HPP Activity A28.v2
Storing Energy in Your Muscles
Storing Energy in Your Muscles
Exploration - Compressing and Stretching
Modeling How Bending Your Legs Helps
You Jump
Think about your results from the jumping
toy in lab #06 (“Bending, Stretching, and
Jumping”) when answering the following
questions.
1a.
Thinking in terms of physics, why does
bending your legs help you jump?
1b.
Is energy stored in your legs when bent?
How do you know?
Modeling How the Stretch of Tendons/Muscles/Ligaments Helps You Jump
Each group will be given two non-identical, unused rubber bands to be studied. Using a
single rubber band at a time, launch a small wad of paper straight up in the air. Do not shoot it
at anyone! Experiment with the function of this equipment. If you have trouble shooting a
small piece of paper, you might just try shooting the rubberband straight up into the air.
2a.
Once you have the system working properly, write a description of the workings and the
motion of this rubber band/paper apparatus. Make a list of all related physics principles
you can identify in this system.
2b.
What aspects of this apparatus seem to change the height to which the paper flies? Make
a list of the properties of the rubber band/paper systems and describe how each one
influences the height to which the paper flies.
Invention Discussion #1
 Humanized Physics Project
2004 - UNL
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HPP Activity A28.v2
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During this discussion, your laboratory instructor will lead a discussion of your results
for the previous activities and define some new concepts.
 Humanized Physics Project
2004 - UNL
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Three big ideas:
A. F  d = Work =  Energy
Energy is conserved. The work needed to store (spring) energy goes into the
other stored work (height of the object). The work done to change the stored energy is
the product of the force applied and the distance over which it was applied (F  d).
B. When a force is applied to any object, it changes its shape (even if you cannot see it).
The force per area applied to an object is called stress (Stress = force/area). So you
are stressing your muscles and bones when you apply forces to them. The change of
shape of an object relative to its original size when it is acted upon by a force, or stress, is
called strain (Strain = L/L0).
If an object is elastic, once the stress is relieved, the object will return to its
original shape. If an object, under stress, has been deformed beyond its elastic limit then
it will NOT return to its original shape after the stress is relieved.
The stresses, or forces, that are exerted by your muscles and bones can damage
them and cause you aches and pains or dysfunction. When muscles pull too hard, they
can over stretch themselves and the attached tendon, and they can compress the joint to
the point of damage. The elasticity of your bones and muscles changes with age,
exercise, etc.
C. When a force is applied to any object and changes its shape, there is energy stored by the
object if it is elastic.
When the force is released, the object may release its stored energy, which may
result in motion. In elastic behavior, when energy is put in, it is stored and then
released. When an object becomes permanently deformed and does not bounce back,
then the energy (F  d) put into the object went into breaking bonds and rearranging
molecules.
Application #1 - Applying the Big Ideas to Something Familiar
Obtain a gummi worm from your instructor. Each group should have 1 to use for the
experiment and 1 for each person to eat (if they choose).
Use your experimental gummi worm to complete the following investigations. Discuss
the questions with your lab partners. Record brief summaries of what you found in your
logbook.
3.
Note the length of your gummi worm. Apply a stress (with your hands) to compress the
gummi worm.
(a) Does it compress? What is the resulting strain?
(b) Is energy stored in the compressed gummi? How do you know?
(c) Is it elastic? How do you know?
 Humanized Physics Project
2004 - UNL
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Storing Energy in Your Muscles
Remeasure and record the length of your gummi worm. Apply a force, this time to stretch
the gummi worm a small amount.
(a) Does it stretch? What is the resulting strain?
(b) Is energy stored in the stretched gummi? How do you know?
(c) Is it elastic? How do you know?
You will now conduct an experiment with this gummi to estimate its elastic limit and its
breaking point. That is, you will answer the questions, how far can it be stretched before it is
damaged and how far can it be stretched before it breaks? Estimate the length of the gummi
when it first becomes permanently deformed and just before it breaks.
5.
(a)
(b)
(c)
What was the elastic limit and breaking point for your gummi?
Compare the value for your gummi with those used by other groups. How similar
are they? Hint, calculate a percent difference.
What might account for any differences?
Invention Discussion #2
You will now complete the following analysis as a class.
Suppose your unstretched gummi worm was 10.0 cm long. Suppose a force of 2 N and 4
N was applied and the gummi worm stretched to lengths of 14.5 cm and 18.1 cm. Using this
information, complete the following data table as a class on this page. You can then cut it out
and put it into your logbook before the end of lab.
Area of gummi worm:
Initial length (L0) of gummi worm:
Applied
Force
(N)
Stress
(N/mm2)
Total
Length
L
(m)
Amount
of Stretch
x
(m)
Strain
Increment of
Stored Energy
(N•m)
Total Stored
Energy
(N•m)
F0=0.0
L0
x0=L0-L0
=x0/L0
0
E0 = 0
F1=2.0
L1
x1=L1-L0
=x1/L0
 Humanized Physics Project
2004 - UNL
E1 = Favg * x1
E1 = {0.5*(F0 + F1)}*(x1-x0)
E1 = E0 +E1
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F2=4.0
L2
x2=L2-L0
=x2/L0
E2 = {0.5*(F1 + F2)}*(x2-x1)
E2 = E1 +E2
Getting Ready for Application #2:


