## Data Analysis Rich Text Content

After playing around with various curve fits for my data, I decided that a fixed natural exponent fit would be most appropriate. Figure 7 shows the curve fits for the graphs

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The fixed natural exponent fits give me equations that will find the force at a given displacement. I then tried to figure out the work necessary to perform a shoulder press exercise using a dumbbell and using a resistance band. Figure 8 depicts the exercise with a dumbbell and Figure 9 depicts the exercise with a resistance band.
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I decided to use my body for certain measurements in the calculation for work. The resistance band is about at equilibrium position from where I step on it to where my fist is for the beginning of the exercise(See figure 9). In other words, the band is not stretched out before I begin the exercise. Thus, it is safe to assume that the displacement for this calculation will be the length of my arm at full extension

Length of arm = 0.6885m

I then used the curve fit equations from the graph to find the work done by a resistance band. In a force vs displacement graph, the area under the curve will equal the work done. Using Wolfram Alpha, I found the area under the curve from 0m to 0.6885m for each resistance band.

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I then calculated the word that would be done in lifting a dumbbell of 5 kg straight upwards.

Calculating Work Done for Dumbbell

W = Fnet*d

W = mgd

W = (5kg)(9.8N/kg)(.6885m)

W = 33.737 Nm

Conclusion

The work done in lifting a dumbbell of mass 5kg straight upwards was found to be greater than the work done in stretching a resistance bands straight upwards from equilibrium. However, the work done by the resistance bands could be greater if the bands were stretched from an initial displacement and not just from equilibrium. This would create a greater force and thus more work would be done.

It would be interesting to see how the varying force of a resistance band affects tears in muscle fibers and how the muscle fibers grow in response.

Works Cited

Maximum Fitness Gear 3pc Resistance Bands. N.d. Photograph. Maximum Fitness Gear. 15 Sept. 2011. Web. 17 Dec. 2013. <http://maximumfitnessgear.com/pics/Image/MF%20Bands%203.jpg>.

Van Such, Larry. "When It Comes To Using Resistance Bands, It's Best To Use Them With An Isometric Training Strategy. Part 3 of 4." Resistance Band Training With Isometrics. N.p., n.d. Web. 17 Dec. 2013.

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