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Young's Modulus: An Investigation of Stress Versus Strain Using PDMS Polymer

Grades: Grades 11-12
Author: Jesse Groff
Source: This material is based upon work supported by the National Science Foundation under Grant No. EEC-1161732.


Abstract

This Lesson is based upon Young’s Elastic Modulus. Young’s Elastic Modulus (E) closely relates itself to the spring constant (K) used in traditional classroom physics when teaching Hooke’s Law. This is outlined in detail in the power point for further information. Through this construction, this lesson can bridge the gap between the engineering scope and traditional physics concepts taught in the classroom. By using a silicone base polymer, we will investigate young’s elastic modulus by changing the chemical composition. This polymer used comes from the Sylgard company. This comes as a mix and pour kit of silicone polymer with a cross linking agent (Sylgard 184).

http://www.dowcorning.com/applications/search/products/Details.aspx?prod=01064291

By creating different weight percent solutions students can vary dimensions and physical properties easily. By mixing the two ingredients, a silicone polymer base and a curing agent, and based on the ratio of the two ingredients; changes in shape/length can be identified and measured based on an applied external force. Also by increasing the thickness of the sample itself, the change in the cross sectional area, can cause changes in shape and length when an applied external force is applied. Students will apply this external force by hanging masses from binder-clips that are attached to the created samples and measuring length changes in the sample. This lesson does not require high tech material and only the silicone polymer would have to be ordered by an outside source, available on the internet.

***Secondary Option: The same principal can be applied to rubber bands so cost can be kept minimal while still investigating the same concept. To facilitate this, different grades of rubber bands can be purchased from a store; this would change the modulus of the material. Secondly, one could keep the same grade of rubber bands and vary the thickness, thereby affecting the cross sectional area.


Objectives

What should students know as a result of this lesson?

  • Students will be able to define and memorize what a polymer is.
  • Students will recall the metric system and use it to measure objects.
  • Students will be able to define and recall and state the purpose of Young’s Modulus Formula.
  • Students will design and construct a simple test for rubber-bands to test Young’s Modulus.
  • Students will be able to properly critique each-other during group tasks to facilitate teamwork.
  • Students will be able to make observations and distinguish a cause and effect relationship between materials and methods used.
  • Students will be able to collect and display data relating it to a relevant mathematic model.
  • Students will be able to explain phenomena in terms of concepts using investigation.
  • Students will connect the concept of Young’s modulus to actual material they synthesized.

What should the students be able to do as a result of this lesson?

  • Students should be able to create roles in their groups to help the procedure run smoothly.
  • Students will be able to precisely measure the change in length of material using metrics.
  • Students should be able to follow safety procedures properly while synthesizing the PDMS material.
  • Students should be able to precisely measure the correct amount of chemicals needed to make the PDMS samples.
  • Students will be able to create and organize a useable data table paired with a corresponding graph that can explain their data.
  • Students will be able to accurately calculate Young’s Modulus.
  • Students will be able to modify their apparatus if they have to make changes to suite the experimental goal.
  • Students will be able to compare the samples and see the differences in each strictly from viewing the data presented.

Materials

  • GLASS Petri Dishes (will be exposed to temps of 120 C°)
  • Sylgard 184 Polymer
  • Various Rubber Bands (see secondary option)
  • Exacto-Knives
  • Test Tube Clamp
  • C-clamp
  • Rulers
  • Hanging Masses
  • Drying Oven (convection)
  • Ring Stand
  • Scissors

***SAMPLES: This lesson is to have SIX samples for each group. Students will be able to choose from the following variables to research: Sample Thickness (cross link ratio constant 20:1). Sample Cross-link Ratio ( Thickness held constant 5mm).


Procedures

Engagement

Day 1:

  • Students will be asked questions paired with demonstration activities that correspond to a direct instruction lecture.

Students will be given a choice of a variable to study:

  • Sample Thickness
  • Cross-link Ratio

**Direct Instruction Lecture Power-point with guiding questions attached.

**Demonstration worksheet attached with slide timeline.

Day 3:

  • Ask students what is in a good scientific test, make a quick list.

Exploration

Day 1:

  • Students will do hands on demo activities while being asked to relate scientific phenomena going on in the demo to corresponding topic from lecture slides.

Day 2:

  • Students will create their test sample in a hands on activity.
  • Procedures for sample creation below in worksheet section.
  • Students will use rulers to measure perti-dish diameter then calculate volume, then mass for proper thickness of sample.
  • Students will develop a plan for testing their samples given a set amount of materials (refer to materials list).

Day 3:

  • Have students perform their testing, data collection by using their developed testing plan for half of their six samples.

Day 4:

  • Analyze data and prepare graphs either on the board, computer lab, small white boards in order to present to the class.

Explanation

Day 1:

  • Students will be asked to explain their understandings of concepts and process while new information will be revealed to help bridge the understanding gap by moving ahead in the lecture slides.

Day 2:

  • Students will explain how they used density to find mass needed.
  • Students will explain how they measured for their samples.

Day 3:

  • Ask students to take part in an in class discussion so they can discuss problems that they are having with trial one, (the first three samples). Bring in some tricks of the trade to assist in making testing better. Create list on board.

Day 4:

  • Present findings to the class.

