### Summary

Students explore the response of springs to forces as a way to begin to understand elastic solid behavior. They gain experience in data collection, spring constant calculation, and comparison and interpretation of graphs and material properties to elucidate material behavior. Conduct this activity before proceeding to the associated lesson.### Engineering Connection

Material selection is a vital step of the engineering design process when creating any type of device. The strength and stiffness of materials can dictate how they respond to forces applied during device operation. Therefore, understanding the properties of the selected materials contributes to the success of a device. Tensile testing, as done in this activity to calculate spring stiffness, is one method of determining material properties.

###
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 Standards Network (ASN)*,
a project of *D2L* (www.achievementstandards.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*.

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 Standards Network (ASN)*,
a project of *D2L* (www.achievementstandards.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*.

###### International Technology and Engineering Educators Association: Technology

- Knowledge gained from other fields of study has a direct effect on the development of technological products and systems. (Grades 6 - 8) Details... View more aligned curriculum... Give feedback on this alignment...

###### Colorado: Math

- For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. (Grades 9 - 12) Details... View more aligned curriculum... Give feedback on this alignment...

###### Colorado: Science

- Gather, analyze and interpret data and create graphs regarding position, velocity and acceleration of moving objects (Grades 9 - 12) Details... View more aligned curriculum... Give feedback on this alignment...

### Pre-Req Knowledge

Students should have familiarity with algebra and be able to solve algebraic equations. They should also have experience graphing data using Microsoft Excel.

### Learning Objectives

After this activity, students should be able to:

- Calculate the spring constant, k, of multiple springs.
- Graph collected data using Microsoft Excel.
- Use Microsoft Excel to fit data with a trend line and equation to interpret the meaning of the coefficients in the equation.

### Materials List

Each group needs:

- set of two (or more) springs of differing stiffness (for example, five color-coded springs 30 cm in length in a storage box, at http://www.pasco.com/prodCatalog/ME/ME-8970_equal-length-spring-set/, for $39)
- ruler (such as 12-inch wooden or plastic ruler with English or metric scales marked, for ~$1)
- spring scale with 10 N capacity (for example, a tubular spring scale measuring grams and Newtons, at http://www.amazon.com/Tubular-Spring-Scales-Grams-Newtons/dp/B004MI9UOS/ref=pd_sbs_indust_3, for $5)
- ring stand (for example, a stamped steel support ring stand with a 4 x 6-in base and 5/16 x 18-in rod, at http://www.artistsupplysource.com/product.php?productid=64115, for $7)
- 3-inch ring stand attachment from which to hang springs (for example, http://www.hometrainingtools.com/ring-support-3-diameter/p/CE-RING3/, for ~$5)
- lab notebooks or paper, and pencils
- Hooke's Law Data Analysis Worksheet, one per student
- access to a computer with Microsoft Excel or a similar spreadsheet/graphing application

To share with the entire class:

- computer and projector to show four-slide Hooke's Law Presentation PowerPoint file

### Introduction/Motivation

For the design project we're working on for this course, we must come to understand how the materials in our bodies behave in response to forces so that we can design biomedical devices that do not harm the body.

The first step towards understanding tissue behavior is to learn how elastic solids respond to forces. To illustrate the concepts that we will learn in the solid mechanics lesson, let's first explore how springs behave, since they are often used to model elastic solid behavior. Most of the materials available to build your devices are also characterized as elastic solids. Therefore, we need to obtain an understanding of how they behave in response to forces so that we can select materials accurately in order to create successful engineering designs.

### Vocabulary/Definitions

elastic: When a material returns back to its original shape after having a force applied and then removed.

### Procedure

(optional: Show students the attached four-slide Hooke's Law Presentation PowerPoint to accompany the activity described below.)

Begin by conducting this activity, then proceed to conduct the associated lesson. Students benefit significantly by completing the activity first because the lesson material is so new and different than anything they have done before and so it helps to have the hands-on reference of what they learned in the activity while learning the theory. We found that when the lesson was taught first, students were completely lost and did not grasp the concepts nearly as well as when the activity was completed first.)

Background

Springs behave as described by Hooke's law, which states that the extension or compression (that is, displacement) of a spring, x, is directly proportional to the force applied to the spring, F. The proportionality constant of this relationship is termed the spring constant, k, and can be thought of as the stiffness of the spring.

*F = kx*

In today's activity, we use Hooke's law to calculate the spring constant of multiple springs. The two variables needed in the above equation are *F* and *x*, so we need to record the resulting displacement when a known force is applied to a spring.

Before the Activity

- Gather materials and make copies of the Hooke's Law Data Analysis Worksheet.
- Clamp the ring stand attachment piece near the top of the ring stand for each group.
- Divide the class into groups of three students each.

With the Students

- Have each group collect a spring set, spring scale, ring stand with attachment, and ruler.
- Have students examine the springs and record their observations and predictions, as described in the Assessment section.
- Connect one spring to the ring stand attachment.
- Hang the spring scale on the end of the spring.
- Measure the length of the spring with the spring scale hanging from it. Record this as your initial length.
- Pull on the spring scale until it reads 1 Newton [N].
- Measure the length of the spring while the force is being applied. Note: Subtracting the initial length found in step 5 from the length measured in this step gives you the spring displacement, which is needed to calculate the spring constant on the worksheet.
- Record the force and resulting length.
- Repeat steps 6-8 for a total of 10 different forces (for example, 1 N, 2 N, 3 N, and so on).
- Repeat steps 3-9 for each spring.
- After students have collected all their data, have them revisit their earlier predictions, as described in the Assessment section.
- Have students complete their worksheets and turn them in for grading. Then proceed to conduct the associated lesson, Mechanics of Elastic Solids.

### Attachments

### Troubleshooting Tips

To reduce time and cost, this activity can be completed using a minimum of two springs of differing stiffness for each group.

### Assessment

Pre-Activity Assessment

*Spring Observations & Stiffness Predictions:* After students collect team supplies ask them to note (in a lab notebook or paper) any similarities or differences between the springs. Are they physically different? Do they feel different? Do you expect them to have the same stiffness? If not, list the springs in order from stiffest to most compliant.

Activity Embedded Assessment

*Revisit Predictions:* After students have collected all their data, have them revisit their predictions of whether they thought the springs have the same stiffness or not. Ask them to describe whether they still think their predictions are correct or not, and why. If they think that their predictions were incorrect, then note how their predictions changed. If they think the stiffness differs, then put the springs in order from stiffest to most compliant.

Post-Activity Assessment

*Worksheet:* Assign students to complete the Hooke's Law Data Analysis Worksheet. Review their answers to gauge their mastery of the subject matter.

### Contributors

Brandi N. Briggs; Marissa H. Forbes### Copyright

© 2011 by Regents of the University of Colorado.### Supporting Program

Integrated Teaching and Learning Program, College of Engineering, University of Colorado Boulder### Acknowledgements

The contents of these digital library curricula were developed by the Integrated Teaching and Learning Program under National Science Foundation GK-12 grant no. 0338326. However, these contents do not necessarily represent the policies of the National Science Foundation, and you should not assume endorsement by the federal government.

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