Use the Hooke's Law Worksheet as an instructional guide when creating strain plots. Use the Generating a 1-D Strain Plot Handout as an instructional guide to the lab; each student is responsible for completing and submitting the analysis and application questions by the end of the class period.
2. Have students move into their assigned groups and go to their lab benches.
3. Direct students to follow the worksheet and handout instructions. Remind them that they may work together, but each student is responsible for completing and turning in their own answers and solutions.
4. When students are ready to move on to the strain plot, have them remain in their groups; only one graph needs to be turned in per group. Remind them to return to their initial thoughts notes and add any new notes that may help them solve the challenge.

Activity Embedded Assessment: The Hooke's law application questions and the 1-D strain plot both function as 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.

Dictionary.com. Lexico Publishing Group,LLC. Accessed December 28, 2008. (source of vocabulary definitions, with some adaptation)