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Page 1: Storing Energy in Your Muscles - Doane Collegephysics.doane.edu/hpp/library/materials/a28sg.v2.pdf · HPP Activity A28.v2 Storing Energy in Your Muscles ... The work needed to store

HPP Activity A28.v2 Storing Energy in Your Muscles

© Humanized Physics Project page 1 of 1 2004 - UNL

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 During this discussion, your laboratory instructor will lead a discussion of your results for the previous activities and define some new concepts.

Page 2: Storing Energy in Your Muscles - Doane Collegephysics.doane.edu/hpp/library/materials/a28sg.v2.pdf · HPP Activity A28.v2 Storing Energy in Your Muscles ... The work needed to store

HPP Activity A28.v2 Storing Energy in Your Muscles

© Humanized Physics Project page 2 of 2 2004 - UNL

Three big ideas: A. F ⋅ d = Work = Δ 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 = ΔL/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? 4. 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?

Page 3: Storing Energy in Your Muscles - Doane Collegephysics.doane.edu/hpp/library/materials/a28sg.v2.pdf · HPP Activity A28.v2 Storing Energy in Your Muscles ... The work needed to store

HPP Activity A28.v2 Storing Energy in Your Muscles

© Humanized Physics Project page 3 of 3 2004 - UNL

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) What was the elastic limit and breaking point for your gummi? (b) Compare the value for your gummi with those used by other groups. How similar

are they? Hint, calculate a percent difference. (c) 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 ΔE1 = Favg * x1 ΔE1 = {0.5*(F0 + F1)}*(x1-x0)

E1 = E0 +ΔE1

F2=4.0 L2 x2=L2-L0 =x2/L0 ΔE2 = {0.5*(F1 + F2)}*(x2-x1)

E2 = E1 +ΔE2

Page 4: Storing Energy in Your Muscles - Doane Collegephysics.doane.edu/hpp/library/materials/a28sg.v2.pdf · HPP Activity A28.v2 Storing Energy in Your Muscles ... The work needed to store

HPP Activity A28.v2 Storing Energy in Your Muscles

© Humanized Physics Project page 4 of 4 2004 - UNL

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 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.

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HPP Activity A28.v2 Storing Energy in Your Muscles

© Humanized Physics Project page 5 of 5 2004 - UNL

• 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)! 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

Page 6: Storing Energy in Your Muscles - Doane Collegephysics.doane.edu/hpp/library/materials/a28sg.v2.pdf · HPP Activity A28.v2 Storing Energy in Your Muscles ... The work needed to store

HPP Activity A28.v2 Storing Energy in Your Muscles

© Humanized Physics Project page 6 of 6 2004 - UNL

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!

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HPP Activity A28.v2 Storing Energy in Your Muscles

© Humanized Physics Project page 7 of 7 2004 - UNL

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) Lightly, in pencil, draw a smooth curve representing the data points. What is the

shape of the stress vs. strain curve for this material? (b) Describe how you can identify an elastic limit. Mark this on your graph, if it exists. (c) 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:

• 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.

9. (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.

Page 8: Storing Energy in Your Muscles - Doane Collegephysics.doane.edu/hpp/library/materials/a28sg.v2.pdf · HPP Activity A28.v2 Storing Energy in Your Muscles ... The work needed to store

HPP Activity A28.v2 Storing Energy in Your Muscles

© Humanized Physics Project page 8 of 8 2004 - UNL

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)