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rubber bands strain

Rubber bands strain

Either have a video ready or demo on the spot:

1) large heavy object breaks through a medium sized piece of wood (a simple bridge), against grain (try brick and 2m dowel), or

2) rubber band and spring scale

Ask students to describe what happened (the video should show the wood bending as the large object decelerates, then the wood gives way, and the object accelerates again due to gravity.)

Ask: What if instead of dropping it, we slowly pile the mass on top until it breaks (It will bend more and more.)

So: As more STRESS is applied, the object experiences more STRAIN, and also pushes back with increasing force. Finally, at a max deformation/force (“ELASTIC LIMIT”), part of the material undergoes a change in chemistry, and it fails.

(draw graph on board)

Note that some materials bend easily but are very hard to break (like fiberglass or thin metal), while others are very stiff but can fail easily (like glass or graphite). Note also that when some things fail they shatter, other things may just bend and flop over, like soft metal.

Elastic (deforms and springs back) vs. Plastic (does not spring back)

How should we measure stress and strain? If the same tension force is applied to a rubber band twice as thick, will the resulting stress (and strain) be the same?

No. I will be spread out among more rubber.

So: The CROSS-SECTION is what is important, and stress is measured in N/m^2, and what does the stress vs.strain curve look like?

Well, have we seen anything similar to this before?

Hint: What if we took a metal “dowel” and wrapped it around in a helix (not a spiral)?

So: the Force that this “spring” can take, and the force it gives back (stress) is proportional to the amount of deformation it experiences (strain). And if we doubled the thickness of the metal in the spring?

The spring constant would be twice as much. The spring constant in this case is called the MODULUS (constant) OF ELASTICITY

Homework: bring in cool materials to subject to torture, and maybe a cool torture method

So far we know about elastic limit and about modulus of elasticity, but only for the situation of bending. But torture comes in many exciting flavors, can you think of some? Twisting, shearing, stretching,…

Begin Lab. Be sure to have backup materials (rubber bands, wood, foam) to supplement the students’. Emphasize the units of modulus of elasticity by having them use different weights (or a spring scale) as well as different cross sections.

Show pictures of stresses from bridge website, and talk about how: bending stress is really tension and compressions, twisting stress is really shear stress.

Start to talk about how we can shape things to take advantage of their particular strengths:

Karate chop demo: try to chop regular wood and plywood.

Talk about how arches work by transferring forces into compression, which is a strength of many materials like stone, wood and metal. (try crushing an egg)

Use Polarized light to look at stress

Investigate the phenomenon of Metal Fatigue

Use ultrasound to look into metal, talk about shockwaves and feedback (watch galloping Gurney collapse)

Rubber bands strain Either have a video ready or demo on the spot: 1) large heavy object breaks through a medium sized piece of wood (a simple bridge), against grain (try brick and 2m dowel),

Rubber bands strain

(Course outcomes 4, 5; Unit outcome 6-3)

Observation

Rubber bands behave elastically and they also appear to have a “crimping” behavior similar to tendons. When relaxed the bands tend to curl up and it takes a small force to straighten them out, then once straight, they provide more resistance to being stretched.

Question

Are rubber bands a good model for tendons?

Search Existing Knowledge

Find an example stress-strain curve for a tendon. What is the name of the region caused by “crimping” behavior? What is the elastic modulus of human tendon? What is the ultimate strength of human tendon? List your sources for this information.

Hypothesis I

Provide a qualitative hypothesis that compares the stress-strain behavior of rubber bands and tendons. That means to state which regions of the stress-strain curve for a tendon you expect will also appear in the rubber band curve. Explain your reasoning.

Hypothesis II

Also generate a hypothesis about whether rubber bands or tendons have will have a larger ultimate strength. Explain your reasoning.

Hypothesis III

Also generate a hypothesis about whether rubber bands or tendons have will have a larger elastic modulus. Explain your reasoning.

To test your hypotheses you will create a stress-strain curve for the rubber band.

Our method will be measure the stretch distance as additional force is added to the band. In order to determine stress and strain we will need to know the original length and cross-sectional area of the rubber band.

Hang the rubber band from a cabinet handle, ring stand, or other feature capable of supporting about 20 lbs (or enough force to rupture your rubber band). If you are using a rubber band larger than 1 mm x 1 mm, then you may have a difficult reaching the ultimate strength of the rubber band:

Photograph of a 1 mm x 3 mm rubber band during stress testing. The band runs through the slots in the gray weights and the hook attached to the bottom of the band is just visible through the slot in the lowest group of smaller (0.98 N) weights. The 119 N of force is applying 1.3 x 10 13 Pa of stress, causing a strain of 660 %. Photo credit: Umpqua Community College student Samual Marsters.

Use your ruler to measure the relaxed length of the hanging rubber band and record here:_________

Measure the width and thickness of the rubber band and multiply to get the cross-sectional area. Record the measurements here: Width_________ Thickness___________ Show your work in calculating the cross-sectional area below:

Convert your area to square meters (m 2 ), show your work below:

If you are using a force sensor, be sure to zero the sensor in the vertical orientation. If you are using pennies, determine the weight of a single penny in units of Newtons, if you are using known masses then remember to calculate their weights as you go.

Now we will pull on the band with the force sensor (or pennies or weights) and measure the force and length, then use the initial length and area to calculate stress and strain. Start with your smallest weight and work up so that you can determine if there is crimping behavior. Be sure to pull hard enough or add enough weight so that the length changes by at least 2 mm, (so the change is not obscured by the uncertainty in your length measurement). Continue until the rubber band begins to rupture. Record the results in the chart below.

Analyze I

Enter your data into a spreadsheet and create an x-y graph of stress vs. strain.

Be sure to give your graph a title and label the axes with the variable names and the units of measure.

Conclusion I

Was your qualitative hypothesis comparing the shapes of stress-strain curves for tendons and rubber bands correct? Explain, referencing your graph and the various regions.

Analyze II

What was the ultimate strength of the rubber band? Record here:__________

Conclusion II

Was your hypothesis comparing the ultimate strength of rubber bands and tendons supported by your data? Explain.

Analyze III

We need to find the elastic modulus, which tells us how the material resists strain. The elastic modulus is defined as the slope of the elastic region of the stress-strain curve. You can find the slope two ways: 1) slope is defined as rise over run. Find the how much the stress changes across the elastic region, then divide this by how much the strain changes across the elastic region. 2) graph only the data from the elastic region and use the spreadsheet to fit a line to the data. Don’t forget to ask your instructor or TA for help if you need it.

Write the change in stress across the elastic region here:__________

Write the change in strain across the elastic region here:__________

Show your work in calculating the slope below:

Write your slope here:_______________. The slope of the elastic region is the elastic modulus.

Conclusion III

Was your hypothesis comparing the elastic modulus of rubber bands and tendons supported by your data? Explain.

Rubber bands strain (Course outcomes 4, 5; Unit outcome 6-3) Observation Rubber bands behave elastically and they also appear to have a “crimping” behavior similar to tendons. When relaxed