HPP Activity A26.v1
This is so stressful An introduction to stress and strain
Muscle transmits a force to a body structure (usually a bone) through tissue called a tendon. In
this activity, we will develop some ways of characterizing such tissue from a physical point of
view.
Exploration
GE 1.
1. Hold your hand out and press on your palm with a finger. What happens
when you take your finger away?
2. Are there other materials that behave the way?
3. Are there mechanical devices that behave the same way?
Obtain a Gummit worm and ruler. The worm represents a tendon.
4. Measure the worm length.
5. What happens when you apply a compressing force to the worm and release
it? Does it return to its original length?
6. Now apply a stretching force to the worm, but do not stretch it more than 2
[cm] or so. Does it return to its original length?
Attach the Gummi Worm to a force probe/MBL system, as shown below.
Activity Guide
 2010 The Humanized Physics Project
Supported in part by NSF-CCLI Program under grants DUE #00-88712 and DUE #00-88780
HPP Activity A26.v1
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Force Probe
Gummi Worm
Motion Detector
Place a motion detector beneath the Gummi Worm.
Open up the StressStrain.ds DataStudio file.
Measure the equilibrium distance from the motion detector to the worm.
Type this distance into the formula for calculating L, the amount of stretch.
Collect F-L data while stretching the worm about 3 centimeters and then releasing it.
GE 2.
1. What happens to the required stretching force as the amount of stretch
increases?
2. Is the relationship between F and DL the same when releasing the worm as
when stretching it?
We want to create a mathematical model of the F-DL data while stretching.
3. What is the Rule of Four?
Select about 6 points from this part of the data.
L [m]
Activity Guide
 2010 The Humanized Physics Project
F [N]
HPP Activity A26.v1
Copy your table to a spreadsheet.
Create a graph of F vs DL.
4. Describe the relationship in words.
5. Find an equation that represents your data.
Collect data for another stretching experiment. This time, continue stretching until the worm
breaks.
Invention
Many materials, including tendons, behave in a simple fashion as they are stretched, so long as
they are not stretched too much. In the simple case, a material is elastic: the amount of stretch is
proportional to the applied force, or vice versa.
F  kL
In this equation, F is the magnitude of the applied force, L is the deviation from the equilibrium
length, and k is a constant called the spring constant (or sometimes the force constant). This
force law is called Hooke's law.
For real materials, k can depend on several factors, including the equilibrium length, the crosssectional area of the sample, and the type of material. To show the effect of these factors,
Hooke's law can be expressed as
F
L

A
L0
where  is called Young's modulus, L0 is the equilibrium length, A is the cross-sectional area of
the sample. The quantity F/A is called the stress. The quantity L/L0 is called the strain. So
Hooke's law can be expressed as
stress    strain
If the stress becomes too large, Hooke's law will not hold. The stress at which the material
actually breaks while stretching is called the tensile strength.
Application
Activity Guide
 2010 The Humanized Physics Project
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HPP Activity A26.v1
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GE 3.
1. What is the cross-sectional area of your worm?
2. Use your data from the worm to calculate stress and strain. Assume that the
area remains constant.
L/L0
F/A [N/m2]
3. Estimate Young's modulus for the Gummi Worm.
4. How does it compare to Young's modulus for a real tendon?
5. What is the tensile strength for your Gummi Worm?
For comparison, the tensile strength of tendon is about 108 [N/m2] .
Activity Guide
 2010 The Humanized Physics Project