Elaboration

Day 3:

  • Have students perform their testing, data collection for the second half of their samples, (2nd 3 samples).

Evaluate

Day 4:

As individuals, have students complete a lab reflection packet including

  • Learned knowledge (quiz)
  • Group feedback peer review
  • Instructor survey (teacher feedback)
  • Scientific-Method and project essay (rubric based - refer to worksheet section below)

Prerequisites

Students must know the following in order to actively participate in this lesson:

  1. A good understanding of the metric system and how to convert between units.
  2. An understanding of the scientific method as it pertains to engineering.
  3. What a polymer is and how PDMS is one of those polymers.
  4. An understanding of cross-linking between molecules, and what cross-linking does.
  5. An understanding and how to find/define cross sectional area.
  6. An understanding on how to define/calculate stress and strain, in script and mathematically.
  7. An understanding on how to calculate density.

Best Teaching Practices

  • Inquiry Activities
  • Conceptual Understanding of Problem Solving
  • Real Life Situations and Problem Solving
  • The 5-E Learning Cycle
  • Hands On/Minds On Learning
  • Metacognition

Alignment with Standards

NGSS Standards:

  • HS-PS2-5 Plan and conduct an investigation individually and collaboratively to produce data to serve as the basis for evidence, and in the design: decide on types, how much, and accuracy of data needed to produce reliable measurements and consider limitations on the precision of the data (e.g., number of trials, cost, risk, time), and refine the design accordingly.
  • HS-PS2-1 Analyze data using tools, technologies, and/or models (e.g., computational, mathematical) in order to make valid and reliable scientific claims or determine an optimal design solution.
  • HS-PS2-2, HS-PS2-4 Use mathematical representations of phenomena to describe explanations.
  • HS-PS2-3 Apply scientific ideas to solve a design problem, taking into account possible unanticipated effects.
  • HS-PS2-6 Communicate scientific and technical information (e.g. about the process of development and the design and performance of a proposed process or system) in multiple formats (including orally, graphically, textually, and mathematically).
  • HS-PS2-6 Communicate scientific and technical information about why the molecular-level structure is important in the functioning of designed materials.

Common Core Standards:

  • RST.11-12.3. Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks; analyze the specific results based on explanations in the text.
  • WHST.11-12.1. Write arguments focused on discipline –specific content.

Ohio Standards:

  • I. Science Inquiry and Application During the years of grades 9 through 12, all students must use the following scientific processes with appropriate laboratory safety techniques to construct their knowledge and understanding in all science content areas: Identify questions and concepts that guide scientific investigations; Design and conduct scientific investigations; Use technology and mathematics to improve investigations and communications; Formulate and revise explanations and models using logic and evidence (critical thinking); Recognize and analyze explanations and models; and Communicate and support a scientific argument.
  • II. Problem Solving using graphs and data.
  • III. Gravitational Forces and Fields.
  • IV. Elastic Forces- as they pertain to Young’s Modulus.
  • Writing Standards for Literacy: Grades 11-12: 1:a-e, 2: a-e, 4

Content Knowledge

  • Problem Solving using the scientific method
  • Proper use of the metric system for conversions
  • Understanding of the Density Formula
  • Data collection and data presentation
  • Gravitational Field forces
  • Elastic forces as they pertain to Young’s Modulus

Safety

Safety Equipment Needed:

  • Safety glasses/goggles
  • Nitrile gloves
  • Razor knife sheaths

Safety Procedures Reminder:

  • Reading an MSDS sheet
  • Closed toed shoes
  • Hair pulled back
  • Safety around the drying/curing oven

Applications

This content is applied to the real world by relating the lesson to testing materials for engineering purposes. Engineering seeks to find uses for inventions and innovations that can make life be easier and have better quality. Materials must be tested and scrutinized before consumers can have a chance to buy and use the new technology. This testing is a skill that must be learned and developed and this lesson gives a window into that process. Students who go on into the engineering field need to be able to do this process of testing and analyzing in order to meet a certain goal.


Assessment

ENGINEERING SURVEY of POLYMER MATERIALS PACKET


Other Considerations

Grouping Suggestions: I have about 25-30 students. I am grouping my students in groups of 5. I think that five is a good number for this lab because materials are costly and there is going to be a high number of samples. In order for this lesson to go smoothly I think larger groups are better than groups of two or three unless you are working in a system that has small class sizes, then groups of two or three would be ideal. It basically comes down to amount of samples and cost for materials.

Pacing/Suggested Time: My classes are 47minutes in length. I will spread this lesson out over four days.

DAY 1: Lecture with quick demos to build pre-requisite knowledge, choosing a variable to study, (thickness/cross-link ratio). Engagement/Exploration/Explanation

DAY 2: Reminder of class goal timeline, Creating of samples, develop a plan for testing their samples, Exploration/ Explanation.

DAY 3: Reminder of class goal timeline, Finish plan for sample testing, test half their samples, discuss problems, guide groups to help properly test remaining samples, Collect data. Engagement /Exploration /Explanation /Elaboration.

DAY 4: Analyze data, prepare simple graphs on boards, present findings to the class, and discuss findings, Exploration /Explanation /Elaboration / Evaluation.


Printable PDF Worksheets

ENGINEERING SURVEY of POLYMER MATERIALS PACKET