Each group will be assigned one of two materials to study during application #2
(stretchable or compressable).
Be sure to verify with your instructor which material you will be using.
Application #2 - Modeling Two Kinds of Physical Systems:
(1) Stretching Your Muscles/Tendons/Ligaments OR
(2) Squeezing Your Bones and the Cartilage Between Your Bones
Each group in your lab will be assigned to study one of the two systems listed above.
The systems will be distributed so half of the class is examining each. Once you are sure which
system you are going to study, then complete the following procedures.
Data Collection - Applying a force and measuring the length
(1) Procedures for collecting stretching data:
Use a piece of wire (diameter = 0.255 mm) to model the stretching behavior of one of
your muscles/tendons/ligaments. Verify that a piece of wire is securely fastened to the
support with a hook hanging from it. Hang a weight-hanger at the bottom and add a 100-g
mass. Measure and record the length of the wire and consider this its initial length. Also,
carefully measure and record the initial starting position of the bottom of the hanger as a
height above the floor. Gently add 100 g to the hanger to stretch the wire, making sure it is
hanging over the carpet piece to protect the floor should it break. Measure and record the
resulting position and calculate the new length. Repeat this, adding more mass. Record the
total amount of hanging mass and resulting position and length values for each trial in your
logbook. Continue until the wire breaks. Calculate the force (in Newtons) applied by each
total amount of hanging mass for each length.
(2) Procedures for collecting squeezing data:
Use a piece of sponge material to model the squeezing behavior of one of your bones.
Carefully measure and record its initial length. Use the force sensor and a flat piece of wood
 Humanized Physics Project
2004 - UNL
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to measure the force needed to compress the material in small increments. You only want to
compress it, don't let it bend up. When you apply a compression force, read the force value
immediately, as it will change as the sponge gets "used" to being compressed. You want the
initial force value. Record the applied force and resulting length of the material for at least 6
different amounts of squeezing force, with at least three values being equal to or less than
6 N. After you have collected your data, remeasure the length of the sponge when no force
is applied.
Data Analysis - Numerical Model
Entering Your Data into Excel
Open the appropriate Excel file (either "1-Stretching Data Analysis" or "2-Compressing
Data Analysis." This file contains a data table (like the one you used for the gummi worm).
Complete the following steps to enter your data.

Type the name of each member of your group into cell D1.

Enter the initial length into cell D3.

Enter the initial area into cell D5.

Enter your force values in the cells in column B, starting at row 13.

Enter your total length values in the cells in column D, starting at row 13.
Now that your data is entered, you can use Excel to make the necessary calculations for
you. Use the procedures outlined below.
Calculating Stress in Excel

Click once on cell C13. Type in the formula "=B13/$D$5" to calculate the stress for this
data point, hitting the return key after you have typed it in. Note! when you refer to a
constant (like initial length in cell D5), add dollar signs ($) to the
cell reference as indicated.

Verify that the result is as expected. If not, then click on the cell and reenter the formula.

Once the formula appears to be working, then you can copy it to the other cells in that
column. Click on the cell once. Then place the cursor on the bottom, right corner of the
cell until it turns into a black cross (  ). Click and hold the mouse button down and
then drag the mouse down to select all appropriate stress cells. Lift up on the mouse,
and Excel should now instantly calculate all of your stress values.

If this did not work, either try again or ask your instructor for assistance.

Make sure that all results seem reasonable before you continue. As always, if you have
trouble, ask your instructor or another student who knows how to use Excel.
Don't forget to save often (like after every calculation)!
 Humanized Physics Project
2004 - UNL
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Other Calculations in Excel
Enter a zero for the initial increment of stored energy and the total stored energy (cells
G13 and H13).
Complete all calculations in this data table so that each cell has a number. Be sure to
check that the numbers seem reasonable. Excel will do whatever calculation you tell it to do
(right or wrong). If you make a mistake, it will just go ahead and calculate the wrong formula.
Here are some hints to help you with the remaining calculations. The function
ABS(number) is "absolute value of the specified number." This will make sure that your results
are not negative numbers.

Amount of stretch or
compression

Strain

Increment of stored energy

Total energy
Select "Print…" from the "File" menu and print a copy of the data for each member of
your group. Affix this data into your logbook. In addition, print one extra copy, which you will
share with the class later on in the lab.
Be sure to save the file!
 Humanized Physics Project
2004 - UNL
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Data Analysis - Graphical Model
Using Excel, create a graph of stress vs. strain for this material using your first six data
points showing a change in length (strain  0). Do not graph any initial points where the strain
remained zero (this may have happened with the wire). Once you are certain your graph is
complete and showing the correct values, then print a copy for each member of your group plus
one extra copy. Please make the background white before printing to save on toner!
6.
(a)
(b)
(c)
Lightly, in pencil, draw a smooth curve representing the data points. What is the
shape of the stress vs. strain curve for this material?
Describe how you can identify an elastic limit. Mark this on your graph, if it exists.
Where was this graph linear? Using a straight edge, draw a linear fit for this region.
Calculate the slope of this linear region, using the procedures outlined earlier in the
semester (in Reference B).
The slope of the linear region is called the elastic modulus and it is similar to the spring
constant in Lab #01.
7.
Create a graphical model of total stored energy vs. strain and print a copy for your
logbook along with one extra. Describe in words the behavior of the total stored energy as
a function of strain for this material.
8.
Do you think the object was permanently deformed after you had applied some stress (but
before the wire broke)? Explain your ideas. Compare this behavior with a group that
investigated the other material.
Save this file one final time and quit Excel.
Application #3 - Sharing Your Results
Complete the following two tasks to share your results with the class:
9.

Record your best estimate for the elastic modulus of this material on the whiteboard.

Exchange your extra copy of the data table and two graphs with another lab group
that used a different material. Briefly explain to this group what you did and what
you found.
(a)
Summarize the results of the class by copying the elastic modulus values into your
logbook. Calculate an average value for each material.
(b)
Briefly sketch the shape of the two graphs into your logbook and describe what they
tell you about the behavior of this second material.
 Humanized Physics Project
2004 - UNL
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HPP Activity A28.v2
 Humanized Physics Project
2004 - UNL
Storing Energy in Your Muscles
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Storing Energy in Your Muscles
The maximum stress of muscle fibers is 0.3 N/mm2 and the maximum stress of tendons
is 100 N/mm2. Also, tendons can stretch to 8% of their original length and muscle fibers only
3%.
10.
How would the stress/strain curves of stretching tendons and muscle fibers compare to
the curve found for a piece of wire?
11.
Consider three situations: compressing sponge material, compressing cartilage, and
compressing bone. How do you think the three resulting stress/strain curves would
compare? Explain.
12.
Now step back from the 4 graphs and compare the stretching and the compression sets.
(a) Compare and contrast the two stress vs. strain graphs.
(b) Compare and contrast the two stored energy vs. strain graphs.
Lab Cleanup:

Throw away all used gummi worm pieces into the trash (not the recycle bin!).

Put the used wires and washers/screws/hooks in the green collection box on the
equipment table. Do not throw them away!!!

Make sure all masses are stored in a safe manner (so no one is likely to trip on them).

If you are in the last lab of the night, then turn off the interface box and "Shut down" the
computer.
Want More Information?



Stored energy (see Walker, Chapter 8)
Stress and Strain (see Walker, Section 17-3)
Elastic modulus (see Walker, Section 17-3)
 Humanized Physics Project
2004 - UNL
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